the other measures are taken jn one as in the other But because that the Torch doth not render an equal shadow in breadth to the body that giveth its shape as doth the Sun We must take this advice which is that instead of drawing the llnes parallels that one to the other as they are in the shadows taken from the Sun we must draw them all from the same point as from a Center that is to say that all the lines which are drawn by the plane must be drawn from the foot of the light A and those above and about the figure must be drawn from the point of fire B in like manner as in all the other orders of the Torch the which maketh me leave the rest that would be but tedious repetitions seeing that the figure expresseth it of its self Of the divers dispositions and heights of shadows by the Torch THe shadows taken by the Sun do cast themselves always on the same side and have ordinarily one and the same disposition it being impossible that the Sun should cause at the same time to cast the shadow of one body towards the West and of another towards the East it is very true that it doth this every day the one in the morning and the other in the evening but in one and the same hour it will never do it naturally The which is done without failing by the Torch the Candle or the Lamp for in what place soever you set one of these lights if there be many bodies about them they will cast their shadow diversly that is to say that the one will cast it to the East the other to the West this to the North that to the South in short on every side according as the bodies shall be ordered about the light the foot of the which marked A serveth them for a Center whether all these shadows draw and the fire B marketh where they must end although diversly by reason that the nearest have their shadow shortest and those that are farther off cast it more at length Although that the second figure hath not the light in the midst yet the order of these shadows ceaseth not to be kept as we see that they all draw to the foot of the light C and that they are bounded by the point of fire D. THE TABLE THe Definitions names and Terms of the Points Lines and Figures which we shall use page 1. The Rest of the Definitions Names and Terms page 2. Some Orders of Geometry fâ—r to make the Lines and Figures which we are about to define page 3. For to frame the Figures page 4. Of Polygones Circular which are Figures with divers angles within one Circle ibid. Of the Rays visual page 5. Wherefore one may see better a Perspective with one Eye only then with two ibid The first definition page 6. The second third and fourth definition page 7 Wherefore the Objects that are far distant seem to approach and joyn themselves together although they be in equal distance page 8. Wherefore the Objects draw near to each other being viewed afar off page 9. Of the Horizon page 11. Of the Base page 12. Of the point of sight Point of Perspective Point Occular or Point Principal ibid Of the points of distance ibid. Of points accidental ibid Of the point of the Front page 13. Of the point of the side ib. Of the Visual Rays page 14 Of the Diagonals or Diametrals and of their sections ib. Of the d stance or Removal and setting page 16 The first advice about the point of the side page 16 The second advice of the Hollowing or deep sinking ib. The third advice of the Measures upon the Base page 17. The fourth advice of the Base and of one only point of distance ib. The fifth advice not to deceive ones self in the Measures ib. The sixth advice of the point of distance only page 18. The seventh advice that we should not use the Diagonal ib. The eighth advice to abridge in divers manners ib. Of planes viewed directly or in front page 19. Planes viewed obliquelie or on the side page 20. Of a Triangle page 21. Of the Pentagone or five angles page 22. Of the Hexagone or six angles page 23. Of the Heptagone or seaven angles page 24. Of the Octogone or eight angles page 25. Of the Octogone after another manner page 26. Of the Hexagone or six angles ib. Of the Octogone double page 27. Of the Circle page 28. Of the Circle double page 29. A plane of the square viewed from the angles page 30. A pavement of squares viewed by the angles page 31. Of squares compassing a Border or Fillet ib. Pavements viewed by the angle compassed with a brand or Fillet page 32. Pavements of squares viewed by the front compassed with Bands or Borders whâ—ch have squares seen from the angle in the midst ib. A pavement of squares seen from the angle with Church of squares on the front page 33 A pavement of squares in front with Chairs of squares seen from the angle ib. A pavement of lâ—ttle squares Octogone mingled with the squares page 34 A pavement of single squares viewed in front ib. The plane of a Garden abridged page 35. The plane of a Building abridged page 36 The plane of a Church abridged page 37. The plane of an House with a Garden page 38. The plane of a Fortification abridged page 39 The plane and figure irregular abbreviated page 40 Another plane of a Church allreviated page 41. Some necessary advice for the orders following page 42. Of the lines of elevation to give the heights to all kind of bodies and figures and in such a place as one would within a plane page 43. The elevation of a Cube in Perspective page 44. The Triangle in Perspective page 45. The Pentagone or five angles in Perspective ib. The Hexagone or six angles in Perspective ib. Of the Heptagone or seven angles in Perspective page 46. Of the Octogone or eight angles in Perspective ib. The double cross in Perspective page 47. A stone flatted or streaked like a Star in Perspective ib. Of Pilasters in Perspective page 48. Of Pilasters viewed by the angle ib. The effects of the diversity of Horizon page 49. The elevation of Objects viewed by the angle page 50. For to raise bodies and remove them as far as one world page 51. Of Walls viewed directly page 52. Another wall viewed from the angle ib. For to place a door in what place one would of a Wall page 53. For to frame Windows in Perspective page 54. Of the Planchers above page 55. Another Ordering of Planchers in Perspective page 57. A single draught of doors and round arches viewed directly page 59. Round arches above the Pilaster viewed directly page 60. Of the third point in the arch ib. A further pursuit of this figure page 61. For to frame and set into Perspective doors and round arches page 62. For to frame and put into
and 52th fol. The Leaf following will give you the Doors and the 54th fol. will shew how to make the Windows there For to raise the Chimneys in what place soever you would you must seek the 77th fol. After that you must lay there the Planchers which may be found in the 55th and 57th fol for the Pavements there are of many sorts in the 31. 32. 33. and 34th fol If one would have open Doors the 93th fol. will shew how to do it and the Leaf following shall be for opening the Windows When there shall be two or three Stories or Chambers the one above the other you must always keep the same Orders and there ought to be but one only point for the view as you may see in the 76 fol. for to ascend into these Chambers there is an Ascent turning or Stairs in the 82. 83. and 84 fol. Ordinarily all the Buildings which are viewed by the inside are garnished with some Moveables he that will place such there shall find of all sorts in the 96th fol. and so forword unto the 103 fol. For the measures of such Figures if any such ore to be placed there they are to be found in the 122th or 125th fol. For to make a Church appear by the inside we must first resolve upon a plane and place that in the Perspective according to the two orders that we have given thereupon in the 37th or 41th fol. You must raise the Walls as is to be seen in the 51th fol. For the Windows one may make them as the Arches of the 62th fol. or as in the 54th fol Except that there is no need of the cross-bars and that they must be round above If one would have Pilasters or Pillers they are to be â—ound in the 48th fol. If one would have Columns there he must take the Order for them from the 87th fol. After all that there must be made a bending Roof or Roofs if one would set it upon the sides fol. 68. 69. 70. 71. and 72. will furnish you with all sorts thereof The Ridge or top of the Church is made after another manner then bending sides the Order for that may be found at the 74th fol. for to enrich it with Cornishes Mouldings and other Ornaments you must have recourse to the 88. 89. 90. 91. and 92. fol. for Altars if one would have them there you shall find the Method of making them in the 104 fol In the midst of the cross-bars of the Church one may make a Lanthorn or Cubeloe as is to be seen in the 75. fol. The Pavement may be chosen in the 31. 32. 33. and 34 fol. As for the Buildings without side of the Doors and Windows they are made like the Buildings in the in-side in the 53 and 54. fol. as may be seen in the 106. fol. When you shall have elevated them to the height that you think fit you shall find the draught there to raise such a kind of covering as you shall think must fitting in the 107. or 103. fol. If one would have there any Cornish or other Ornaments you may find how they ought to be placed in the fol. 88. 89. 90. 91 and 92. Galleries Arch-wise either for the out-side or in-side may be found in the fol. 63. 66 67. and 106. He that would make a whole street of Buildings he must multiply the houses and place them on the one side and on the other as one may see in fol. 109. When one shall make houses at a distance in the Perspectives and that they shall be parallel to the Horizon you ought to allow them the single draught only without the thickness f the Doors or the Windows as I have made at the 110 fol. In the large open places which are ordinarily in Streets in Perspective one may raise a Pyramide there the 80 fol. will shew how to elevate it upon steps or any other figure or Statue upon a Piedestal the 91 fol. will furnish the Piedestal and the 124 fol. will shew the figure When one would have Buildings seen by the left Angle he may take the planes of the fol. 19. 30. and make the Elevations as he shall find them in the fol. 50. and 111. which shall give Orders how to make the Doors and Windows there Gardens made in Perspective do more delight the sight then any thing in the World as well for the colour that is so pleasing there as for the variety of things which may be set there The planes are to be made as in the fol. 35. 38. or 113. In the which one may make such divisions as one shall desire If we would have Bowers the order therefore may be found in the 60. and 61. fol. If one should like better Hedges or Arbours he may find them in the fol. 51. and 52. If instead of Bowers and Hedges one would have a Wood or Alleys of Trees the 112 fol. will shew the Orders for divers sorts When one would make Fountains there or spouts of Water the Round of the 29 fol. may serve for a Bason its elevation is at the 73 fol. If one would have a square he must take the fol 19 or 44. For to have thereof with divers quarters he must seek in the 45 or 46. fol. where he may find Polygones He that would set Statves or Figures vpon Piedestals which is a very fair Ornament for a Garden he must take their measures in the fol. 122. or 125. If one would place there any Caves or Grottes the 74 fol. will shew him how they ought to be made When one oeould cause an Ascent from one Garden to another he shall find many sorts of steps in the fol. 78 79 80. and 81. Every one may choose amongst all these things that which shall please him best and may put them all there into the same piece and without confusion only he must keep the proportions and symmetryes which ought to be observed therein If one would have Shops open where there is nothing but the Walls the 55 fol. will shew If one would that they should be garnished with Boards or little Tables he shall find the order thereof in the 105 fol. There is also another fashion for a a Shop which is not in the from like this and whereof the Opening is altogether different one may set it in the 95. fol. Ampl theatres were heretofore more in use in Pictures then they are at present which is the cause that I have not set any of them here accounting them unuseful here If I shall know that any one desire them I will set forth some in the second part in the mean time if any one would raise up one thereof he may use the plane that is in fol 29. in the which he must make a greater number of Circles according to the number and bigness of the Stages that he would have therein For to raise the Stages he must use the line of elevation which he shall
these Points being joyned together of the lines will give you that which you desire The Figure will serve to make one understand the Order better A Plane and Figure Irregular abbreviated HE which shall do well that which we are about to leave shall not be much trouqled with all the rest for this is that which is the hardest of Planes in Perspective I beleeved nevertheless that it was good to set yet further something irregular which appeared difficult at the first sight that I might make it known that there is nothing which one may not abbreviate of whatsoever view or Aspect it may be Another Plane of a Church abbreviated IT seemeth that this Order of Perspective is altogether another then that which we have used because that the ordering thereof is not the same The which I have done on purpose to give to understand that there are many fashions and orders which all come but to the same for this is the same with that which we have used for to abridge the Fortifications the irregular Pieces and other planes according to the eighth Advice with this only difference That we have marked the Parallels o the base upon the line on the side And here we have marked them upon a line in the midst of the Plane And as well in the one manner as the other we have always the same effect for drawing from all the divisions of this line of the midst to the Eye A you shall have the line of the section B C which shall be made upon the line which we may call the base D E. For to set it into Perspective transport into what place you would all the length of the base as here above D E and the height of the Eye A F. Then having set on the one side and other or in the midst of the line of the section B C draw Parallels to the base by all these divisions unto the outmost Ray D A E A you must set the bredth of the Pilasters D K upon the base and draw a line at the point of sight A and the section of the lines Parallels by these K A shall be the bredth of the Pilasters THE ORDERS OF THE ELEVATIONS Some Necessary Advice for the Orders following IT seemeth to me that I have given sufficiently to understand that which belongeth to the Ichnography and Planigraphy or description of Planes which is necessary for the foundation of Orthography and Scenography The Orthography is the face or fore-part c. As one may see in the Definitions Scenography is the Elevation of all that which any one hath a designe to make c. See the Definitions which are at the beginning of this Book For to make this more clear to those that are not acquainted with these words we shall Name hereafter as I said already in the Definitions the Ichnography the Plane and the Orthography and Scenography by a Word common to the one and the other the Elevation So that instead of saying the Orthography we shall say the Elevation of the fore-part And for Scenography the Elevation of the whole Before we pass any further it must be observed that the Elevations do never give to the eye all the Angles of the Plane and the Quantity of faces depend on the Aspect which causeth the object to be seen for if it be seen on the front as the figure A it will shew but one face although that the Plane have four If it be view'd from the Angle although on the front it will shew two as B and never more with what Aspect soever one look on it This ought to be understood of a square seeing that figures with divers Panes may give thereof 3 4 5 and more Now it is that if the objects decline a little from the point of sight they are seen from the Angle whence they ought to shew two faces And the further they are removed from the point of sight the more they are discovered As K E are more discovered then C L although their thickness be equal Another thing also that is further to be marked is That which is Parallel to the Horizon when the object is view'd in front although in Perspective as C D E F from the Gate in the first figure becometh a visual Ray when the same object is view'd being in a Return or obliquely As in the second figure that C D E F which is in the front above is made a visual Ray to that which is under And on the contrary that which is a Ray to that above is made a Parallel to the base to that below as D G F H L. The Perpendiculars are always Perpendiculars 1. fig. 2. fig. Of the Line of Elevation for to give the Heights to all kinde of Bodies and Figures and in such a Place as one would within a Plane WE must endeavor to understand well and remember this Rule which is of such importance that he that shall know it perfectly will not be troubled in the Elevations whatsoever they be of As for to make the Planes we have used the base for the Elevations we ought also to use a line which shall direct us and shall bring the Measures of the Heights that are needful to every thing which one would elevate This line of Elevation must be Perpendicular upon the base A B which is always the nearest to our sight and the first of the Plane By consequence capable of giving and bearing the Measures of all that one would make in the Picture and therefore the line of Elevation C D is placed upon the line A B Perpendicularly as all those must be upon the Plane which we shall use henceforward We must then remember that when we shall speak of Perpendicules or Perpendicks in the rest of our Orders we must always understand of Plumb-lines upon the Plane or base Seeing that this line of Elevation must receive and give the Heights to all the Objects that one would elevate from a Plane it must have the same Horizon with the Plane Therefore we must from the foot of this line which one may set on the left or right side draw within the Horizon as one would have it that is to say that it is no great matter where the Point be set within the Horizon for in what place soever it be it will always give the same effect as it is from the foot of the line C to the point E one may set it at the point of sight if one will I have set this line on the one side and other in the first Figure and their point different within the Horizon for to give to understand that it is well throughout If from the point H which is in the Plane of the second Figure you would elevate a line of two foot high you must set upon the line of Elevation two equal Parts which you shall make to serve each for a foot beginning at the point C as are C F which is
two foot high to draw to the point E and you shall have an Elevation of two feet between the two lines C and F drawn to the point E. For to give the height of two feet to a line elevated from the point H you must from the point H. draw a Parallel occult to the base until that it divide the line below C E which shall be the point I. If from the point I one elevate a Perpendicule I K between C F it shall be the height that it ought for the line of the point H which you must take with a Compass and carry it to the point H which will give H L of two feet high If from the point M you would have one of the same height of two feet you must make the same Operation and you shall have between C F the Perpendicule N O which shall be the height that it ought at the point M. And making the same Operation from the point P you shall have the Perpendicule Q R for the height of the line of the point P. For to give them the height of 3 4 5 10 20 and 30 feet It is always the same Order there is nothing but to set these distances and heights abovesaid upon the line of the Elevation And from the point of the height that you would give to draw to the point of the line within the Horizon which is here the point E and to make all the same Operations which we are about making and you shall have that which you desire The Elevation of a Cube in Perspective HAving made the Plane by the Orders foregoing and having set the line of Elevation upon any side of the Plane as is F L upon the base We must set upon this line F L the height of a Cube which is a Figure square on all the sides as a Dy which shall be F M from which points F M we must draw to the point of the line of Elevation E. Then from all the Angles of the Plane A B C D to bring Parallels to the base until that they meet with the line F E which is the bottom of the line of Elevation and from their sections F and H to raise the Perpendiculars F M and H K between the lines M F which are drawn at the point E. Then to take its Measures with a Compass and to bring them Perpendicularly upon the Angles for example to take with a Compass the height F M and to bear it Perpendicularly upon the lines elevated from the Angles A B which will be A G B G. Then to take also the height H K and to carry it upon the Angles of the bottom C D which shall give C O D O then to joyn the right lines G O O G. This shall be the Cube elevated If you would have the Elevation of any Figure whatsoever draw always from the Angles of its Plane Parallels to the base unto the draught of the foot of the line of Elevation and keep the same Method that we spake of for the Cube and you shall see that there is not any thing how difficult and unequal soever it be but that you may put into Perspective as we shall make to be seen in the Poligones following The second Figure is another Cube elevated after a manner very little different from the former which I shall speak of in three words And he that will may use it not to be rejected Having made the Plane by the ordinary way we must from all its Angles B C D E elevate Perpendiculars And upon the first set the height which one would give to it as B A C A. And from the points A A to draw to the points of sight F or to the points of distances G H and where the Perpendiculars of the Angles D E shall be divided at the point I L this shall be the line of sinking and the top of the Cube wholly elevated This last Order is not so universal as the former which hath always been in use and practised by the Ancient Authors It hath nevertheless some benefits which we shall know in some of the Orders following The Triangle in Perspective IN the first Order I have promised to make the easiness of elevating all Figures appear whereof the most difficult are the Poligones or Figures with many sides and to keep some Order we will begin by the Triangle Having framed a Plane by the Orders foregoing fol. 21 where we teach to make it with a List or Border we must as we were speaking set the line of Elevation on the side of such an height as we would have as is A B of three feet Then from all the Angles of the Plane to draw Parallels to the base unto the bottom of the line of Elevation B E And from their sections elevate Perpendicules between the lines A B and to bring all these heights upon the Angles from whence the Parallels proceed for example the height A B must be carried to the Angles C D which will give C R and D S. The other height F I at the Angles G O which will give G T and O V That of H L to the Angle K which will give K X and the last height N P to the Angle Q which will give Q Y. Then to joyn with right lines all these Points R S Y then T V X for the thickness of the stone in the first figure The Pentagone or five-Angles in Perspective THE Pentagone is a figure with five faces or sides and with five Angles We have given the Method of framing it and setting its Plane in Perspective in the Treatise of the Planes fol. 22. It would be loss of time to give the manner of elevating it seeing that the second figure causeth it to be known that it is the same Order with that of the Cube and the Triangle The Hexagone or six-Angles in Perspective THE Hexagone is a figure with six Angles and six faces or sides as is to be seen in two Manners in the Treatise of Planes fol. 23. and 27. where it is abbreviated The Order for to elevate them is to be seen sufficiently in the third figure 1. fig 2. fig 3. fig Of the Heptagone or Seven-Angles in Perspective THE Heptagone is a figure with seven sides or faces and seven Angles Of the which we have set heretefore fol. 24 how it ought to be made and to set its Plane into Perspective It s elevation is the same Orders with that of the Triangle as one may see in the first figure Of the Octogone or Eight-Angles in Perspective THE Octogone is a figure with eight angles and eight faces as the second figure sheweth it in the Treaty of planes fol. 25. and 26 One may see how it ought to be set in Perspective in two different Manners The elevation is as in the fore-going A double Cross in Perspective I have set this figure and that below it which the Sieur
Marolois hath in his Works according to the first Order that we follow The which would be more difficult to set into Perspective by another manner of the diversity of the Angles And by this Method it is very easy Elevating it from all the angles of the Plane c. as we have said of the Polygones and may be seen cleerly in the first figure A Stone-fluted or straked like a starr in Perspective HAving not set the Plane of this figure with the other figure I thought it fit to set it under its figure for to abbreviate it in the Ordinary way as we have set the others The Geometrical Plane is easy to make This is a Circle divided into six whereof the divisions ought to be joyned with right lines leaving a Point between two As for example from I to 3. leaving 2. Then to take 2 and 4 leaving 3. and so others the rest is seen sufficiently in the second figure 1. fig 2. fig. Of Pilasters in Perspective VVHEN one would make some Pieces as Columns Pilasters or Walls which shall have the same height There is no need of the line of Elevation It sufficeth to do as in the second Order which is that having elevated Perpendiculars from the Angles of the Plane as is A B C D of the first figure we must set the height that we would upon the first or second Perpendicule as is A F or D E. Then to draw the Ray E to the point of sight F All the Perpendicules that one shall elevate must be unto this line E F and then that the Pilasters G H shall be equal to the first If one would not use little squares in the Plane we must set upon the base the Measures and draw the Rays to the point of sight F and that which ought to abbreviate at the point of distance K for example L M is one side of the Pilaster We must draw these two Points L M to the points of sight F for the bredth of all the Pilasters which one shall set there for the depth of each Pilaster which we would make square we must take the distance L M and set it before L as is N then to draw the line N K which is the distance and it shall give the depth of the Pilaster at the point O from which points L M O we must elevate Perpendicules and do the rest as we have said If one would have the bredth of two Pilasters between the one and the other he must set them upon the base and after set the depth of the second Pilaster equal to the first as is P Q and from these two points P. Q. to the distance K which shall give the points R S upon the Ray L from S we must draw a little Parallel which shall divide the Ray M F as is S T then from these points R S T to elevate Perpendicules and to do as in the first The third and more if one would have them ought to do the same keeping always the Measures upon the base as in the first Figure Of Pilasters viewed by the Angle VVE have said heretofore that the Plane of squares is made hy drawing Measures from the base to the Distances As concerning the Elevations it is the same that we are speaking of For having set the height A B upon the first Perpendicule we must draw from the point B to the distances C D which shall divide and give the heights to the two other Perpendicules elevated on the sides Then having given the Distances which one would between the two Pilasters which are here two little squares you must elevate the second and by the same Order the third Their height shall be found drawing a visual Ray from the point B to the point of fight E at the section which this Ray shall make of the first Perpendicules at the point F F and from the points F F to the distances as in the first Pilaster Those which are made without a Plane must take their Measures upon the base as if one would give them the like bredth to those above viewed on the front It must be set as G H and to draw the Ray G to the point of sight E for to have all the Middles or the Diameters Then to set also the same bredth of G at the point I and from these three points G H I to bring lines to the distances C D for to frame the first Plane from this Plane he must elevate Perpendicules And upon the first to set the height as is G K and from the point K to draw to the distances for to have the Abridgement of the Perpendicule of the sides for the second Pilaster The same shall be done from the Points L. M And the third from the points N O. The rest is easy enough to doe viewing the second figure 1 fig 2 fig The Effects of the diversity of Horizons THE more that any one is Elevated above any Object the more he discovereth that which is above By consequent if one be lower he shall discover less and if one be under it he can see but that which is under and nothing of that which is above The first Proposition is verified by the first Figure The second by the second and the third by the last The first and second Cube is made as we have taught the third is made also by the same Orders although they seem more hard by reason that we see the Objects by the upper part But if you turn up the Paper or the Picture and draw at the point of sight and at the distances B C as in other Orders you shall have the same facility I set nothing of the Objects viewed on the side seeing that I have said so many times that it is the same with those on the front And for to give further knowledge how to set them in order There is one in a single â—â—aught and the other shadowed also Before we leave this third Figure we must observe that the lowness of the Horizon is the cause that we see the bottom of the Objects which are elevated above as D E F and of the two others which are G H placed above the Horizon one cannot see neither above nor below Above because the Horizon is lower nor below it being placed upon the Horizon There are many Painters that do fail in this making the upper part of many things appear although that the Horizon be much lower 1 fig 2 fig 3 fig The Elevation of Objects viewed by the Angle WE have snewed by the two Figures of the 19 h. and 20th fol. how the Planes are made drawing to the points of distances and never to the point of sight if it be not for to finde the Diameter We must keep the same rule for the Elevations as it is easie to see by the first Figures which have all their lines abutting at the points of distances B C and not one at that of the
sight A. The first Figure D is for to shew that whensoever there shall be an infiniteness of Parts in one and the same Object viewed by the Angle we must draw them all to the points of distances B and C. If you would make one of the same see here the Order Having made a Plane and elevated occult Perpendiculars as we have said you must set the height that you would give unto it at the first Angle E F and draw from the point F to the points B C for to have the height of the second and third Angle at the point G Then from this point G to draw again to the points B C and you shall have the fourth Angle of the Platform The other little Bodies are elevated in the same manner by setting the height that one would give them upon the first Perpendicular as from F to H and from H drawing to the points as we said but now from the point F we shall have the heights of all the Angles And the points I K shall give the thicknesses of all the little Bodies and the Platform of that of the midst by drawing always to the Points B and C The rest is seen sufficiently by the Figure which one may make to serve for a Castle defended with four square Towers or for a Palace quartered with four Pavilions The two other Bodies which are on either side of the great one are seen from the side whereof the Order is alike to that which is seen from the front for example if you elevate Perpendiculars from all the Angles of the Plane L and that you give your height to the first as M N by drawing from the point N to the points of Distances B C they will give the Angles 2 and 3 at the point O. Then from the point O drawing still to the points B C you shall have the fourth which is the Elevation of the whole This being practised by the first and by the second Order you shall have the same The second Figure below is of the same Order There is no difference but of the Horizon which is lower The third sheweth the under-part of the Objects but the order is altogether the same with that above drawing all to the points of distances Q R which is the Horizontal line 1. fig 2. fig 3. fig. For to raise Bodies and remove them as far of as one would IF you would have the first Body of two feet high and one foot deep and one broad at two feet distance one from another of two feet deep of one foot broad and three feet of height and three feet distance Another of one foot broad five feet deep and four feet high Thus you must proceed Having made a Plane of little squares which we shall make to a foot square one may make them of what size he will by the points of sight A and distances B C. You shall raise from the first Angle a Perpendicular according to the second Order which shall bear the Measures that you would give to the Objects as this D E upon the which you shall transport four times the Measure D F seeing that the highest ought to have but four feet From all the Angles of this first little square F I G D you must raise occult Perpendiculars And having given the Measure to the first distance D and 2 because you would have it two feet high you must draw from the point 2 to the point of sight A and it shall divide the Perpendicule of the Angle G at the point H you must draw Parallels to the base which shall divide the Perpendicule of the Angle I at the point K and another Parallel from the point 2 which shall divide the Perpendicular of the Angle F at the point L And joyning these 4 points H K L 2 of right lines you shall have your first Body Then because you would give 2 feet of space between the first and the second Body you must leave two little squares of the Pavement between the one and the other body and upon the first Angles of the third to raise Perpendicules and to do all the same as at the first body with these differences that the height of this second ought to be taken at the third point of the line D E seeing that it must have three feet of height and must containe two little squares seeing that it must be of two feet deep Beâ—ween this second and the third Body you must leave 3 little squares seeing that you require it at three feet distance the one from the other and from the first Angles of the fourth to raise Perpendiculars as at the first and the last after 5 little squares which is the depth of your body and the Term of 5 feet which the third Body ought to have of depth The fourth point of the line D E shall give to it its height which ought to be of 4 feet by dividing the Perpendiculars as you have done in the first Those which are shadowed on the other side are made by the same Order and of the same Proportion But the Wall of the midst is of Equall height four feet only an Opening of 3 feet in the midst In the second figure is a Wall of equall heights There being distances of 3 foot left for doores or windows The first part of the Wall is but 2 foot deep The other two 3 foot in depth a peice on the other side there is a Continued Wall of 14 feet of depth and of height like unto the others The Order is the same with that of those above That which we have called a Wall may also serve for an Hedge or Rowes for Gardens Of Walls viewed directly BY that which we have said one may make all sorts of walls viewed obliquely And although this very Order may serve for the same walls viewed directly it hath seemed necessary to me to set also this figure for two Reasons The first for that they do not always make Planes and in this case one should be troubled for thicknesses The second for to give the thicknesses to the doors and windows which may be to be set in those walls For to make walls Parallel to the base or to the Horizon upon the Plane you shall give them such a length as you shall please upon the Parallels to the Horizon for the bredth you may take that of one little square from the Angles of which you shall raise the Perpendicules A B which you shall make as high as you shall please as C. Then from the point C draw unto the point of sight D this Ray C D shall give the diminution and the perfection to the wall When one hath not a Plane we must set at the first corner of the wall upon a Parallel to the base or to the Horizon the thickness that we would give to the wall as E F. Then from the point F to draw to the point of sight D and
which making a crooked line for to joyn them together we shall have the thickness of the Joynts of the Cross of the Vault as one may see at half of the left side of the Figure aforegoing A Vault made by the Orders aforegoing ALL the Orders aforegoing do shew sufficient easiness for to make a perfect Vault as this here except what concerneth the Pillars or Columns which we will shew hereafter Of Arches and Doors with three squares THere is another kind of fretted cieling which holdeth the place of a Roof for Gates and Galleries and also in Churches which maketh well also in Perspective and is very easie to practise I have set it after the Round because that it is framed of a demi-Circle as a round door which after is to be divided Having elevated the walls A B we must make a demi-Circle which containeth all the bredth C D then holding the Compass open of the bredth of the half Diameter E C you must hold one leg firm at the point C and with the other E to draw an Arch on high which divideth the demi-round at the point G and to make likewise from the point D the Arch E H. Then to joyn these four Letters C D G H with right lines which will give you the Arch half-Hexagone or with three squares You must also make a demi-round upon the bredth I K for the bottom and for to divide it you have only to draw from the Angles of the first C D G H to the point of sight F at the sections that it shall make of the demi-round at the point L M you must draw right lines which will frame the Arch of the hollow Of another Arch Half-Decagone or of five squares THIS Arch is ordered altogether as the former and there is no difference but in the division of the Circle The first is divided into three and this into five so if you divide the demi-Circle L M into five Parts N O P Q and that you draw from all these points to the point R you shall divide the demi-Circle of the hollow so as we have said in that above of three squares The Elevation of round Figures in Perspective THE desire that I have to shew the easiness of setting all things into Perspective hath made me set here also how one ought to elevate from a Round or Circle such an height as one would have and this Order shall serve for all round Figures as Tops of a Church Amphitheaters Towers c Having made the Plane of the Round in Perspective as it is ordered heretofore and set on the side of the Plane the line of Elevation A B according to the height that one would give it We must from the Angles of the Plane which are here the Points of which they have framed the Round as are 1 2. 3 4 5 6 7 8 9 to draw Parallels to the bottom of the line of Elevation A B and to elevate them as we have said and with a Compass to transport them upon the Perpendiculars elevated from the points 1 2 3 4 5 6 7 8 9. c. as in the former Orders The demi-round before hath but half of the Elevation of that behinde and the one and the other but the single draught without thickness By this Order there is no round thing which one may not set into Perpective I mean Rounds Parallels to the Horizon The other Rounds which are Perpendiculars to the Horizon are taught in the Orders of Vaults The Elevation of Pilasters set into a Round WE must double the Round as is taught in the Plane fol. 29. and between the two Circular lines set the Plane of the Pieces which one would elevate as we see the Places before A B C D the which do draw to the Center E Then from all the Angles of these Planes to raise Perpendiculars and to give them their height according to the line of Elevation F G by the ordinary Rule as is sufficiently seen by the second figure 1 figure 2 figure A Vault like a Scallop-shell set into Perspective THIS Figure may serve for the hollow of a Church for a Grotte or Cave for an hollow Nest in a Wall and the like Pieces the Elevation is made in the same manner and by the Orders that we have spoken of For this flat Band A B which may serve for a Cornish its diminution must be taken upon the line of Elevation in C D and to carry it upon the Pilasters For the Vault we must make the first Arch E F in the manner that we have said and in the midst within to make a demi-Circle O to the which we shall draw crooked lines which shall rise above the Pilasters and shall make the sides or Nerves of the Vault as we see G H I K the heights of the Windows shall be taken upon the line of elevation between L and M. The figure will help for the rest Of open Rounds in Steeples or Vaults pierced in Perspective HAving made the Plane of the double Round fol. 24. and marked between the two Circles the places and the numbers of the Pilasters which one would have there the which ought to draw towards the Center A we must mark the height which we would give from the ground unto the hollow of the Lovure as here the line D and E on high the which must serve for the base where we shall transport the same Measures which are upon the line B G. And from the same point of sight G to make a Plane on high as that below whence all the places of the Pilasters shall draw towards the Center H for to frame the Pilasters we are only to draw lines from the places which are opposite the one to the other and which shall give their bredth and their thickness I have not drawn lines to the three Pilasters before as well to cause these of the bottom to be seen as also to make it known that there needs on high as below For to give the thickness of the Round from I unto H and from K unto L we must set the height which we would have upon the line of the Elevation D M drawing to the Horizon at the point F And from all the points whence we have framed the Round to draw to this line D upon the which we shall elevate Plumb-lines as D M which we take with a Compass for to transport all these heights upon the Perpendicules which shall be raised from the points as K L N O P Q and so of the others He that in the place of the Round would have a square or a Polygone hath need only to keep the same Method and he shall do all that he would with the same facility seeing that this which is the hard is not difficult That the multitude of Objects and the Plurality of stories ought to have but one point of sight I Have already said elsewhere that one never ought to set more then
one point of sight in one Picture and that hence we may know the great ignorance of Painters which do give as it were as many points of sight and of Horizons as they make lines I remember I have seen a Picture where there were many Chambers the one above the others and each had two or three points of sight and after that the Master thought he had done a Miracle The present Figure is to correct this Errour and cause us to know that there ought to be but one point of sight only as is A to the which all the Objects ought to draw and all the Chambers if there should be fifty one above the other or on the one side and the other as we see these three here which draw all to the point of sight A. All the rest is made as we have said heretofore For to set Chimneys into Perspective WE must take the Measures upon the base A B which must be divided into equal Parts You may make the divisions of what quantity you will This A B is into eighteen of each one foot for to make a Chimney at the Wall A three feet within the Chamber we must take three Parts as A C and draw from the point C to the point of distance D which will give the sinking of three feet dividing the Ray A E at the point F you must set the thickness of the Jaumbs of the Chimney beyond the point C as is G then drawing from G to D it will give this thickness at the point H. You must also set the bredth of the Chimney from G unto I which is of four feet and an half and for the thickness of the second Jaumbs an half foot as at the other Beginning at the point I unto K then to draw from I K to the point of distance D which will give their Measure upon the Ray A E at the points L M from which four points F H L M you must draw little Parallels to the base as F N H O L P M Q for to give the bredth to the Jaumbs you must take a foot and half A R and the Ray A E shall divide the little Parallels at the points N O P Q from which and from F L you must raise Perpendicules for the height of the Mantle-tree of the Chimney you must take five feet upon the base and carry them to the corner of the wall A unto S and from S to T for Cornish all the rest is seen clearly in the first figure The other Chimney which is opposite to it is made of the same manner for we ought always to make the Jaumbs as in the first and of these Jaumbs to make Columns Termes and all that one would I have made Brackets to this The Chimney of the bottom must also take its Measures upon the base 1 2 3 4 drawn to the point of sight E for to finde the hollow of the Chimney or the bredths of the Jaumbs you must draw from 7 to E and divide the lines of sinking at the point 5 which shall be a foot and half then from the point of distance V to draw the Diagonal passing by 5 which shall divide the Ray 2. E. at the point 6 and from this point to draw a Parallel which shall divide the four Rays 1 2 3 4. at the points 9 6 9 9 from which you must raise Perpendiculars and make all the rest as in the others The second figure sheweth plainly and without lines that which we are speaking of Of Stairs in Perspective THere is nothing that giveth so great a grace to a Perspective nor which more easily deceiveth the eye there is a muititude of Returns by reason that there is need of many lights and divers shadows which give such force to the Objects that they seem to cast them out of the work Now stairs have this advantage that in what fashion soever one set them they have always lights and shadows and by consequence they are pleasing to the sight I will set down some here If one shall use little squares they will have the more easiness having only to raise Perpendicules from so many squares as he would have steps then to set at the first square the line of Elevation divided into as many Parts as one would and from these divisions to draw to the point of sight and they shall divide the Perpendicules where the steps ought to be For example you would have a stair-case of eight steps and that the last may have the bredth of 3 you must take upon the Plane the number of little squares beginning at B as are 1 2 3 4 5 6 7.8 And 3 for the last marked 11 from all these Angles we must raise Perpendicules which we shall divide according to the divisions of the line of Elevation B D in this manner The first division four inches high supposing the square of one foot shall divide the first Perpendicule and it must be continued unto the second for that maketh also the upper part of the step as is E F and so of the others You shall make these steps as long as you would as these are of three feet taking as I have said the square for one foot so as is B G at this distance You must also raise Perpendicules as we have done on the side B but for to save this pains it were better to take the height of the last step H and that of the first I. Then to draw the line H I which must grate upon the Angles or the outward edge of the Steps as E K grateth upon them on the side B for this being there is but onely to draw parallells to the Base from all the Steps on the side B untill that they divide the line H I as we see L M N O P Q c. without making squares we need only to set the Measures upon the Base and to draw them to the point of distance We may have the same Measures upon the line A B. I set no other figures seeing that this sufficeth for to Understand them all and for to make them Other steps hollowed underneath in Perspective THIS manner of steps is made as those which we are now leaveing As for the hollowness there is need only to see the Figure for to know the manner of setting them into Perspective These two that I present shall give an open way to the Practiser of this Art to invent others by Steps in front in Perspective THIS manner of steps is according to the Order of the line of Elevation you must raise as many Perpendicules from the Angles of the squares of the Plane as you would have of steps as are C D E F and from the same Angles to draw little Parallels unto the bottom of the line of elevation A which shall be the points O O O O which you must raise until that they divide the occult Rays of the divisions of the line of Elevation
we must set the measure for the Travers as O shall be for the Bars below P for the bars of the seat And Q shall be for the backs of the Chairs All being disposed thus we must from the Angles of the plane draw parallels to the base unto the line of Elevation and at the section to elevate Perpendicules which shall give the measures as we have said of other figures heretofore All the lines of the sides ought to draw to the point accidentall of the plane For example in the chair of the midst all the sides ought to draw to the point G which is the point of the plane as I make it to be seen in the figure Of Moveables lying or thrown upon the Ground FRom the same Plane of the Chairs aforegoing which are upon their feet it is easie to make these which are cast upon the Ground We must raise Perpendiculars from all the Angles of the Plane and give to the Side lying the same Measures as to the side upright For example having rais'd Perpendiculars from all the Angles of the Plane we shall have the bredth M which is in the Chair lying upon its side which draweth to the point K we must double this Measure M which will give O for the Barre below of the Chair and the Perpendicules elevated from the Plane will give the Barr of the Seat P from which drawing to the point K we shall divide the other Perpendiculars of the front at the place that it ought for to make the same Barrs appear from all the sides whence they may be seen for the height of the back of the Chair there is but only to give to it the same Measure that the Seat hath of height And for the back of that in the midst you must double the Diagonal on the Plane and take notice where it divideth the Rays or Ascents lying R S. the rest is clear enough The two other Pieces which are under the feet upwards are very easie to make the one draweth to the point of sight T the other to the point of distance V X the line of Elevation is Y Z. The Order for to elevate these is the same as to make them upon their feet that is to say that we must raise these Perpendiculars from the Angles of the Plane and from the same Angles to draw to the line of Elevation which will give the Measures which we must give to every Ascent and the place for the Travers as well above as below For to set Altars into Perspestive THE Order of Altars is the same with that of the frames of a long Table that which is more in this is the Round of the midst the Borders of the Table-cloth and the Laces which shall be found in their place doing that which followeth First for the body of the Altar which we see in front there is no difficulty for having given to it the height and length there is nothing but to draw from all the points above the base to the point of sight E and from the sections that these points shall give to the line of the bottom of the Altar you must raise Perpendicules for the Round of the midst it is made with the Compass The rest is clear enough within the Figure For to make an Altar on the side we must set the bredth and height which we should give it at the place where we would begin it as is A B the bredth and B D the height Then from B D and C to draw to the point of sight E seeing that B F is the length of the body of the Altar and that we would give the same to this we must from the point F draw to the distance G and take notice where we shall divide the Ray B E and from the section elevate a little Perpendicular until that it touch the Ray D at the point H and from H to make a little Parallel which shall give I at the Ray C and then we shall have the upper part of the Altar C D H I for to have these two laces which are on one part and the other of the Round the points K L will give them upon the Ray B E by drawing them to the distance G and M will give the bredth of the Borders of the Table-cloth and having taken the measure B M we must bring it to D which will give O for the bredth of the Border of the Table-cloth on high As concerning the Round I will not repeat that for I have spoke of it elsewhere where any may have learned how it is set into Perspective it is enough that we know that from all the divisions we must draw to the distance G And at the sections of the Ray B to raise Perpendicules then to take these same Measures and transport them from B unto O as are P And from all these Measures to draw to the point of sight E and to observe where they shall divide the occult Perpendiculars for to make by these points a crooked line which shall give the Rounds in Perspective If instead of these laces and of the Round there were an Embroidery we should use the same Order for to abbreviate it In the Figure below I have made the same Altar without line and adorned with a Cross and two Candlesticks for to finde the place of these Candlesticks we must prolong the line of the corner of the Altar as is Q R then from the distance G draw a line by the corner of the Altar T and to continue it until that it divide that Q R and this line Q R shall be the length of the Altar equal to B F of the first figure upon the which we shall set the Measures of the Cross and of the Candlesticks as are V for the Cross and S for the Candlesticks from all these points S V we must draw to the distance G and take notice that at the sections of the Ray Q E we must draw little Parallels which we shall divide by the Ray S E and will give the squares above the Altar X for the Cross We must leave the square for the foot and from the midst of the square elevate the Cross for to finde the Measure of the Arms of the Cross we must from the corners of the square raise the occult Perpendiculars as it is mark'd Y and draw to the point of sight E for the Candlesticks Of this square we must make a Round and observe where it shall divide the Diagonal for to elevate these Perpendicules which shall give the bredth of the Basons from the which we must draw to the point of sight E from the middle square or round foot of the Candlestick we must elevate a Perpendicular for the Body of the Candlestick and for the Taper which we shall make as high as we will for to proportion it we must from the top of the first draw to the point of sight E the rest hath already
draw back the houses we ought only to advance or draw back their elevation upon the plane of the squares as L is more advanced by one square then K and M more advanced then L and so of others and for the rest to follow the Method which we have given the figure above to that below That the Objects afar off shew not the Thickness HE that practiseth this Art shall be advertised that the objects neer to the Horizon that is to say very much distant must not shew the Thickness being view'd in the front For example the houses A B C D ought not to have thickness at the Windows and at the Door But only a single draught The reason of this is that the Rays which part from the Object unite themselves in the Eye with those that are Collaterals I would have brought the demonstration of this if I had beleeved that it would have served but as it is not Necessary for my design and that it would be unprofitable I have let it alone remembring my self that I promised at the beginning of the Book that I would not give any seeing that I have to do with many persons which would be in trouble to understand them For the Buildings viewed by the Angle OF these two buildings view'd by the Angle that of the first figure is made in the same manner as we have said of the little squares view'd by the Angle and at the beginning of the elevations of other pieces view'd in like manner But to avoid the trouble to run back to the one and to the other I will say that for to make these buildings we must always set the measures upon the base and draw them to the point of distance and at their sections to raise Perpendiculars and the first Angle shall serve for the line of elevation For example this body of an house hath for his breadth A B and for its length B C which is the double of its breadth A B from thâ—se points A B we must draw to the point of distance D and from B C to the point of distance E from their sections B F and G we must raise Perpendicules which shall serve for the corners of the house For the measures of the doors and the windows they must be set upon the base between the letters A B and B C and drawing from all these points to the points of distances D E we must take notice where the B D or B E shall be divided for to elevate there the ascents of the windows The Perpendicule of the first Angle B must serve for the line of elevation which shall give the Travers and height of the windows all the rest is intelligible enough For the figure below it is the same order with that of the Chairs without order which is that having made the plane Geometrical we must set it into Perspective as the irregular pieces Then to set the Rule at every bending of the plane and to observe where the Horizon shall be divided for to make a point there to which we must draw as if it were the point of sight of each side of the building each side having its particular point For example the plane being set in Perspective the side H I giveth upon the Horizon the point K to which we must draw all the Rays of this side The other side I L must also have its point within the Horizon but our paper is too short for to make it be seen These 2 points being found we must place there the Rule and make an occult line to pass by the other side of the building parallel upon the plane to that which hath given the point within the Horizon and to continue it unto the base as from the point K by the corner L unto M and by the corner H unto N. Then to set between N I the number of the windows which must be on the side H I and between I and M to set the measures of them that we would have on the side I L All these measures being upon the base we must draw them to the points that we have found and do altogether the same as in the figure above For to set Alleys of Trees in Perspective ALthough that by the orders fore-going one might draw sufficient instructions for to set Alleys of Trees in Perspective yet I did believe that it would not be unprofitable to give a particular order therein which might make the method more easie If one would have but one Rank of Trees on each side of the Perspective there will be no need to make a plane of little squares he may only do as I have said in the fourth advice Fol. 17. But when one would make a company of Alleys to appear it seemeth to me that he sh ll do very well to frame with occult lines a pavement of little squares with the Oaks even as it hath been taught in the planes Fol. 31. And from the Diagonal of little squares to raise Perpendicules as one may see A B If one desire the Trees to be farther of or nearer the one to the other he must encrease or diminish upon the base the distances of the squares When one shall have given such height as he would to the trunk of the first Tree as is A C from the point C he must draw to the point of sight D to the end that all the Trunks of the other Trees may not pass the Ray C D the first Tree A B maketh it to be seen that between 2 right lines one may give to the Trees such compass as he shall find good and that they ought not to be drawn by the Rule The figure below is ordered as that above there is no difference but only that above giveth the squares Right or in Front and this giveth them view'd by the Angle that is to say that from the measures upon the base we must always draw to the points of distances E F and from the little squares to raise Perpendicules and to do the rest as we have said heretofore One may within the same Perspective where some Alleys should be drawn to the points of distances set also those that should draw to the point of sight as one may see by this of the midst which draweth to the point G which is the point of sight and the others draw to the points E F which are the points of distances For Gardens in Perspective I Have given in the Treatise of Planes the Method to abbreviate and set into Perspective the Plane of a Garden with its Compartments by an Order sufficiently easie supposing that you have the Plane But as I avoid these Geometrical Planes because there is need of too much time for to make them I have set these here by the which we shall know that having made a Plane of squares we may take as much or little as we will for the squares of the Garden as are here A B which
Perspective doors and arches round double shewing their thicknesses page 63. Of figures in arches of another fashion Arches viewed obliquely in Perspective ib. Of arches slat or in manner of a basket or Demi-circle page 65. For to set arches or half circles upon Pilasters or Coâ—â—mns page 67. Arches in the third point ib. For to set into Perspective Vaults or cross arches page 68. For to make the same Vaults more exactly page 69. For to make the Vaults more strait and large page 70. A Vault made by the Orders page 71. Of arches and doors with three squares page 72. Of another arch half Decagone or 5 squares ib. The elevation of round figures in Perspective page 73. The elevation of Pilasters set into a round ib. A vault like a Scâ—llop shall set into Perspective page 74. Of open Rounds in Steeples or Vaults pierced in Perspective page 75. That the multitude of Objects and plurality of stories ought to have but our point o sight page 76. To set Chimneys into Perspective page 77. Of Stairs in Perspective page 78. Other steps hollowed underneath in Perspective page 79. Steps in front in Perspective ib. For to make Stairs which one may shew from four sines page 80. Stairs viewed on the sides in Perspective page 81. Stairs within a Wall in Perspective ib. For winding stairs with Rests in Perspective page 82. Stairs winding upright in Perspective page 83. Sqâ—ares set into around in Perspective page 84. Round Stairs in Perspective page 85. Round Stairs viewed from the side in Perspective ib. For the winding stairs vp turning ascent page 86. Of Columns or Pillers in Perspective page 87. Of Cornâ—shes and Mouldings in Perspective page 88. A great Cornish above the Horizon in Perspective page 89. For to find the undâ—r part of the great projectors page 90 Of the Cornishes and the Mouldings under the Horizon page 91. For Cornishâ—s with many Returns page 92. For the op ning of doâ—rs in Perspective page 93. F r the opening of Windows in Perspective page 94. For the opening of the Window with Chamfretiâ—gs ib. Of divers â—ther openings page 95. Of planes and the first elevations of moveables page 96. Of the Elevations of Moveables page 97. For to make the upper part of Tables Stools c. page 98. For to elevate a Court Cupboard or Cabinet page 99. For the elevation of Chairs page 100. One other fashiono of Moveables in Perspective page 101. Of Moveables set without order page 102 Of Moveables lying or thrown upon the Ground page 103. For to set altars into Perspective page 104. Of Merchants Shops in Perspective page 105. Of the out side of Buildings page 106. For to set the Roofs of Houses in Perspective page 107. The rest of the Roofs in Perspective page 108. For to set a street into Perspective page 109. That the Objects afar off shew not the thickness page 110. For the buildings viewed by the Angles page 111. For to set alleys of Trees into Perspective page 112. For Gardens in Perspective page 113. The little squares with borders ib For to elevate and set in Perspective Fortifications page 114. For to make the designs of Perspective page 115. For to draw little perspectives into great and gr at into little page 116. Orders to facilitate the Vniversal manner of the Steâ—r G. D. L. page 117. Of a general manner for to exerâ—ise perspective without setting the point of distance out of the picture or field of the work by the Sie r G. D L. page 118. For to give justly the distance removed the po nt remaâ—â—iâ—g in the picture page 119 A very fine inveâ—tion for to make naturally perspectives without keeping the rules page 120. Another pretty invention for to exercise the perspective without knowing it page 121. For Figures in perspective page 122. For the Figure having the Eye within the Horizon ib. For the Figure having the Horizon below ib. For the Figures having the Horizon high page 123. For the Figure that have feet as the Horizon ib. For figures elevated above the planes page 124. Of the postures that we should give to figures in the perspective page 125. Of Beasts and Birds in perspective ib. For to finde the height of Figures far removed the first being upon a Mountain neer to the Eye page 126. For to give the Natural height or such as one would to Figures Elevated on high page 127. For to know how much figures equal deminish to the Eye the one set above the other in height ib. Of Measures for the figures Elevated page 128. The Original of shadows page 129. Of the difference of shadows page 130. For to find the shape of the shadow page 131 Of shadows taken from the Sun page 132 â—Te shadows â—f the Sun are equall to the Objects of the same height although that they bâ— removed the one from the other page 133. Of the shad ws when the Sun is directly opposite to the Eye page 134. For to give the shadows of thâ— Objects pierced by the light page 135 The shadows take the shape of the planes where they are cast page 136 For to finde the shadow of the obâ—ec when they have more bredth above then below page 137. For to finde the shadow of Objects Elevated from the Ground page 138. For to finde the shadow at the Sun in all sorts of figures page 139. For finde with facility the shadow by the Sun page 140. The Shadows taken from a Torch from a Candle and from a Lamp are found by one and the same Order page 141. Of the foot of the light page 142. For to finde the shadows by a Torch on all the sides of a Chamber page 143. The shadow by a Torch of a Pyramide upright and another upside down page 144. The shadow of a Cross ib. For to finde the shadow of round Objects by a Torch page 145. Of the shadow upon many planes parallels page 146. The shadow of boarded Floors by a Torch page 147. For to finde the shadow by the foot of the light page 148. Of the Shadow doubled ib. For the shadow of figures by a Torch page 149. Of the divers dispositions and heights of shadows by the Torch page 150 FINIS A CATALOGUE of Books Printed for Rob. Prick and are to be sold at his Shop over against the Cross-Keys in White-Cross-street and the Golden Lyon at the Corner of New-Cheapside near Bethlehem A New Treatise of Architecture according to Vitruvius Wherein is discoursed of the five Orders of Columns viz. The Tuscan Derick Ionick Corinthian and Composite Divided into seven Chapters Which declare their different Proportions Measures and proper Names according to the Practice of the ancient Architects both Greeks and Romans As also of their parts general and particular necessary in building of Temples Churches Palaces Castles Fortresses and all other Buildings with their Dependents As Gates Arches Triumphant Fountains Sepulchres Chimneys Cross-barr'd windows Portals Platforms and other Ornaments serving as well for the beautifying of Buildings in Cities as for necessary fortifications of them designed by Julian Mauclerc Lord of Lignâ—ron Mauclerc Brossand ere and Remanguis Whereunto are added the several Measures and Proportions of the famous Architects Schamozzi Palladio and Vignola with some Rules of Perspective The whole represented in fifty large Prints enriched with the rarest Ornaments of Antiquity and Capitals of extraordinary greatness with their Architraves Frieses and Cornishes proportionable Large fol. price bound 12 s A New Book of Architecture wherein is represented fourty figures of Gates and Arches triumphant Composed of different Inventions according to the five Orders of Columns viz The Tuscan Dorick Ionick Corinthian and Composite by Alexander Francine Florentine Engineer in Ordinary to the French King With a Description of each figure Large fol bound 10 s The Art of Fair Building Represented in several Uprights of Houses with their Ground-plots fitting for persons of several Qualities Wherein is divided each Room and Office according to their most convenient occasion with their Heights Depths Lengths and Bredths according to Proportion VVith Rules and Directions for the placing of Doors VVindows Chimneys Beds Stairs and other conveniencies with their just Measures for their best advantage both of Commodiousness Health Strength and Ornament Also a Description of the Names and Proportions of the Members belonging to the framing of the Timber-work with Directions and Examples for the placing of them By Pierre le Miet Architect in Ordinary to the French King and Surveyor of his Designes and Fortifications in the Province of Picardy Large fol. price bound 8 s A Book of Architect containing Cieling-Pieces Chimney-pieces Fountains and several sorts useful for Carpenters Joyners Carvers Painters invented by J Barbet Gethings Red vivus or the Pens Master-piece Being the last work of that eminent and accomplished Master in this Art Containing Examples of all curious Hands written and now in Practice in England and the Neighboring Nations with necessary Rules and Directions towards the attaining of Fair writing c. An Excellent Introduction to Architecture being a Book of Geometrical Practice VVhich is the first degree of all Arts wherein is contained Variety of Examples of that admirable Science shewing and describing the making of several Figures in that Nature with the proper Names belonging to each Member and Figure and how to begin and end them after a plain and easie manner it being of great use to all Artists and VVorkmen concerned in Building More especially Surveyors Architects Engineers Masons Carpenters Joyners Bricklayers Plaisterers Painters Carvers Glasiers c In general for all that are concerned or delight to practise with the Rule and Compass 4to price bound 2 s Mâ—gnum in Parvo Or the Practice of Geometry VVith a new Order and particular Method thereof VVherein is contained Examples of Landskips Pieces of Perspective and the like Represented by Eighty two Plates Each Plate having a full Descrptiion bound with fillets 4 s. Likewise there is Choice of Copy-books Maps Landskips Cieling-Pieces Books of Birds Beasts Flowers and Fruits coloured or black and white Also very good Choice of Italian French and Dutch Prints there likewise you may have mony for such like Books or Prints in English Italian French and Dutch or others in Exchange for them FINIS
of the Eye by reason that it is opposite to him which looketh upon it Of the Points of Distance THE Point of distance or Points of distances Is a point or points for they make two although it be not necessary which are to be set equally distant from the point of sight They call them points of distance because that the Person must be as much distant from the Figure or Picture and from the base as these points are distant from the Point Ocular and they must always be within the horizontal line as H I is the Horizon K the point of sight L and M are the points of distance which serve to afford all the Abridgements As for example if from the ends of the line E G one draw two lines to the point K and from the same points F G one draw two lines to the points of distances M and L where these two lines G L and F K shall be divided at the point X and G K and F M at the point Y this shall be the line of sinking or hollowing and the abridgment of the square whereof F G is a side and the base the lines that go to the point of sight are all visual Rays and those which go to the points of distance are Diagonals Of Points Accidental POints Contingent or Accidental Are certain Points where the Objects do end which may be cast negligently and without order under the Plane it is because they are not drawn to the Point ocular nor to the points of Distances but by chance and at adventure where they meet each other in the Horizon as for example these two pieces of wood X and Y do make the points V V V V above the Horizon P and Q and go not to the point of sight which is R nor to the points of distance S and T And sometimes the Bodies or Objects are so ill ordered that one must make these points without the Horizon as we shall cause to be seen in its place They serve also for the Openings of doors of windows of stairs and such like things The which shall be seen hereafter 1. Fig. 2. Fig. 3. Fig Of the Point of the Front THE point of sight direct or of the front it is when we have the Object whole before us without being more on the one side then the other and then one hath the Object wholly right that is to say that it sheweth nothing but the fore-part when it is elevated and a little above if it be under the Horizon but it never sheweth its sides if the Objects be not a Polygone For example the Plane A B C D is wholly the front so that one can see nothing of the sides A B nor C D if it were elevated but only the fore-part A D. The reason is for that the point of sight E being directly opposite to it it causeth the diminution of the one side and the other this ought to be understood if the Object were an Elevation for when there is nothing but the Plane it sheweth all as A B C D. Of the Point of the side THE oblique point of sight or on the side Is when we see the Object on the side of us and that we see it not but athwart or with the corner of the Eye our Eye being nevertheless always over against the point of sight for then we see the Object on the side and it sheweth us two faces for example if the Eye be in F the point of sight the Object G H I K will appear to it athwart and will shew to it two faces G K and G H and then it will be a point of the side We ought to do altogether the same in the points of the sides as in the points of the front setting a point of sight and those of distances c. briefly the same is to be done as at the view of the front 1. Fig 2. Fig. Of the visual Rayes THIS is a general Maxime That all the lines which are Perpendicular to the base within a Geometral Plane ought always to be drawn at the point of sight when one would set the same Planes in Perspective for example in the little Plane of the first figure the base is A B upon which all the lines Z are Perpendicular to it This being supposed that if one give a less or a greater line then that of the Plane as the great line A B which hath the same number of divisions with the little one and from all these divisions Z one draw to the point of sight all these lines of Z to E they will all be perpendicular to the base according to the Reasons of Perspective we may also name them Radial and properly visual Rayes the last of which are called Extremes by reason that they are at the end of the base as are these A B. Of the Diagonals or Diametrals and of their sections IT is also a Maxime that all the Diagonals of squares in Perspective are drawn at the Point of distance For example at the little Plane of the second Figure the Diagonals D O F O are drawn at the points of distances in the Plane in Perspective the which maketh that the points of distances do give us the Abridgements of the Objects that the point of sight doth remove from us in such manner as we have already said that if one draw from the ends of the line of the base F G to the points of distances L M they shall be Diagonals and where the lines shall divide the outmost Rayes F K and G K at the points O this shall be the Abridgment of the square whereof F G is one side and where the same lines shall divide the lines Z at the point Q one must draw Parallels which shall give the Abridgement of all the squares and a like number of all the sides as in the little Plane And the more these points of distances are removed from the point of sight the more the Objects do abridge themselves and close together And this is it why all the Beauty of the Perspective dependeth on the points of distances which ought neither to be too near nor too far off from the point of sight the which made me set this third figure with diversity of removals for to cause a belief of the verity of that which I am speaking Let us suppose then that R is the point of sight and S S the outmost Rays if one sets the point of distance at T he shall divide the Radius S R at the point V which shall be the abridgement of the square whereof S S is one side the which is ridiculous to see a square which should appear three times more hollow then it ought to be by reason that the point of the distance T is too near to the point of the sight R for it must be at the nearest that the point of distance be as far removed from the point of sight as the half
side behold it here Take a Compass and set one leg upon the base with the other take the most perpendicularly that you shall be able the section that you desire to transport as D and carry it upon this line Perpendicular as E O and mark your measure F then draw from D to F and you shall have the same as if there were two points of distances And so of all other sections The seventh Advice that we should not use the Diagonal WHEN one would use the outmost Ray for the line or section as it might be G H He ought to set the Objects upon the base as are K L M N O and from thence to draw them to the point of distance L which ought to be drawn back as far as shall be possible to the end that the Abridgement of the Perspective may be the more pleasing thereby for if the point were nearer to the point of sight G the Objects would have too much hollowness I mean for example that a square would appear a Parallelogram And from this point I to run through all the Objects K L M N O and to mark the section of the Ray G H And from these points to draw Parallels to the base or of the Horizon as is here P Q. This Method is the least in use although some do take it The Eighth Advice for to abridge in divers manners IF sometimes one be taken in a strait and that one cannot remove the point of distance we must elevate from the foot of the Ray S R a small Perpendicular as T S which shall receive the sections and give a lesser Abridgement and if one would have it yet more little he shall but only bend a line as is X the which by reason of its inclination causeth that the sections are closer together Then for to draw the Parallels he hath only to transport this line X or T upon the foot of the other Ray as is V and from all these points to draw lines Parallels to the base and you shall have that which you desire 1 Fig 2 Fig 3. Fig THE ORDERS FOR PLANES IN Perspective Of Planes viewed directly or in front ONE may have seen at the third and fourth Advice and the Elevations following will cause to know that it is not my purpose that one should use Planes Geometrical for to make Perspectives for this would be to double the labour and no Painter would take this pains seeing that I teach him to make the same thing by means of the base But as there is no Rule so general which hath not its exception so there are certain Figures which one cannot set into Perspective but by the help of these Planes further also one should be troubled if one should give one of these Planes to be set into Perspective and that one had not learned how he ought to prâ—ceed These Reasons have obliged me to set these which follow the which will suffice to learn to set into Perspective all those which may be presented and also be imagined 1. To contract or abridge a square A B C D. One must draw A B at the point of sight E and from the same Angles A B two Diagonals F B A G and where they shall divide the Rays A E and B E at the points H and I. This shall be the square A B C D abridged into A H I B for to make it without the Geometrical Plane we must draw from B to F or from A to G or else transport A B upon the base as B K and from the point K to draw to the point F it will give the same section I upon the Ray B E. 2. To abridge a square viewed by the Angle D having made the Plane A B C D. We must draw a line which toucheth the Angle B and it must be in right Angle upon the line B D. This base being produced we must set the Rule upon the sides of the square as A D and D C and where this Rule shall divide the base there to make the points H I then to draw H and B to the points of distances P and B I to the other point of distance G. And at the section of these lines to make the points which shall give you the square K L M B for to make it without the Plane you must set the Diameter on the one part and the other of the middle B as H and I. But as well in the one manner as the other you must not draw at the point of sight O. 3. To abridge a Circle It must be enclosed in a square A B C D And from the Angles A D and G B to draw Diagonals which shall divide the Circle into eight parts and where they shall divide it at the point O to draw upon the base the Perpendiculars E F then to draw two lines Diametral Q R S P which divide themselves in right Angles at the Center G. The Plane being ordered in this manner you must draw all the Perpendiculars at the point of sight H and where they are divided the Diagonals A K and B I to make points of the which the two latter M N are the draughts of the square which are to be divided into four by the section of the Diagonals at the point P. Then from the ends of this Cross they draw bended lines by these points which give the shape of a Circle in Perspective This manner may pass for little ones but we shall give one more exact for the greater 4. This Figure is composed of the two first wherefore I will say nothing of it for he that shall have made one or two of them shall be able to make it easily 5. The fifth depends also upon the two first but there is also more a Border round about which they have not for to set this Border into Perspective we must draw these four Rays A B C D at the point of sight G and where the inward Rays B and C are divided by the Diagonals A F and D E we must draw Parallels to the base and you shall have that which you demand 6. It is the same with the second except that it is compassed about with two Borders wherâ—fore I will speak no more of it Planes viewed Obliquely or on the side THESE Planes being those that we will soone dispatch ought to be made all in the same manner which maketh me believe that it would be loss of time to repeat how one ought to abridge them in Perspective for it seemeth to me that the Figures do suffice to make it appear that there is no other difference from them that went before but the scituation of the Object which is here seen on the side and the other is view'd in front All the A A A are Points of sights and the B B B points of distances Of a Triangle THE Triangles according to the Numbers ought to precede the squares but according to reason they
marketh them both and is divided at the Point C. The 3 and the 6 will give the section at the point D. And the 4 and 5 will give the last at the point E. This line A B being so divided we must transport it upon the Base of the Plane which one would abridge beginning to set the point B at the point F. as he e and then to mark the other divisions C D E from the which one shall draw to the point of distance O and from the sections of the outmost Ray to draw Parallells to the Base and where they shall divide the Rays which beare the Numbers of the Angles there we must make Points the which being conjoyn'd by right lines will give the figure which we desire For the thickness or Border it shall be made by one of the two orders afore-going 1 Fig. 2. Fig. Of the Octogone or Eight-Angles THe Octogone is made of a Circle divided into eight Parts of 45 degrees for each side from the which divisions drawing lines we have the shape of the Octogone that is to to say a figure that hath eight Angles and as many sides The fore going Orders do cause sufficiently to know how one ought to set it into Perspective either on the front or on the side I will only Advertize that the Plane abridged on the front is made according to the eighth advice And that of the side according to the seventh The point of the sight is A and that of the distance B. The rest is sufficiently seen without an Exposition Of the Octogone after another Order THe manner of making this Octogone hath bin Invented by Serlio It is made in this fashion Having framed a Square by the Ordinary way as is A B C D we must divide the base C D in ten parts and leave 3 thereof on each side and from the third division of one part and the other E F to draw lines to the points of sight G and at the sections of these lines by the Diagonalls O we must draw Parallells to the base which touch the sides of the Square at the points H I K L then joyning together by the lines of the points E H I E F K L F you shall have an Octogone as may be seen by the first figure Of the Hexagone or six-Angles The same Serlio hath made also the Hexagone after the same fashion Let a Square be drawn as this before A B C D and that the A D be divided into four Parts from one of the which on each side E F let lines be drawn to the Point of sight H Then from the section of the Diagonalls which is the midst of the Square G to draw a Parallell to the base which toucheth the sides of the square at the points I K Then draw lines by the points E I E and F K F there will be framed an Hexagone The second-figure I will say nothing of this Octogone view'd on the side seeing that as we have already said so many times it is the same Order with that of the sight of the front The third figure 1. Fig. 2. Fig. 3. Fig. Of the Octogone double SUpposing that we have already made an Octogone single for to make it double or to give it a thickness or Border you must proceed in this manner Set such a bredth or thickness as you would give to it within the square which containeth the Octogone single as here A B on one side and the other and draw from these points to the point of sight C. And where these lines shall Cross the diagonalls at the point O draw the Parallells D The which will make a welt or guard about the square Then draw from Angles unto Angles occult lines or points passing by the Center N And where these shall Cross or divide the lines of this inward square at the points E F G H I K L M it shall be the Bounds of the Octogone of the Inside Of the Hexagone double ONe may do the same with the Hexagone figured within a Square The which maketh me beleeve that there is no need to use any repetition seing that one may see by the figure that whereof he might any ways doubt The Octogone view'd on the side is all of the same frame with that of the front The point of sight is A and that of the distance B. 1. Fig. 2. Fig. 3. Fig. Of the Circle THe more that any Circular forme shall have parts the sooner and more easily shall it be converted into a Round hence it is that Serlio saith that we must frame a Demi-Circle and of this circumference one may make as many equal Parts as they would for the more that it shall have of them the more this Rotundity will be perfect for example the Demi-circle a Plomb or Down-right is divided into eight Parts which will give sixteen for the whole Round and from these divisions Z to elevate Lines Perpendicular upon the base at the point E. Then we must draw two Diagonals at the points of Distances which are here farther removed then the Plate is broad but which one ought to suppose within the horizon ordinarily which will give a square A H I B now the square being framed we must draw all the points E at the point of sight F unto the line H I and at the sections of these lines to draw Parallels throughout Then we must begin at the midst of one of the sides of the square to make a point as a another point at the Angle opposite as if one would draw a Diagonal as b continuing so to do from points of Angles to Angles following the Diagonal lines as a b c d E f g h i K l m n o p q. These points will frame a perfect Rotundity then you must bring with the hand bended lines or circular and you shall have your round in Perspective The Perspective must have this Rule and Order to abridge the Rounds very familiar and usual for it is oftentimes used as well for Columns bending Roofs Arches opening of Gates and Windows as for many other Rotundities Of the Circle double WE must suppose that the first Circle A B is that which we are now to make and that we would give it a thickness or border by making another more inward in this manner We shall give it such a bredth as shall please us as A C and from the center the great Demy-circle G we will draw the little one C D which we will divide as the other great one by drawing occult lines from the divisions of the Great unto the center G. And at the section of these lines of points of the Great upon the less demi-circle at the Points I we must draw Perpendiculars I as those that we have made in the great upon the base And to the end that they may confound nothing we must mark them with points from the points I of the base we shall draw to the
equal parts and drawing lines to the point of sight for to frame the bands or chains G H I yet nevertheless there is more to do for we must take heed to give to the Chains that go across the same largeness as to the others which go to the point of sight O which is a square throughout all and that there be the same number of Squares between the void ones The rest is seen sufficiently A Pavement of little Squares Octogones mingled with the Squares WE should never have done if one would set here all the fashions of Pavements which might be made by the means of the little Squares for an ingenious person would invent an infinite Company according to his fancie The seventh fashion is plain enough neither have I done it but only to open the Ingenuity and to give means to compose others thereby There is nothing to do but to divide the base into a quantity of Parts of the which we shall frame the little squares as we have said heretofore And of these squares to take a number as here nine whereof there are five all full and four at the half The full do give the inside of the figure 1 2 3 4 5. And the Diagonals of others 6 7 8 9 give the Panes or Sides The rest is sufficiently seen A Pavement of single Squares view'd in Front I Have set this manner of Pavement the last not because it is the hardest seeing that it is the beginning of all Perspective and the most easie of all the Planes but to cause to be known that it is the most useful and necessary for all the other may be made and are made ordinarily when all is done serving only for ornament And this serveth for a foundation upon the which we raise that which we desire to make appear As we shall see hereafter 1. fig. 2 fig. The Plane of a Garden abridged THAT which we are speaking of is confirmed by this Plane for drawing all these divisions which are upon the base to the point of sight the Diagonals will give the depth of the whole Plane and the Abridgement of the little Squares Then taking the same quantity as well for the Alleys as for the figures which the Geometrical Plane taketh up you shall have in Perspective the same Garden which is upon the Plane As the figure sheweth it What plane soever you have to abridge And to set into Perspective The easiest way is to Enclose it into a Square and to divide this square into many little squares For setting the square and the quantity of little squares into Perspective by the ordinary wayes You have but to take heed that you take the same Number of little squares in the Plane abridged as in the Geometricall Plane And you shall make in the one the figure of the other The Plane of a Building Abridged SErlio in his Treatise of Pespective doth highly esteem this Invention of setting the Planes into Perspective as a thing very useful to chief Builders or Architects by the which they may cause to be seen all at once a part of the buildings elevated and the rest in Plat-form and as upon the base But seeing that it is the same Order with that of the Garden which we are making now we will say nothing further of it The Figure will cause to understand the rest and by this little to gather how the greater and more hard should be In the second part you shall have the method to make to be seen in Perspective a perfect House where you shall see the Building finished and accomplished and by the same means all the divisions of each Story from the Carpenters Work unto the Cellar and the only space which the Geometrical Plane would take up The Plane of a Church Abridged THis plane of a Church is made according to that we have said at the seventh Advice That is to say that all the sides which are Perpendicular to the Base ought to be drawn upon the Base as are here the places of the Walls and of the Pilasters and from the Base to draw them to the point of sight And all the other sides which are Parallel to the Base ought to be drawn on the side And to mark upon a line as O P all the bredths as we see A b c d e f g h i k l. And then to transport all these Measures upon the Base from the which drawing to the point of distance the sections of the outmost Raye will give the Termes for to draw the Parallels which will give the Abridgement of every thing the which is shewed by the Letters a a b b c c c. This manner of Abridging upon the outmost Radius is practised by many But he that would believe me will leave it for to take the Orders of the Eighth Advice where we set a Perpendicular line at the end of the Base for to receive the sections and to take away the default of this present Practice which doth not abridge it sufficiently if it be not that the points of distances are very far removed for then the effect is wholly alike to the other Methods The Plane of an House with a Garden THE Order of setting this Plane of a House in Perspective is altogether the same with that of the Garden whereof we were speaking the which ought to suffice for the one and for the other that we may not repeat so often It is set here for to shew that one may abridge all sorts of Planes whether they be composed of equal parts or unequal The Plane of a Fortification Abridged FOR to set all Fortifications and whatsoever other Piece it be into Perspective we must use the Sixth and the Eighth Advice It is the Order that we spake of for the Church and for the House Which is to draw from all the Angles lines Perpendicular upon the base and from the base Rays to the point of sight and from the same Angles to draw also Parallels to the base which shall mark the divisions upon the line on the side as A B The which line A B ought to be set upon the base And from these Measures to draw to the point of distance for to give us the line of the section C D But because that the Place suffereth us not to set it upon the base I have transported it under the Figure as is A B. Then having set the point of Distance in E of the height E F there you must draw from all the divisions of A B to the end to divide the line of the section C D into so many parts The which line C D with its divisions ought to be transported to the foot of the outmost Ray or on the one side and other D D And from all these Points which are upon the line D C to draw Parallels or else only to mark a point upon the Ray which goeth from the Angle of the Plane which is proper to it And all
then the other Having made from the Center A the demi-round or the whole Circle B H I. You must from the Center A and from the end of the Diameter B draw Rays to the point of sight C then set upon B I the bredth or thickness that you would give as is D A. And from this point D to draw to the distance E and at the section of this line D E upon the Ray A C to the point F you must draw a Parallel to the base until that it divide the Ray B C at the point G then to set one leg of the Compass at the point F and with the other leg to take the distance G for to make the demi-round or the whole round which shall be the thickness of the Arch or of the Round as may be seen in the Figures All the lines K ought to be drawn at the Center A and the other L at the point of sight C. This may serve for round windows made of stone and these lines shall make the points as also for great Vessels Pipes bathing Tubs c. Arches view'd obliquely in Perspective THis Order may serve when one shall be in haste and that one would not be so exact and also to avoid a multitude of lines which the other Order doth oblige to make I say then that having framed the first Arch N O as we have said heretofore we must make upon the first draught little Parallels to the base in such number as you shall please as are these Q then to take with a Compass the bredth where the Arch beginneth as is P O and to bring it upon all these little Parallels Q which shall give the points R by the which we shall bring a crooked line which shall frame the thickness of the Arch. It is certain that according to Perspective the Objects are enlarged when they come near to us and that the line O P ought to be smaller but in this the difference of these bredths is so small that it signifies nothing And yet I give not this for a Rule but for an ease to those that are in haste Of Arches flat or in manner of an Handle of a Basket or demi-circles THE Order to set them into Perspective is the same with the demi-Round and of the third points as we see in the Figure A B. All the difficulty is to finde the draught which is made in two Manners The first by two centers and a line or thread as we have said in the Orders before speaking of the Oval by reason that the Handle of a basket is properly an half-oval The second is practised thus If one give you the line C D for to make there a low Arch which may have the height E F you must from the center F make the demi-round C G D and to divide it into as many equal Parts as one would as this here into twelve and from all those divisions to draw to the Center F then again from all these divisions to draw Perpendiculars upon the line or Diameter C D as are the lines L. After these works we must of the height which one would have the Arch of make also a circle as from E F the demi-round H E K and from the sections which this little circle shall make upon the divisions of the great we must draw little Parallels until that they touch the Plumb lines or Perpendiculars which fall from the same divisions as for example L O and from all these points O frame the Arch as we see it here made of Points The other Figure maketh yet the Arch lower and one might make it yet more couching keeping the same Rules and Orders The Figure below maketh one of these Arches to be in Perspective view'd in front as it ought to appear being finished I will set nothing of the Practice having already said that it is the same with that of the demi-Rounds ONE may see in this Figure the good effect of the Arches when one giveth them well the Center or the draught of the Roundness that they ought to have For the Degrees and the Figures we shall have here after the manner of giving them their just Measures For to set Arches or half-Circles upon Pilasters or Columns ONE might say that in the Figure which we are about to behold there are Pilasters which are not in the draught which goeth before the which hath made me resolve to set this here which shall serve to make it known that it is the same Order and that we have only to leave the place and bredth of the Pilaster which we would give them between two Arches the which is done by the means of the Plane or of the Base even as we have seen the demi-rounds which are between each Pilaster the which are made as we have said in the last Order Arches in the third Point THE Arches and the Vaults or bending Roofs in the third point are ordered in the same manner with the demi-round wherefore having made one of them we may very well make the other it sufficeth only to know the draught seeing that the Figure sheweth sufficiently the rest for the draught we have already said that there is nothing so easie The bredth A B being given for to make there an Arch in the third point we must open the Compass for all this bredth and holding firm one leg at the point A with the other to make the Arch B C then to bring back the leg to B and with the other to make the Arch A C where they shall divide themselves it shall be the point of the Arch C The other sort of the third point is the true which we have set heretofore marked ✚ Seeing that all the rest is ordered as in the demi-round we will not make any repetitions thereof there are only here Pilasters between two which are not in the others that we may cause the better to understand that which I have said here above that we have only to draw these Measures from the base to the point of distance O which shall divide the Ray D E at the point F for to elevate the Perpendicules before then having set the thickness G to draw the Ray G E for the bredth of the Pilasters H from this point H they elevate Perpendicules which bear the same divisions with those on the fore-part the which are joyn'd with right lines and as in the demi-tound For to set into Perspective Vaults or Cross Arches WE must remember or see it anew that which we have said at the 28. fol. speaking of setting the great Round into Perspective by reason that we have divided the Circle into many Parts for to make it the most exactly that may be and by consequence the Vaults or Arches more round and more just But as there are a great Company of lines in this division of 16 parts I thought that it would be better to begin by a division of 8 although
it be not so exact so will it also be less confused We will take again the other in the following leaf Having then made the Plane of a Round divided into eight parts 1 2 3 4 5 6 7 8. We must draw from all its divisions Parallels to the base unto the Ray B A which shall give the points C upon the which we must elevate the Perpendiculars C D We must transport upon the first Perpendicular B and D which is the line of elevation the Measures of the half-Circle B E F which shall give the points D H G from the which we must draw Rays to the point A and at the sections of the Perpendiculars C D we shall have the same divisions as in the Plane 1 2 3 4 5. for an half-Circle we must draw crooked lines as may be seen in the Arch of the first side the measures of which we must transport to the other for to have the two Arches collateral from the risings of which we shall make two Circles with the Compass the one before G K from the Center M the other at the bottom 5 L from the Center N and so we shall have the four Arches which do meet ordinarily in the cross Vaults at the outmost Mouldings Ogees or Circlets There remaineth nothing but to make the Cross or the crooked Diagonals which ought to rest and bear upon the corners G 5 K L passing by the knot or fcutcheon O. Seeing that the Circle is divided into eight Parts the Arches which are but the half of the Circle ought to have but four as have those of the sides whence we ought also to divide into four the half-Circle before G K at the points G P Q R K the which ought to be drawn to the point of sight A unto the Circle of the bottom 5 L Now that which followeth is the secret of the Cross it is that we must draw Parallels to the Horizon or to the base from all the sections of the Circle on the side 1 2 3 4 5. at the divisions of the Circle before in such manner as G which is the first division of the Circle touch in a point the first section 1. from 2 to draw a Parallel to the second division P and to make a point S from 3 to the third division Q which shall give O the place of the Knot from 4 to the fourth division R at the point T then to joyn the crooked lines G S O T L and you shall have already a Diagonal a d do as much on the other side and you shall have the Cross entire and your Vault compleat For to make the same Vault more exactly HE that shall understand well the foregoing Order will not be much troubled to do this seeing there is nothing but to double the lines and to take heed to the sections which are in a greater Number by reason the Circle is divided into more Parts One may learn to make the plane at the 28. fol. you must draw parallels from all the divisions of this plane from i unto 16. or the half only to the Ray B A which will give the points O upon which you must elevate perpendiculars c. All the rest is done as we have said in the foregoing Order But this is the more exact and doth make the Vault more easily because the divisions are more near the one to the other For to make the Vaults more streight then large THere are two Orders in this Figure the one for to streighten the Vaults on the sides the other for to give a Thickness to the Cross We will begin with the former The two Orders of Vaults which we are about leaving supposing that they are all square that is to say that the distance and bredth of the Arches is equal as well on the sides as those on the front and he that cannot make but of this fashion shall finde some trouble if he were to set up a Church where ordinarily the Arches of the sides are much closer then those of the front See here a fair Invention by the which you shall give such Measure as you please to those of the sides by the means of the base A Q. Suppose then that the Arch before it Q is 40 feet broad and that in that of the sides you would allow but 15 20 or so much or little as you please you must according to the fourth advice in fol. 17. set this Measure upon the base and draw to the point of distance which will give the sinking of the same Measure in A E as by example we have set here A C of 20 feet drawing from the point C to the point of distance which is a little farther off here where our Paper is too narrow for to cause it to be seen it will divide the sinking of 20 feet upon the Ray A D at the point E then coming back to the Base you must make an half-Circle of this distance A C and divide it into as many parts as the greater Arcade F G shall have of division as here 8 and from all these divisions I to elevate Perpendiculars I H and from the points I H being drawn to the point of distance they will divide the Ray A E at the point O which you must also elevate into the Perpendicular O P you must make in some place separate the Plane of this demi-round F G. Supposing that it hath not been made for to take the divisions thereof and to carry them from E unto B And seeing that the Plane of the Figure foregoing is equal to F G take the Measures of the half B C D E F and carry them upon the Perpendiculcs A F and from these points E F D C B draw to the point of sight D and from the sections which these Rays B C D E F shall make at the Perpendicâ—les O P you must draw crooked lines which shall frame the Arch of the side and drawing Parallels from the sections 1 2 3 4 5 6 7 8 9 to the divisions of the Arch F G you shall have the points F R S T V X Y Z for to frame the Cross even as we have already said heretofore For the Thicknesses of the Joynts of the Cross you are only to make a little line of Elevation a b which I have set at the top of the Perpendicule elevated from the point O and this line a b being drawn to the point of sight D divideth all the other Perpendicules at the points c d for to give the heights Proportionate to every Perpendicule elevated from the sections of the Cross that is to say from the sections which must be made for to finde the draught of the Cross following their Order for example the first Elevation a b shall be given at the first Perpendicule G The second Elevation c d at the second Perpendicule F c and so following for all the others which shall give the points C by the
A Then to take these Measures with a Compass and carry them upon the Perpendicules elevated from the Angles of the Plane each according to their Order The first for the first step the second for the second c. For to finde these Returns P you must from the same Corners P draw to the distance Q and to take heed where that divideth the line of the Plane or the under-part of the step for example above the fourth step I have made the Plane of the fifth step Now to have its Return P we must from the same points P draw to the distance Q and take notice where it shall divide the Ray R which shall be at the point S and this point S shall be the point for to draw the line of Return S T. And so of others For to make stairs which one may shew from four sides THere are many wayes to make these Stairs see here are two which seem the most easiâ— The first Being about to make one of these Stairs we must take the lengâ—h of the first Step and set thereon the quantity of Steps that you would have as upon the line A B I have set the points C C C for four steps From these points we must make Rays to the point of sight D the Rayes shall be divided by the Diagonals A F and B E at the points I from the which we must raise Perpendicules and draw little parallels unto the bottom of the line of Elevation G which shall give the points H which they shall raise as H K. We must upon this line of Elevation G set as many equal parts as we would have Steps as here 4 from these four points 1. 2. 3. 4. We must draw to the point D for to divide the Perpendiculars H K and to give to each the height that it ought to have as that which is made of points sheweth it We must take these measures with a Compass and transport them the one after the other beginning at the first G 1. and carry it upon the first Perpendicular to the corner A as A L then to draw a parallel unto the other side B. but here I have not set it but at the half for to make the plane to be seen in the other for the second Step you must take the second measure H. 2. and carry it upon the second Perpendicular I then to draw Parallels as at the first And so of all the others Another manner The side M N being given we must make a parallel above for the thickness of the first Step as O P from which points O P we draw 2 Rayes to the point of sight Q and also to the distances R S And these Diagonalls shall frame the square in the ordinary manner and this shall be the first step For the second we must set the measure of the breadth which we would give it upon the line O P as is O T and from the point T to draw to the point of sight Q. and this line or Ray T Q. shall divide the Diagonals O where we must raise the second Step at the point V. The height of this Step shall be taken from the half of V X as M O is the half of O T. This measure being given at the point Y we must draw parallels unto the Diagonal of the other side which is drawn from the corner P then from the points Y Z to draw to the points of sight and of distance for to frame the square as at the first Step. For the third Step we are only to carry upon the line Y Z the measure V X which shall be Y A and from the point A to draw to the point of sight Q for to divide the Diagonal of the point Y which shall be the point B and the place of the third Step. Its height shall be the half of B C which is alwayes that of O T in Perspective All the rest is the same as in the first and second if there should be an hundred you must work always in the same manner The third figure causeth these Steps to be seen clearly without the confusion of Draughts which we should make for to find their places these Draughts should be made in white or in such manner that nothing may be seen of them when the figure is finished Stairs viewed on the side in Perspective YOu must set upon the base the number of steps that you would have that is to say as many points at an equal distance as here the three A B C from these points you must draw to the points of sight D. Then from the point A to the point of distance E And this Diagonal A E shall give the plane and the place of the steps at the section of the Rays B C at the points I and upon the Ray F which is the foot of the Wall the point G which is the midst of the plane of the steps from this point G you must draw to the other distance H for to find the corner of the last step at the point K and the place of others at the points I. Then from all these points I to raise Perpendiculars For to give them their height you must from the points A B C which are upon the base raise little lines for to serve for the line of elevation upon the which shall be set the heights according to their number For example A which is first shall have but one B which is the second shall have two and C which is the third shall have three Draw from all these points 1 2 and 3 to the points of sight D and you shall divide the Perpendiculars elevated from the plane to the points O which shall be the height of each step That of the other side is for to make it seem without points and without lines This manner of steps may serve for many things as for an Altar for a Throne for the forepart of a Church for a Gate c. Stairs within a Wall in Perspective SEt as many divisions at the end of the Wall as you would have steps as here for three between A and B and draw A B to the point of sight C. Then having determined the space that you would give to the steps as D E you shall draw the parallel to the base E F which shall receive at the points I I the sections of the lines drawn from the points G H to the point of sight C and from these points I I you shall raise Perpendiculars I K I K which shall receive the heights of the steps drawing from the points 1. 2. 3 to the point of sight C as is to be seen in the second figure 2 Figure For winding Stairs with Rests in Perspective WE must remember the fore-going orders about Steps and it will be easie to frame these winding Stairs but to avoid the pains of searching we will unfold the whole matter here By reason that the
winding Stairs of this figure have ordinarily twice as much at the bottom as they are broad When one would raise then into Perspective he shall first set the Horizon where he would Then he must make a square according to the ordinary rules and double it according to the second advice of Fol. 16. and to divide this square by an unequal number of little squares that the Walls which should be in the midst may be of the measure of one little square In this figure each square hath 9 sides or little squares of each side the which being doubled maketh 18. for all the hollow Of these 18. you must leave 4 at each end for the Rests there remains 10 little squares which we will make to contain 1 foot eevry way of which we shall make ten Steps or degrees as followeth Having left 4 squares A B beginning at the point A which holdeth the place of the Wall we will raise a good height the Perpendicule B then the second C and the third D and so from the other Angles of the squares until that one have made the 10. which we have here This being done on the one side you shall do as much on the other and all these Perpendicules shall give the depths of the steps For the height if they have one foot of depth or breadth we shall give them one half foot of height which is the half of the little square A O this height being taken with a compass we must set it upon the first corner which shall serve as for the line of elevation beginning all below at the point A and to mark it as many times as we would make Steps as here 10 unto the first Rest from which we begin to ascend again on the other side opposite where which we shall take again the Rest of the numbers following are marked there on the one side and other unto the 23. From all these 23 points we must draw to the point of sight E and to take heed to divide the Perpendicules according to their order that is to say that having placed the rule upon the first point and at the point of sight E we must divide the first Perpendicular B unto C with a small draught for the first Step For the second Step we must from the second point divide the second Perpendicular C unto D And so of all as well of one side as the other From all the Angles of these small draughts between the Perpendiculars we must draw parallels to the Horizon unto the Wall F which is raised in the midst as are the small draughts I I I I which I have made only on one side for to avoid confusion It is only these parallels which must frame the Steps All that is made unto that ought to be of occult lines which ought not to be seen when the figure is finished The Rests ought to be taken from the defect of the last Perpendiculars unto the Wall as from G unto H their thickness H K is of one half foot as of one Step. The figure below is the same wiâ—h that above but this is made and the other sheweth how it ought to be made Stairs winding upright in Perspective YOU must set upon the base one side of the Ascent and divide it into so many Parts as you would set steps there for example the side of the stairs let be the distance A B if you would have 16 steps for the whole Circuit of the square each side shall have four This is why this Measure A B being divided into four you must make thereof a square divided into sixteen according to the Orders afore-going From all the outward divisions which divide into four the lines of each side you must raise Perpendicules which will give the bounds of the steps Let then the Perpendicules be A A B B C C D D E E. This E E made for three by reason that the point is in the midst for that it serveth for the Nuell or Spindle which is the Center of all and the half of the line before and of that of the bottom there follow F F G G H H I I K K L L M M N N O O P P. You must set upon the first Perpendicule A. which we will make to serve for lines of elevation the height of one step or degree Q A And from the point Q you must draw to the point of sight X for to have the Measures of all the steps at the sections of the Perpendiculars Q R S T V A Q is the height of the first F R of the second G S of the third H T of the fourth and I V of the fifth this of all those of the bottom as A Q is of all those before Seeing that G S is the measure of the third which is the midst of the side it must also be the measure of the Center and of the Nuell of the stairs therefore having taken this Measure G S with the Compasses we must carry it to the Center of the square and mark it in going upwards as many times as we would set steps in the whole Ascent as I have set it here eighteen times for eighteen steps or degrees All being ordered in this manner the rest is easie enough seeing that for to make the first step we must take the measure A Q and carry it upon the Perpendicular D to the point I and from this point I to make a Parallel unto the other Perpendicule B then from these two points I I upon the Perpendiculars to draw to the other I which is at the Center of the square these three III will frame the first step For the second seeing that its Corner cometh to the Perpendicule B which is on the side before you must give it the same measure A Q which shall be 1 2. And from the point 2 to draw to the point of fight X for to divide the Perpendicule P or the point 2 from the which points 2 2 Perpendiculars you must draw to 2 of the Center which will frame the second step For the third seeing that it meeteth upon the Perpendicular P you must take the measure F R for its height and do as at the second and so of all the others He that would make them round needeth but only to reduce the square into Round according to the Orders aforegoing and he shall have the same facility wholly as in the square in whatsoever remaineth Squares set into Round in Perspective THIS Order is the same that we have given in the Planes for to set into Perspective the Round divided into 8 as one may see in the figure A where the perfect Round of the forepart of the Cube giveth the draught how to abridge that above And that above with that before for to abridge all the other sides as we see the Figure B where the Round is abridged on three sides and at the other C where it is
of all the faces of the Cube The third Figures D E F are pierced or hollowed each on two sides according to the Plane of the Figure where the Round A as we see the Cube D pierced by the face before and through that we see the bottom pierced likewise E is pierced by the sides and F by the upper part and the face which lieth upon the Ground which cannot be seen supposing that the Cube be of matter which is not transparent These three Figures which are under are as the Pieces which one hath drawn from each Cube this G should be drawn from the Cube D H is drawn from the cube E and I is drawn from the cube F. That which causeth to understand the easiness of setting all square Figures into Round and that one shall not be troubled to set Columns in what place soever he would The reason why I have set none of them heretofore hath been for to render the Elevations more easie to conceive and to facilitate the Orders the which being well understood and remembred one shall be able to make a round figure of whatsoever he will This is the beginning of Columns We shall further speak how one ought to proceed for to make them perfect Round Stairs in Perspective FOR to elevate these three Stairs or round Steps view'd by the front which are in the first figure we must make a Plane of three Rounds the one within the other as it hath bin said in the Planes fol. 28. And from all the points that frame the round to draw Parallels to the Base unto the Ray A which is the foot of the line of Elevation A B which shall give the elevations by the Ordinary Rule which must be taken with the Compasses and to carry them upon the perpendicules elevated from the Points of the Plane as we have done at the Pilasters set into Round Round stairs viewed from the side in Perspective THE Order of Figures or Objects viewed from the side is altogether the same with that of those of the front But that it may be known that we are not always bound to follow the division of the Circle into 16. I have made those of the side into 8 as may be seen in the Circle made of Points in the Figure which is not shadowed for all the Rest it is as in other Orders the line of elevation C D which is drawn to the point of sight E. 1. Fig. 2. fig. For the winding stairs or turning Ascent THIS Figure is the same with that before-going which I have not shadowed on purpose to make the Order to be the better understood And for this reason I have reserved for this the Tree or the Nuell of the Ascent which one may finde by making at the center A a Round in Perspective or rather a demi-round seeing that we can see but the half as is B C at which demi-circle we must draw lines to the Center A from all the divisions of the square of the first Plane which will give G E F G H I K which will divide this Arch B C into eight parts And from the section O we must raise Perpendicules and observe that they shall divide justly at the point where we must place the steps or degrees which we shall have made as for example the step I shall be divided by the Perpendicule elevated from its point upon the demi-round as we see in A the other step after which is the second shall be divided by the Perpendicular of the point which K shall have made at the demi-round and so of all the others The rest which is in the figure as the doors and the windows shall be made according to the foregoing Orders Of Columns or Pillars in Perspective THat which we are speaking of is not only for the Cube but it ought also to serve for all that we would make round For example if from the square A you would elevate a round peice you must make a round within this square according to the ordinary Orders and at the height which one would give to this piece to make also another square and a round within as is B. For to know to give the 2 lines D E which make the thickness or the Diameter of the round We must take notice where the round divideth the Diagonal of the square and to hold for a general maxime that it ought always to be taken at the round pieces seen from the side as it is in the figure C that the Perpendicules are elevated from the section of the round upon the Diagonal of the square at the points D E For the pieces viewed by the Front as the figure F they ought always to possess the Demy-round G H I and to elevate the Perpendicules of the Diameter right G H and from the one and the other as well on Front as on Side we must elevate a line from the Center which shall serve to give the Diminutions to the Columns For these three pieces below besides that they serve to make the others seen clearly and with their shadows they serve also for to shew how we must proceed for the Columns This piece of the midst K is exactly round without ornament nor intent to make any there The second marked L causeth to be seen that when we desire to make a base there we ought upon the square which must serve for a Plinthe whereof M N is the upper part to make a double round whereof the distance from one to the other may be the Projector of the base and the round from within the plane of the shaft of the Column from which they shall raise the Perpendicules The third marked O is a Column with its Ornaments which every one may make at his pleasure and we must take notice that the uppermost square of the Capital answer to the Plinthe or top of the basie Of Cornishes and Mouldings in Perspective IN pursuit of Columns which are the principal Ornament of Architecture we will set the Cornishes or Mouldings with their Projectors which we have not set hitherto for fear of giving confusion to the Elevations which it behoveth to be understood with clearness and easiness It is true that there are not many Buildings made which have not some few Mouldings and Projector for their Ornament for to make them more pleasing to the eye where-I thought fit to set here the manner not of framing them seeing that dependeth on the pleasure of every one nor to give them their Measures and Projectors for that were to oblige my self to sit down here the Orders of Architecture and a thousand other Inventions of Ornaments which one may finde elsewhere and which I suppose are known But only to set them into Perspective according to the Orders following when any shall have occasion for such an Order For to set then the Ornaments for a Pilaster in Perspective we must take the Measures upon the middle line of some other with
drawn right as is the door N. For the Openings of Windows in Perspective ALL the difference that there is in the openings of windows from those of the doors is that the doors have the demi-round of their opening upon the Plane and the windows have it in the Air by reason that the windows make their Openings being elevated from the Ground and the doors do grate upon it wherefore we must make this demi-round above or below the windows and within this demi-round to take the point for to open them For example if the side of the window hath 2 small squares of bredth as A B and that one give it its whole opening it will take up two more squares C A whereof A is the middle and the center of the demi-circle A B C. But by reason that the windows are elevated from the Ground the demi-round also must be elevated as they are here above the windows from the corners D and E which are the centers of these demi-rounds which shall be easily framed raising Perpendiculars from the squares which are between C and B until that they divide the Rays which pass by the corners of the windows D E. And from these sections you must draw to the base and give them the measures of the little squares of the plane 1 2 3. from which points 1 2 3. on high you must draw lines to the point of sight F which shall divide the Parallels of points and frame the little squares for to make the rounds of the openings which shall be taken in the same manner as at the doors as if one give within the highest demi-round the point G for the point of the opening from this point G you must draw 2 lines the one which falleth plumbe G H the other which passeth by the corner of the window E for to divide the Horizon where it can which is here the point I from this point I you must also a line by the corner of the window K until that it divide the line plumb at the point H which shall give the window open K E G H we must do the same of all the others and take the point within the Horizon as L is the point for the window M and N is that of the window O. The window P hath none being Parallel to the Horizon The windows which are opposite are made by the same method without the confusion of lines the one and the other are equal with the wall for to facilitate the ordering thereof The door at the bottom is made as we have said and the window followeth the Method of these For the Opening of the windows with Chamfrettings THE Order of this is as the others upon the side of the wall except that these cannot be opened wholly by reason of the thickness of the Chamfring which causeth that the whole demi-circle is not allowed but as much as the opening can have of it They ought always to take their point within the Horizon as we see Q and R for the opening of the windows on high that below is Parallel to the Horizon Of divers other Openings THE Openings of Cupboards and of Chests are at least as Necessary as those of Doores and Windows and the fault would not be less to forget these then not to set down those Let us see the Order in these two Figures The Cup-boards A are opened according to the Orders of the Windows and it would be loss of time to busie Ones-self in repeating them here we are to observe only that one height is Parallel to the Horizon and the other below draweth to the point of distance B. This Manner of Shop which is on the other side hath its Opening with two Shuts whereof one is lifted on high and the other cometh down below and each maketh its demi-round from the Center C and D which one maketh with the Compasses then we may take the Openings where we will as here at the point E from which we draw a Ray to the point of sight F untill we divide the demi-rounds of the other end at the point G from which points E G we must draw to the Centers C D for to have the Shuts which close up the Shop as we see In the figure below there are 3 Chests opened several ways for to open the first H I have made the quarter of a round M in Perspective following the Measure of the little squares of the Plane keeping the bredth of the Chest as this is of 2 little squares from which we must raise Perpendiculars and thereof frame the half or quarter of a Round for the opening which we may take at pleasure as here the point N from which we must draw a Parallel unto the other quarter of the round O and from these 2 points N O to draw to the Center P If we would open it wider we must make a demi-round instead of a quarter The Chest I is the most easie of all the Openings for having taken the bredth of the Chest Q R we must from the center R make with the Compasses the demi-round Q S. Then to take what opening you will as T and to draw a Ray to the point of sight V which shall divide the other demi-round at the point X and from these 2 points T X to the corners R. He that would open them further hath but to set the point of the opening higher within the demi-rounds as Y is to the Coffer K All the rest is ordered like as in the Coffer I as one may see Of planes and the first elevations of moveables I Had set these planes in their order among the others had there not been one consideration which made me defer them until now which is that if I had handled them in the beginning without making known the necessity thereof they would have been also too soon forgot and held as unuseful they are now more seasonable and without doubt they will be well received pleasing and learned with pleasure seeing there are not only moveables nor peices of houshold-stuff which depend not thereon The first plane A serveth for Beds Tables Chairs Stools low Stools c. The other B which beareth in length two times its breadth serveth for long Tables Cabinet Court Cup-boards Coffers Trunks The third C which is long and narrow serveth for Benches or Forms and other things which have need of six Feet or Pillars as great Tables and Cup-boards The knowledge that one hath of other planes will give the facility of making these seeing there is nothing but to set their measures upon the base to draw them to the point of sight and to abridge them by the points of distances For example for the plane A you must set upon the base these two measures D E and draw them to the point of sight F then from one of the distances you must draw to one of these measures as here E to the distance G and where that shall divide
the Rayes at the points H I you must draw parallels for to frame the 4 little squares which one may make to be for as much or as little as he will Because for a Table they must be of more bigness then for a settle or stool that is to say that they must have more breadth for if for this we allow 2 inches for that there must be four The plane B is made of the same manner except that by reason of its length which is the double of the breadth we must draw from the point B to one of the distances for to find the half K for if one should draw from the point L he would divide at the point M which would be the whole square and we would have but the half Wherefore from the point K we must draw parallels to the sections of the Ray and from the corner L we shall divide also the Ray for the first squares at the point N. The other plane C hath no need of explication for we see well that it is made as that A and that you must double the square for to have 6 little squares We see at the figure below that from all the Angles of these squares you must raise Perpendiculars for to begin to give the frame to the pieces that we shall make hereafter Of the Elevation of Moveables HAving raised the Perpendiculars of the Plane as aforesaid we must in some Place of the Picture make the line of Elevation upon the which we shall set the cross-lines or Travers and the height that one would give them For example the line C D shall be the line of Elevation and C E and D F shall be the bredths for the Travers from all these four points we must draw in some place within the Horizon as here at the point G. Then having from the Planes A B raised the Perpendiculars from all the Angles we must from the same Angles draw Parallels to the base unto the Ray C G which is the bottom of the line of Elevation which will give the points 1 2 3 4. which we must raise into Perpendiculars and the sections which these Perpendiculars shall make at the Ray C E D F shall be the points to divide the Perpendiculars of the Planes whither we carry them with the Compasses or that we divide them with Parallels as we see in the Figure That drawing a Parallel from the point E we shall divide the first Perpendicules of the Planes A B at the points O from which drawing to the point of sight H we shall divide the other Perpendiculars of the Planes at the points P and doing the same from the point F we shall frame a Cube pierced round on all sides or composed of square pieces the which being well understood we shall easily make all the Pieces following and whatsoever other may be It is easie to see that the two frames or feet of the Tables I and K are made by the same Order that those above A B they having no difference but in the Barre below which is more elevated in the line of Elevation at the point L which giveth the Barre M and that which is under may be made into Bowles or to leave the feet square as they are For the latter frame N and Q there is no more then in I and K except that they are seen by the Angle and the others are seen in front the Planes of these I and K draw to the point of sight R and these draw to the distances S T. These Figures shews the ordering of all Pieces of Houshold-stuffe for example if of the Figures I or K we would make a bed there is nothing but to give to it its bredth and height for it is the same Order in all the rest and if one would make a low stool or flat base for a Table there is nothing but to make that above for a stool besides that above we must give it more height then bredth but all the rest is ordered in the same manner For to make the upper part of Tables Stools c. HAving raised the Perpendicules from the plane as we have spoken and given the height that we would they should have we shall have the frame for to make there an upper part wholly by the line and which passeth not the frame we have only to leave the upper part of the cube without marking any thing there and this shall be the uppermost be it of a Table Stools low-stools c. But if one would that the upper part should have any Projector or Border we must from one of the corners of the Frame or foot of the Table draw a little parallel as A B and upon this parallel set th' measure of the Projector one would give it as we have set here A B. Then from the distances C and D we must from the corners of the square made of points which is the breadth of the Frame or feet of the Table draw small occult lines as are A E. Now for to know how this measure A B shall give in Perspective the breadth equal to all the sides and corners of the Table We must from the point of sight F draw a Ray passing by the point B and continue it until that it divide the line C A E which shall be at the point G from this point G we must make a parallel which shall divide the other occult line at the point H. Then drawing from the points G H to the point of sight F we shall divide the other lines Diagonal of the corners at the points L and K and then we shall have the upper part of the Table with the Projector which we have given to the line A B. For the thickness of this upper part we may give it at pleasure This order may serve for to make the upper parts in all whatsoever we would whether they be above or below the Horizon whether they be on the front or sides In short they make them all after the same manner For to Elevate a Court-Cupboard and Cabinet HAving made the Plane and Elevated Perpendiculars from all the Angles as we have said we shall set upon the line A B which shall serve here for the line of Elevation the Measures that we will give as well to the distance of the boards as in their thickness as are C D E from the which points C D E we must draw Parallels to the Base unto the other Ascent or Column F G. Then from the points which shall be marked upon this Ascent G F we must draw Rays to the point of sight H unto the other Ascent of the Hollow I K. This Hollow is given at pleasure setting upon the base that which we will give it for example for to have the hollow or bredth of this Cupboard I have set the Measure F L from this point L we must draw to the distance M and where the Ray F H shall be divided
at the point L that shall be the place of the last Ascent The Cup-board which is over against on the other side is ordered in the same manner and for to finde the Measure of this little Cabinet which is in the midst bore up by two little Columns we must take the points L P which are in the midst of Q N and the bredth of the little Cabinet and draw them to the distance O and where the Ray N H shall be divided we must draw Parallels to the base which shall divide the Ray T H at the point V from which raising Perpendiculars we shall have for the little Cabinet of the middle The great Cabinet of the second figure are of the same Order with the Court Cup-boards above There is none but that of the midst which is at the bottom which we must a little explain by reason that it is of the front and that one might be in some trouble for to determine its hollow I say then we must frame its Plane as we have said heretofore and as we see it finished in the half for to give it the Traverses equal to the first in the fore-part we must from the first Ascent R draw occult Rays to the first Perpendicular of the hollow S and there to make little sections from which we must draw little Paralels to the base and we shall have that we desire For the Elevations of Chairs FOR to elevate a Chair you must of the Measures A B C make a Plane by the ordinary Rules and from the Angles of this Plane elevate Perpendicules and follow the same Method that we have given speaking of the feet of the Table or of the frames for windows without the upper part there is nothing more in this then the Back of the Chair which one may make of such an height as they will here it is the height of A unto the seat K and this height is as well for the single Chairs as for those with Rests to lean on We see sufficiently by the Figure that for to make them with backs we must only prolong the Perpendicules of the Ascents on the side that we would make it as is here the first A E and from the point E drawing to the point of sight G. We shall divide where it ought the Ascent elevated from the Plane or from the foot H which shall be the point F. The rest is clear enough by the Figure When we would have Rests there we need only to prolong the Ascents before as they have made these behind for the back Then to make there a Barr which serveth for a Rest as is L M. In the second Figure below you see a Form or a Bench garnished with carving and two little Couches to rest in whereof one hath the back turned on this side and the other view'd obliquely It would be to lose the time to instruct how to make them seeing that the Order to elevate them is the fame with the foregoing which we have given for the Moveables which is that having made the Plane we must elevate Perpendiculars c. One other fashions of Moveables in Perspective CErtain moveables which close themselves Those which they make to serve for Seats Tables and Beds c. are very easie to set into Perspective We must only make the elevation as if for a Cube as is A B C D or E F G H. Then to make there two Diagonals A C and B D for that of the midst of the Front or E H and F G for that of the side which shall serve to bring in the 2 crosses to take notice that there be an half which entreth within the other as G K do pass within H I and the one and the other are fastned by the midst for to make them bend In this piece which is below I have made a Table upon Tressels that we may have the smallest moveables for to set them into Perspective We must from the measures A B which is the interval for the Feet of the Tressels draw to the point of sight C Then having set upon the base the thickness of the same Feet as are D and E we must draw them to the point of distance F and observe where we shall divide the Ray B C for to draw little parallels to the base which shall give the little squares or the planes of the Feet as we see in A B between this distance D and E we must set the breadth which we will give to the top of the Tressel and draw it to the distance F which shall divide the Ray B C at the points G H from the which points G H we must elevate 2 Perpendiculars to such an height as we would have as here at the point I. Then from the Angles of the small squares of the plane to draw lines bending unto the piece I. The second Tressel is ordered all alike with the first The form K nor the Table or high Stool L have no need of Explication nor Instruction for to set them into order seeing that they have nothing which is not common to them with the fore-said pieces Of Moveables set without Order WHen the moveables are set in order along by the Wall or according to the Rays and the base it is easie to set them into Perspective by the Rules that we have given but supposing that one set them by chance and without order as these are we must do as I shall say You must make the Geometrical plane R S T for the plane of three Chairs which you must abridge by the Order that we have set at the irregular figure Fol 40. and the planes shall remain turned as are the Chairs or rather the Chairs turned as are the planes I say then that having set these planes into Perspective as it is taught you must set the Rule along by one of the sides for to see what accidental point you shall have within the Horizon For example having set the Rule along by the side A B I shall have within the Horizon the point C for the accidental point at which we ought to draw all the lines of this side and of that which is opposite to it as we see that A and D draw to the same point C It is true that every plane set irregularly must have 2 But they meet sometime so far within the Horizon that it is a hazard when one can find them both together These have each one within the Horizon as A B giveth C. A D which is the other side should give another point but our paper is not long enough E F giveth G And H I giveth K for these small squares 1.2.3.4 they are the plains of the Feet of these Chairs which one may make more large or more streight at the pleasure of the Artist Now from these planes you must elevate Perpendicules from all the Angles and set on the side a line of elevation M N upon the which
only a third of the bredth for the descent as is A 9 B Before we pass any farther we must know that which I call the middle Top are Pieces elevated Perpendicularly upon the Beams which bear the Ridg where all the rafters do meet as is G H The rafters are pieces of wood that give the descent of the Roof as is H I. The other Pieces which are set in the corner and which go unto the middle Top are called Stays and are ordinarily longer then the Rafters as is H K. Three sorts of Roofs are in use Pavilions Pynions and Appentis or Pent-house like The Pavillions have four sides the Pinions have but two and the Appentis but one for to make a Pavillion in Perspective we must know the place of the Balls or middle tops for to draw the stays thither the which hath made me make this Geometrical Plane L M N O for to shew that of the bredth of the house L N we must make a square L M N P from which we shall draw two Diagonals which shall divide themselves at the point Q some set the Ball at this point Q but that is too much advanced and maketh this bending of the end lie too flat it hath more comeliness when it is straighter wherefore we must advance it towards the wall L N by the third part of the distance Q R which shall be the point S and by this point S we must draw a Perpendicule upon the line N P which shall be T. Then to transport these Measures L T and T M upon the base and draw them to the point of distance which is here farther off then ordinary and to observe where they shall divide the Ray V and from the sections to elevate Perpendicules unto the height of the wall which shall give the points X from which me must draw Parallels to the base unto the other Ray I. Then from the midst of the wall Y to draw to the point of sight for to divide those Parallels at the point Z and from these points to elevate the Balls for to give the height to these Balls we must know wherewith we would cover them and according to that to give them the Measure that we have spoken of supposing that it be of Slates we must of the bredth of the wall make a Triangle equilateral 1 2 3. And from the point 3 to draw to the point of sight and to divide the Ball at the point 4. At which point 4 we must draw lines from the corners of the House which will give the shape to the Pavillion For the Roofs with Pinions there is not so much to order we must only of the bredth of the wall 5 6 make a Triangle equilateral 5 6 7. and as much on the other end of the wall which shall give the point 8. Then to joyn this 7 and 8 the Roof will have its shape and its measure The Figures on the other side do shew the same thing without being confused with lines This projecting which goeth beyond the Roof is made according as one will This House on the Floor is covered with a Pavillion which is made by the same Orders as that on the side In this Figure where are the Letters I have set the Horizon on very high for to make the upper part of the houses to be seen and to give the more easiness to understand the Order but as this is seldom met with I have set the other Figure above where the Horizon is low as it is ordinarily which nevertheless is not therefore any other Rule for to make the Roof then that below as one may see by the Figure The rest of the Roofs in Perspective IN the figure aforegoing we have set the Roofs with small Pinacles view'd in front to which we must give the Triangle equilateral for their height when we do make them of slate If they make them of other things as of Tile or Thatch we must take their measures at the little figure below For to set this fashion of Roofs in return we must set upon the base from the foundation of the house the breadth that it hath as is A B and of this breadth to frame a Triangle according to the height that we would give to the Roof as to this which hath a Triangle equilateral whereof C D is the height which must be set Perpendicularly at the first corner of the house at the whole height of the Wall as is E F. Then to take the breadth of the house C which is the midst of A B and to draw it to the distance and where it shall divide the Ray A at the point G to raise a Perpendicule then you must from the point F draw to the point of sight X and the section that shall be made of the Perpendicule H shall be the point of the Pinacle to which you must draw from the corners of the house E I if one would have there any advancings he may set them there at his pleasure as we may see on the other side K. For the sloping we must only prolong the line where one would set the top of the Roof as is here the line L M and to give it such a bending as we would To this there is as much of the height M N as the house hath of breadth N O if from the points M O we draw to the point of sight X we shall divide the Perpendicule of the Hollow at the point P Q. which we must joyn with a right line which shall finish the framing of the Roof The figures of the other side make the house covered to be seen after these fashions The figures above are only to make it seen that we must always keep the same order although the Horizons change I have set a Church within the floor which is covered with Pinacles and the wings of the two bendings which have only the simple draught There is also a Pavillion seen by one end of which we have spoken in the figure preceeding For to set a street into Perspective IT might suffice to see the figure for to know the order thereby which is very easie we must only make a plane of single little squares by the ordinary way and to take one square or 2 or 3 for the bredth or length of every house And upon this breadth which we shall take to set the measures of the Doors and Windows for to have thereby the abridgement by drawing to the point of distance A as are the Measures B C D E and F. The first Angle of every house may serve for the line of elevation as we at the first house the Angle G for the Roofs we have said already how they ought to be set When we would have streets going a cross we need only to leave 1. 2. or 3 little squares without elevating any thing even as are H and I. The figure below is to shew that when one would advance or
have each three squares on every side and the squares that remain shall serve for the Alleys C. He that would make some Compartment within the squares of the Garden he must use the little squares of each square dividing them and giving them such a figure as he would have so as we may see the little square A B and on the other side D E the hedge-Rows and Arbors are placed opposite to each other and of the bredth of the Alleys The little Squares with Borders WHEN one would set Borders to the squares he must set at the corner the heights and bredths that he would give them And from these Measures to draw to the point of sight I. For example in the figure below F G is the height and bredth of the Borders of the little square H from the corners of this little square F G we must draw to the point of sight I and do all the rest as it hath been said several times For the Arboâ—s we must from the Angles of the squares of the Alley elevate the Ascents or Perpendiculars O. All the rest is done as in the Arches view'd by the side fol. 60. The little wood which is at bottom is made by elevating Perpendiculars from all the Angles of a Pavement of little squares c. For to elevate and set in Perspective Fortifications I Will not repeat here the Order of Abridging and setting the Planes of all sorts of Fortifications in Perspective that which we have spoken thereof fol. 39. is plain enough For to elevate them there is no more difficulty then in one single wall but there needs more time by reason of the multitude of Angles which we must always bring to the line of Elevation for to take there the heights that they ought to have so as we have said elsewhere many times speaking of other Works The little line of elevation is divided into four Parts I he first from 1 unto 2 is the height of the Parapet of the way covered from 2 unto 3 is the height of the Rampart from 3 unto 4 is the height of the Parapet of the Rampart And from 5 unto 1 is the depth of the Trench For to make the designs of Perspective THere is not so excellent a Master which hath not some design in such pieces as he would willingly attain to If this be ordinary almost in all sciences it is necessary in this more then in any other by the great substitution of points and of lines which we must therein exactly observe and without which nothing can be done which may content those that have any understanding therein Seeing that one is obliged in some manner to make designs we must search out that which may help to make them exactly that may be possible and as every one knoweth that all the length of these works is to draw lines parallel and Perpendiculars having then searched the Invention as well by experience as in the Authours to be able to make them readily I have found nothing which can help us in that but the board and the square which Viator hath left us in his Works All those that would pass the time in designing ought to have one from the which they shall draw the delight and benefit which experience will make them to understand Although that the Figure giveth sufficient understanding how it ought to be and the manner of using it I did believe that I ought to give a more clear understanding thereof This Plank or Board A B C D ought to be perfectly by the rule or square of a Foot and half long of fifteen inches broad and half an inch thick that the Wood be good very dry and well united one may past a sheet of Paper on it for to make it more smooth and to help the Pen. The square E F is a Rule of a foot and half long as the board an inch broad and of thickness 2 lines which is helved at the right Angle within another frame of a Rule G H eight inches long one inch broad and three quarters of an inch thick for to draw lines they hold this latter Rule G H closed against the board A B C D and the other Rule E F is assuredly strait if so be the board and the Rule be well ordered When one would work we must fasten the leaf of Paper I K L M upon the board with 4 little bits of Wax N O P Q and then from one only point you may draw lines with assuredness that they will be right And when you would have Perpendiculars set the handle of the Rule G H on the side C D the Rule E F shall be Perpendicular to C D. For my part I find that this easeth exceedingly and that without this invention you must always have the hand at the Compass There is no further need of substitution but for the visual Rays and there are also those that use a Rule pierced at one end which they fasten with a Needle to the point of sight but this is too much intangling I would not counsel any to use it one may as soon do it with the common Rule and so is not in danger to spoil any thing R. Is the common Rule T. A common Compass V. Another Compass which beareth the Ink for to make circular Lines See here are all the Instruments that one hath need of for to make the designs of Perspective For to draw little Perspectives into great and great into little SEeing that designs are made in small with more facility then in great it is credible that they will be made therein always the which hath made me resolve to give the Method of setting small designs into great upon Cloth The Painters use ordinarily Squares or Checquers that is to say that they divide the small designes and the clothes where they must be painted into the same number of squares and set proportionally that which is within one square of the design into the square of the Cloth which answereth to it some do like well of this Order But here is another which in my judgement is more easie more facile and more assured we must have a skale proportionate to the less design and another skale proportionate to the bigger When one would make a design the first thing that he resolveth on is the skale which must give all the Measures of all the other pieces of the design For example in the less design A the skale B C of five little parts which one may take for feet Royal hath been made the first upon this skale they have taken the Horizon the height and distance of the Trees the bredth of the Alleys c. For to fet this small into great observe how we must proceed First we must know if the Perspective must have the natural Horizon that is to say that the bottom of the Picture being on the Ground the Horizontal line be at the height of our eye which is
A C and draw from C to E and where this line should divide A G at the point H we shall draw H I which will appear of 24 feet of sinking in the picture According to the Perspective this line H I is equal to that A G and containeth as many feet or parts so that if one draw from the point I to the point E the section of this line I E at the Ray A G shall be for to draw a line K L sunk of 48 feet If from this we draw further to the distance E we shall have the section of the Ray A G yet a line removed 24 feet more then the others And if one would have a line sunk 30 feet we must from the point A reckon 6 small parts and from the sixth draw to the point of sight G and take notice where we shall divide the line H I as here at the point M. Then from the point M to draw to the distance E and this line M E shall divide the Ray A G where we must draw this line N if it were of 40. We should from A reckon 16 and do all the same if it were 60 we should from A reckon 12 and from 12 draw to the point of sight G unto the line K L which should be the point O Then from O to draw to the distance E and from the section of the Ray A G shall be for to draw this line For the second figure BY that which I have spoken it is easie to find a point for such a sinking as one would have There remaineth to shew how we may find it within or without the Ray A G or B C for this the line B C shall serve as a scale of six feet the one of which I shall divide into twelve inches that I may there find the half the third and the 4th of a foot All being thus ordered If one require of me a point which appeareth of 17 feet long and of a foot and half within the Ray A G. I will draw from the 17th part of the base to the point of distance E and where the Ray A G shall be divided in P I will draw a line P Q now when one requireth a foot and half within the Ray A G I will take with a Compass upon the same line P Q but on the side B C a foot 6 inches which I will carry from P unto R. And this point R shall be the point which hath been demanded And if one would have one yet at 29 feet distance within the Picture and seven and an half beyond the Ray A G. We must draw from C to the point E. and where it shall divide A G to draw a line which shall be of 24 feet then from A. taking five little parts to draw them to the point of sight G until that we divide this line at the point S and from this point S to draw to the d stance E Where the Ray A G shall be divided we must draw a line T V seeing they require 7 feet and an half beyond the Ray A we must upon the same line T V but on the side B C take 7 parts and 6 inches with a Compaâ—s and carry them from the point T. to the point X And this point X shall be the point that one desireth And so of all others at such a distance and removal as one would have Of a general manner for to exercise Perspective without setting the Point of distance out of the Picture or Field of the Work by the Sieur G D L. THIS Order obligeth us to make a Geometrical Plane or at least a device of Measures as well for thâ— Plane as for the Elevation that by the one or by the other it may be brought to set into Perspective I will take for the object or subject the same Example of the Author which is a Cage squared covered with a Point or a Building covered like a Pavillion or Tent to the which we shall give the Measures by the means of a Scale Having then made the plane of this Cage m i l k which I have set on the top of the figure it must be thâ— at such a distance as one wâ—uâ—d have that the Objâ—ct seeme recoyld within the Picture as it is here of 17 feet we makâ— a line a b which shall be the base or the bottom of the Picture which we shall place according to the aspect thâ—â— the object ought to be seen Then from the two ends of this line a b we must draw two lines Parallels the oâ— to the other and undeterminate thrt is to say it is no matter if they divide the plane nor in what place â— are a g b g upon the one of these lines as here this a g we must make little Parallels to the line a b which maâ— go unto the Angles of the plane and by the means of the scale to see how far each Angle of the plane shall be râ—moved from this line a g. the which shall be marked near to each line Now from the place which one shâ— choose for to view the Picture which is here the point c at five feet near to b. We must make a Perpendicular 〈◊〉 a b which shall be the line c t to this line c t we must give as many little parts of the scale as we would have 〈◊〉 be removed for to view the Picture which is for this 24 feet and at the end of these 24 feet which is the poinâ— t to raise a small Perpendicule of the height of the eye which shall be the line c t of four feet and an half The Cloth the Wall or the Paper being ordered for to set the plane in perspective and upon the planeâ— make the Elevation We must divide the bottom of the picture or the base A B into as many parts as that a bâ—â— the plane this having 12 thereof We must divide the great A B into 12 which will be of value each a fooâ— Above the points A B we must set the height of the line s t which is of four feet and an half Take then with thâ— Compasses four parts and an half of those which are upon the line A B and carry them perpendicularly upoâ— the points A B which shall give the points E F and draw the line E F parallel to A B and this line shall bâ— the Horizon Seeing that in the plane the point C which is the place for to view the Picture is removed â—iâ— parts from b we must reckon as many parts from B and from the fifth C Elevate a Perpendicule to A B which shâ— divide the Horizon at the point G which shall be the point of sight to which we must draw the Rays A G B G which shall represent the Parallels of the pâ—ane a g b g for the point of distance it shall be the point F and by reason that the line c t hath 24 feet
the second to retract that which one hath done there and in this we design but once and as exactly as the other I will not set down the framing of this instrument it having no difference from that which I have now given but only that instead of a leaf of Glass we must set there a frame divided by little squares with threads very slender as the figure sheweth it the which I shall call a Lettice for the number of the squares I leave that to the discretion of every one I shall say only that we must not make them too great for to work more exactly nor too little for fear of being confused For the order there is need that this piece H be placed in such manner that one may see by the hole of the spectacle I all that we would design if the design which we desire to make must be greater then the frame or then the Lettice is or as others will the Checker-board we must make the squares of linnen-Cloth or of Paper greater then that of the frame and if it be lesser we must make the squares lesser but we must always make squares for to carry in each square of its paper or of the Cloth that which we shall see within the squares of the frame looking upon it by the spectacle I and if all shall be represented proportionably the design will be as just for the Perspective as if one had used Rules and the Compass I have set the two figures for to cause to be seen how this piece H must be placed for to use it in designing upon a Table and when one would paint by the one and the other manner we may make more exactly all sorts of Perspectives counterfeit Pictures and draw to the life I doubt not but many will say that this method is not new and that there is not a Painter that knoweth not how to enlarge and diminish Pictures using this Checker-board that is true but I beleive that not any one hath ever used the spectacle which is the secret for to make every thing in its perfection MEASURES AND PROPORTIONS OF FIGURES IN PERSPECTIVES PICTURES AND VVORKS EMBOSSED For Figures in Perspective AFter that we have set down that which may serve for to make all sorts of Perspectives with the means to give them a pleasing and ornaments for to content the eye there remaineth no more but to find out a way for to deceive it altogether which is to set down the figures there But before we pass any further we must make a distinction of figures for it is another thing to represent a History then to intend to deceive the eye in a peice which shall be set at the bottom of a Gallery of a Hall or of an Alley in a Garden for to these all figures of repose or resting are the best and for a History they must be all lively and spirited by the diversity of their posture The multitude of Horizons which the Painters take in their Pictures is the cause that they make an infinite company of Faults there by not knowing to give the height that they ought to the figures proportionable to their Horizon I will give them a Rule that they may not fail there whatsoever Horizon they shall have For the Fig re having the Eye within the Horizon IN the Perspectives which are set at the end of a Gallery of an Alley of an Hall or of any other place for to deceive the sight we must always set the Horizon at the natural height that is to say at 5 Feet Royal which are the height of the common size He that would set there figures for to appear in the natural they ought to have the eye within the Horizon for if the Figures have the eyes within the Horizon as we have they will appear to us of our height this ought to suffice for the instruction but for to be more clear and to make my self better understood I shall make use of these three figures instead of many others which one may set there if he will The first Figure A shall have the natural height and the eyes within the Horizon if I should yet have ano h r Figure at the place B I must from the point B raise a line unto the Horizon and that shall appear of the same height with the first He that would have a third at C let him always set the eyes thereof within the Horizon it shall be of the height of the others within the appearance In short although there should be a thousand there is no other Rule to be kept when the Horizon is at the natural height I intend not to speak of Children which oughr to be made in proportion to the great figures and according to the discretion of the Painters For the Figures having the Horizon below WHen Pictures are made for Halls where ordinarily they hang them and place them somwhat high we must take the Horizon lower for to approach to the eye as far as shall be possible Now for to give justly and with proportion the height to each Figures in what place soever we meet with them we must make one at what height we would in some place of the picture as is the figure D E which is here that which we have cal'd the line of elevation in the proceeding orders For to find the height of other Figures which one would set into this picture which should appear as high as the first D E we must from the Feet of this F and from the top of its head D draw lines where we will within the Horizon as is the point E and between this Triangle D E F shall be found all the heights of the others For example if I would find the height that the Figure must have of the point G from this point G I draw a parallel to the base G H untill that it divide the line F E which shall be at the point H from which I raise a Perpendicule until that it divide the line or Ray D E at the point I and this Perpendicule H I is the height of the Figure which we must take with a Compass for to carry it to the point G if I would have another at the point K I have only to make the same operations and I shall have the Perpendicule M N for its height and so of as many as one will For the Figures having the Horizon high WHEN the Horizon is high as one is sometimes obliged to set it for it represents sometimes which one hath viewed from an high eminent place we must keep the same Rule with the Precedent although it seem the contrary in that of the Horizon below all the Figures are above the first and go always by diminishing And for this of the Horizon high all the Figures raise themselves above the first and the furthest distant is always the most elevated but nevertheless the lesser in proportion and according to the
Point and frame it into a Pyramide whereof the Sun is the Base This truth is shewed in the Ecliepse of the Moon which is seldom wholly Covered with the shadow of the earth which nevertheless exceedeth it in greatness forty times by reason that the Sun which is the body full of light is an hundred sixty six times and more greater then the Earth which it enlightneth more then the half and by consequencee causeth to give a shadow to it in a point The second having the body of light F G equal in greatness to the enlightned H I it enlightneth the half of the Object and giveth its shadow parallel H I K L. The third maketh appear that the lightsome body or the light M being less then that which is enlightned N O is not enlightned by the half the which causeth a shadow unto it N O P Q which enlargeth it self according as it is removed from the object and maketh a Pyramide whereof the light is the point Of the difference of Shadows BY that which I have spoken in the Leaf aforegoing we must conclude that one and the same Object may give divers shapes of shadows or projections although that it be enlightned of the same side by reason that the Sun giveth it of one fashion the Torch of another and the Day doth not frame it The Sun rendreth always the shadow equal to the object that is to say by parallel as the first figure sheweth it I shall teach in the Leaves following how we ought to use this method and to give to every object the natural shadow which the Sun would cause it to have All Painters Gravers and others may if they please observe these Rules when they would make any thing pleasing and not to take the Rule of the Candle or Torch for this as divers have done The shadow of the Torch is not given by parallels but by Rays which issue from the same Center that which causeth the shadow is never equal to the body but more large and is greater always according as it is removed the which may be seen in the second figure where the shadow is larger then in the first although that the Cubes of the one and the other be of equal breadth and height See then how one should be much deceived if one should make the shadow of a Torch like as that of the Sun and of the Sun as that of the Candle seeing that the difference is so notable There is a third sort of shadow which is neither of the Sun nor of a Torch but only caused by a fair Day the which having not strength enough for to frame the figure rendreth only a confused blackness at the object as in the third figure Now this hath no Rule wherefore every one giveth it and practiceth it according to his fancy All these shadows as well of the Sun as of the Torch and of the Day ought to be more dark then the parts of the objects which are not enlightned as A it not so dark as B by reason that A receiveth the reflection of the clearness which is about it and B hath not the reflection that A which is in obscurity We must observe also that the part of the shadow most distant from the object is also more dark then the part nearer as G is darker then H by reason that A cannot communicate that little reflection which it receiveth unto G as it doth to H. 1. Figure 2. Figure 3. Figure For to finde the shape of the Shadows WE shall observe at the beginning of this Book that the Definition of Perspective is to give upon a Plane perpendicular to the Horizon the Representation of Objects which are upon the Ground or upon a Plane Horizontal And for shadows it is altogether contrary seeing that one supposeth a Body elevated upon the Plane the which being enlightned casteth its shadow upon the same Plane as we see that the Body A giveth upon the Plane the shadow B for to finde the shadows we must suppose two things the Light and a Body The Light although it be contrary to it it is that nevertheless which giveth it its Being and the Body or the Object giveth it its shape and its figure I shall not discourse here but of shadows for I suppose that we have learned to set the Bodies or Objects into Perspective For to understand these shadows more easily and render the Orders following more easie we must mark that we must make use of two points the one of the foot of the light which ought always to be taken upon the Plane where the Object is placed and the other of the Torch or lightsom Body seeing that the Rule is general for the Sun and for the Torch with this only difference that the shadow of the Sun is given by Parallel and that of the Torch by the Ray of the same Center We will begin with that of the Torch seeing that it will help the better to comprehend that of the Sun which shall follow We say then for example That if one would have the shadow of the Cube A as we see B that we must from the point O foot of the light draw lines by all the Angles of the Plane of the Object as here by the plane of the Cube O D O E O F O G Then you must draw other lines from the point of the light of the Torch by all the same Angles elevated and to continue these lines until that they divide the other lines drawn from the point O for example having from the point O drawn the line passing by the Angle of the Plane D if one draw from the point C a line passing by the same Angle elevated this shall divide the other at the point H and the point H shall be the shadow of this Angle If from the point C we do the same by all the Angles elevated we shall divide the lines of the Plane at the points H I K L the which points we must joyn with right lines and we shall have the shadow of the Cube as is to be seen at the Figure above and more clearly at that below Of Shadows taken from the Sun THE Sun that glorious lightsom body being far greater then the whole Globe of the Earth as I have already said in the beginning of this Treatise should make all its shadows in point seeing that he doth always enlighten more then the half In pursuit of this demonstration we should conclude that all the shadows of the Sun ought to be less then the Body that is opposed unto it and to diminish as it removeth it self far off which would be true if there were any correspondency of the Body enlightned to the Body enlightning but all the Objects which are upon Earth are so small a thing in respect of this great light that the diminution of their shadows is unperceivable by our eyes which acknowledged them all equal that is to say that they are
neither larger nor streighter then the Bodies that give them their shape for this reason we give all the shadows caused by the Sun by Parallels as we have seen at the second Figure of this Treatise It followeth from all this discourse that for to have the shadow of what body soever it be being opposed to the Sun we must draw a line from above this great light which may fall plumb at the place where one would take the foot of the light and from this place to draw an occult line by one of the Angles of the Plane of the Object and another of the Sun by the same Angle elevated and the section of these two lines shall shew how far the shadow must go all the other lines shall be drawn Parallel unto these For example for to take the shadow of the Cube A the Sun being at B we must from under the Sun C which is as the foot of the light draw a line which toucheth an Angle of the Plane as C D. Then from the oâ—her Angles E to draw Parallels to this for to finde the end of the shadow we must draw a line from the Sun B passing by the Angle elevated F which shall divide the line C D in G. Then drawing a Parallel to this by the Angle H it will divide the line E at the point I and we shall have the shadow of the Cube D G L. He that would cause the shadows to cast before or in any other way he must determine the place of the Sun and the point underneath to draw the lines of an Angle and make all other lines parallel to that as you may see by the figure below without repeating the Practick which is the same as that above The Shadows of the Sun are equal to the Objects of the same height although that they be removed the one from the other EXperience teacheth us that many stiles or elevations of the same height removed the one from the other cease not to give their shadows equal in the same time I say in the same time for they do lengthen or shorten themselves according as the Sun cometh near or retireth himself the which he doth every moment seeing that he never standeth still Wherefore when one desireth to cause the shadow of some object to cast we must determine of the place of the Sun and the point under it to draw from thence the two occult lines which give the term of the shadow as here the Hedge-row A giveth the point of its shadow in B and if from the point B you draw to the point of sight C this line B C shall be as well the shadow of the Hedge-row D as of that A and of all those that should be in the same line unto the point of sight and you must hold for a maxime that the shadows do always keep the same point of sight with the objects Following this experience that the objects of the same height do give the shadows equal if one would give the shadow to the Hedge-rows E F which are of the same height with A D we must only take with a Compass the distance A B and carry it to the foot of the Hedge-Row E for to have E G and from this point G to draw to the point of sight C and to make always the same Practice even when these Alleys were prolonged infinitely But if the light come from the bottom or from before as in the figure below must we change the Order No we most only set forward or draw back the foot or that under the Sun and draw lines from the one and from the other by an Angle as are H and I which shall give the bound of the shadow of the Hedge-Row K to the point L and from this point L we must draw to the point of sight M Then from all the Angles of the Plane of the Palissades we must draw Parallels to the line H unto the Ray L M and we shall have the natural shadows of the same Palissades or Hedge-Rows Of the Shadows when the Sun is directly opposite to the Eye AS often as the Sun is before our eyes that is to say above the point of sight the sides of the shadow that it shall cause shall be parallels as are all the visual Rays wherefore the point of sight shall serve always for the foot of the light And the other Ray which shall determine the shadow shall be taken from the center of the Sun For example when we would find the shadow of the Cube A we must by the Angles of its plane B C draw Rays to the point of sight D as are B E C F. Then from the center of the Sun G draw also two Rays which shall divide those at the point K L passing by the ends of the lines elevated from the angles B and C which are H and I In such manner as the shadow of this Cube shall be B K L C. The shadows of the two other pieces M and N shall be taken by the same order and so of all the others which may there be met withall It cometh into my mind that one might be troubled if instead of a Cube there were a Pyramide by reason that the Ray of the midst of the plane of the Pyramide and the Ray of the Sun that passeth by the point made but one line and by consequence can terminate nothing for to take the shadow from the point of this Pyramide When this shall happen we must from an Angle of the plane as is here O draw a Ray to the point of sight P which shall make O Q And from the same Angle O elevate a Perpendicular O S then from the point of the Pyramide T make a parallel to the base until that it divide the Perpendicular O S at the point V We must make the Ray of the Sun to pass by this point V and continue it until that it divide the Ray O Q at the point X from this point X we must make a parallel to the base unto the Ray of the midst of the Pyramide which shall be divided at the point Y the bound of the shadow We must draw to this point Y from the Angles Z and O and the Triangle Z Y O shall be the shadow of the Pyramide These Walls which are at the bottom of the one and the other figures take their shadows as we have said of the Cube A. For to give the shadow of the Objects pierced by the light WHEN the Object is square or of a right line we must from the point A from under the Sun draw lines Parallels from all the Angles of the Plane Then from the midst of the Sun B draw a line to the Angle the farâ—hest removed C which shall divide the line A at the point D and to draw from the point D to the point of sight E until that it finde the last line of the Plane F for to have
the rest of the shadows we must draw Parallels to the line B C D by the corners G H I by reason that the Sun enlightneth two faces and maketh the shadow larger as is to be seen in the first figure that G C and H I are the Diagonals of these square Pieces enlightned on two sides and where these lines drawn by C G and H I shall divide the line A we must draw to the point of sight E and we shall have all the Projection or the shadow of the Object If it be a Round as in the second figure we must make the Round by the Order of the Arches on the side as fol. 62. and 63 by elevating the Perpendiculars and when the Round shall be framed with its thicknesses we must from the foot of all these Perpendiculars draw Parallels to the base as L K then to take for the under-part of the Sun L which is the Parallel of the midst of the Round Then from the midst of the Sun M to draw a line passing by the upper part of the Round N and to continue until that it divide this Parallel L at the point O which shall be the bound of the shadow The empty part of this Round shall be found drawing a Parallel to N O from the point P which is the upper part of the Round opposite to the Sun until that it divide the line I O. The rest of the Round shall be found drawing also a little Parallel to N O from the point R which shall give S. All the rest of the Rounds are found by making parallels to N O by all the points of the Round of the Perpendicules which we must continue until that they divide the Parallels to the base so as I have made that of the midst L O I had marked them all with points but I am such an enemy of confusion that this hath caused me to omit them The Shadows take the shape of the Planes where they are cast HItherto I have given the shadows within a Plane united being assured that he which shall understand them well shall not have any difficulty to practise these here and the others that follow because that it is all the same Rule and that one only direction shall suffice for to make to understand how these shadows do raise and abase themselves according as they finde their Planes For to make it appear that these shadows are found by the same Rule that the former is it not sertain that he which should draw a line from under the Sun A passing by the Plane of this Gate B and that from the Sun C one should draw another by the top of the Gate D that these lines would divide themselves out of our paper and would give the bound of the shadow so as I have said of others But the wall E hindring the line A B to prolong it self as it would do if the Plane were united obligeth it to raise it self as we see E G wherefore it is that the Ray of the Sun C which ought to go very far to seek the line A B divideth it against the wall at the point G and there marketh the shape or the shadow of this Gate whereof the Top draweth to the point of sight H. The shadow of this piece K easteth its self with its whole length K I passing over this other piece I and we must mark that the shadow keepeth always its length although that it meet with something between two and it must be that the shadow which passeth over something observeth the figure and the forme of the same thing as here the shadow M and N keepeth the shape of the Piece L. Although that I have made the Sun to appear in the other figures we must not think that he should be so near the Objects it hath bin only for to give to understand that the Rays do come from thence whenas he is in this height but nevertheless out of the Piece as in this second Figure which yet ceaseth not have the line from under the Sun A B and that of the Ray of the Sun C by reason that we ought always to suppose them for to finde the bound of the shadow The shadow of the Piece O is found by continuing the line A B and making it to ascend the steps and raise it self against the wall until that the Ray C passing by the corner of the Piece divideth it at the point S then from the point S to draw to the point of sight T For to finde the shadow of the Piece P we must remember that which I said at the beginning of this Treatise that we must always suppose the foot of the light upon the Plane where the Object is placed and so the Ray C dividing the little line A B sheweth how far the shadow of the little piece P ought to go which must be drawn to the point of sight T. The Piece V giveth its shadow all along although it descend into a Pit the shadow of the wall R is found by the same Order that the others as also the lines A B and â—he Ray C cause it to be seen For to find the shadow of the Objects when they have more breadth above then below WHEN one would have the projection below or shadow of Figures whereof the upper part hath more breadth or length then the lower how these two figures ought to be They make ordinarily a plane from which they raise the Perpendiculars A B. The plane being made we must from under the Sun draw a line as I have already said and from all the Angles of the plane draw parallels to that then to draw one from the Sun C passing by one of the Angles of the Object as D until that it divide the line of the plane of the same Angle A so that it make the line D E at the point F and to draw E and F at the point of sight G which shall give the shadow of the square above the Object then drawing from the point of the figure H to the point F and L we have the whole shadow of this Pyramide turned down-wards We may see well that the projection or the shadow of this cross below is made by the same Order which I will not repeat that I may not be troublesome For to find the shadow of Objects elevated from the Ground THis order will be rendred easy by that which I have newly given seeing that in the one and in the other we need only to find the plane and from this plane to draw lines parallels to those under the Sun by all the Angles then from the same Angles of the Objects elevated into the Air to draw also lines for to divide those which are drawn from the plane and to find the bound of the shadows as I have here already said many times in the figures foregoing The which maketh me believe that any one shall easily understand all that I can
make of the shadows taken from the Sun without that there be any need of other explications for the figures seeing that they are sufficiently intelligible and all made by the Rules which one may have learned by others heretofore But as every figure hath always some particular observation it will not be besides the purpose to give notice thereof to the end there may be nothing which may not be easily understood I say then that in the first figure I have only made use of the plane A B C D for to find the shadows of the objects E and F by reason that they are both upon the same line and of the same height In the second we must observe that the piece of wood G casting its shadow upon the Wall H this shadow maketh the same figure that the Corniche I which is below the which is seen also at the Staff K set against the same Wall H. For to find the shadow of the board L we must remember the order afore-going of the Objects broader above then below for having drawn the Perpendicule M where it shall divide the Ray N O we must draw the line from under the Sun M P then from the board elevated L to draw a line which divideth M P and this section shall be the bound of the shadow The shadow of the Boul Q shall be found also making two Perpendiculars to fall of which we must frame the plane Then by the Center of this plane to draw the line from under the Sun R and from the Sun a Tangent as Q S until that we divide the line R at the point T and also another V which divideth the same R and this distance T V shall be the greatness of the shadow of the boul For to find the shadow at the Sun in all sorts of Figures THE shadow of these Figures is found by the same Orders of other bodies that is to say by parallels as well of them from under the Figure as of those that come from the Sun with this only difference that the shadow of the bodies or objects is found by the help of their plane and that the figures have none thereof but instead of these planes we must from the aspect whereby we see the Figure draw a line by the under part and upon this line make to fall perpendicularly that which is most remarkable in the figure for to help to find the shadow and then this line from below shall serve as for a plane For example the figure being naked or cloathed and without a Cloak as the first that turneth the back to us We must from under its feet A draw a line to the point of sight B and upon this line A B make to fall occult lines from all the points which can help to find the true shadow as from the hand C to make to fall a Plumb-line which shall divide the line A B at the point D and from the Elbow E to make one fall to the point F and yet another from the head G which shall give the point H from all these points D F H from the feet of the figure and from the end of his Staff I. We must draw parallels to the base Then the height of the Sun being determined of we must draw a line as K passing by the fore-part touching the brim of the Hat G and to continue the same until that it divide the line H at the point L which shall be the end of the shadow And also from the brim behind his Hat M to draw a parallel to K G L until that it divide also the line H at the point N these points N L shall be the shadow of the Hat We must draw a parallel by the point C until that it divide the line D at the point O. This point O shall be the shadow of the hand which holdeth the Staff Wherefore drawing from this point O to the point I this line O I shall be the shadow of the Staff We must also draw a parallel to the point E which shall divide F at the point P and shall be the shadow of the Elbow and so of all the places that one would as of the Knees upon the parallels which pass under the feet and from all these points to mark the shadow of the whole figure the little figure Q hath taken its shadow by the same order I have not marked all the points nor the parallels for to avoid confusion When they are cloathed at length for to find the shadows of the figures we must as I have said draw from under their feet a line to the point of sighâ— R as this S R and from the bottom of the garment on the one side and the other draw two parallels to the base as T V and between T V another X which is the midst of the figure Then from the top of the Head to draw a line Y which shall be for the Ray of the Sun which we must continue until that it divide the line X at the point Z and this point Z shall hâ—â— the bound where the shadow must end the rest of the shadow shall be drawn between the two parallels T V and if any thing flow over as the two folde ✚ and * we must draw them by parallel to Y X untill that they divide the Ray V as we see that the ✚ giveth the shadow of the Elbow and the * giveth that of the folds of the Cloak For to finde with facility the shadows by the Sun IF I would here set down the shadows of all the Objects which may be given it were to take in hand a design without end for the Objects may be given infinitely for besides the great number that there is of them each would suffice to make a Book seeing that it may be turned bended and lie down in divers manners each having its shadow different But this labour would be very unprofitable seeing that every one may make those which shall please him so that he remember well two or three Rules which he must keep as I have shewed in the Orders of the shadows taken from the Sun where two sorts of lines give the means to finde all the shadows which may be the one coming from under the Sun passing by the Plane the other which parteth from the Sun by the upper part of the Object and goeth to divide this other line where the shadow must go but as these lines must be each Parallels that is to say those from under the Sun Parallels between themselves and those of the Sun also Parallels between themselves I believed that I should oblige I gave an Invention to draw them readily the one and the other I have said elsewhere how we should draw Parallels to the base by the means of a Board well squared as this here A and of a Rule as B the which shall serve to draw lines from under the Sun when it meeteth directly opposite to
the face of the Object as may be the line C D but if it enlighten by the Angle we must use another instrument as that marked E which is a Rule fastned to the End of another piece of Wood well squared and hollowed of one side and the other in such manner that the Rule F G may move with force to the end that having taken a line bended as H D one may therby make one which may be Parallel to it which is I K with this false square or Grashoper it is so as the Workmen call it E F G this Instrument doth abbreviate exceedingly when one would make shadows of the Sun for there is not a line and of what inclination soever it be whereof one may not draw Parallels The use will make us to know its profitableness But for the shadow by the Torch and the Candle it is of no use at all by reason that all the lines are drawn from one Center The Shadows taken from a Torch from the Candle and from a Lamp are found by one and the same Order I Have already said that for to finde the shadows we must necessarily have two points the one from the foot of the Torch or of the Candle or of the Lamp which ought always to be found upon the Plane where the Object is set the other from the flame of one of these lights From the first point which is the foot of the Torch the bottom of the Lamp or of the Candle we must draw Rays by all the Angles of the plane of the Object of which one would have the shadow And the second point which is the flame will give other Rays which passing by the Angles from the top of the Objects will go to divide these lines drawn from the plane and to mark where the shadow must end it self I shall shew this by example using the same Letters for these three lights in which it shall be easie to see that it is all the same order in the one as in the other with this only difference that the foot of the Torch or of the Taper is set below and that it must suppose in others that they set it there I say then that if one would have the shadows B of the Cubes A that we must from the point O foot of the light draw lines by all the Angles of the planes of these Cubes as O D O E O F O G Then from the point C which is the light or the fire of these Luminaries draw other lines which must pass by the Angles of the objects elevated and continue these lines until that they divide the other lines drawn from the point O. For example having drawn a line from the point O passing by the Angle of the plane D if one draw from the point C another line passing by the same Angle elevated P this of the point C being continued shall divide the first of the corner D at the point H and this point H shall be the shadow of this Angle D P. If from the point C we do the same by all the Angles elevated we shall divide the lines of the Angles of the plane at the points H I K L the which points H I K L we must joyn with right lines and we shall have the shadow of the Cubes as is to be seen in the three figures By this example it is easie to see that it is all the same order in the one as is in the others In the leaf following it shall be taught to find the under parts or the feet of the Candles and Lamps Of the foot of the light SEeing that the Order for to finde the shadows for the Torch for the Candle at for the Lamp is altogether the same in the one as in the other as we have sai but now There will be no more need to set down distinctions in the Order following for when I shall set a Torch one may set a Candle or Lamp in the place by reason that the flame of the one hath the same effect with that of the other wherefore from henceforth I will use the word of light for all three For the foot of these lights which must be upon all the Planes where they set the Objects they shall be found by this Method Having a Torch lighted within a Chamber whether we shall set it in a corner on the side or in the midst as this it must be that all the Parts of the Chamber or of the Hall as the Boards above and below the sides and the bottom have a point that serveâ—h for the foot of the light that from this point we may draw by all the Angles of the Plane of the Object of which we would have the shadow as I shall shew in the leaf following contenting my self to shew in this how we must finde this point which I call the foot of the light The Torch being placed in A this point A is the foot of the light and B the fire or the light of the Torch this fire or light B remaineth firm and never changeth but the foot must be found on all sides For to have the foot of the light at the wall on the side C we must from the point A draw a Parallel to the base until that it divide the Ray D E at the point F and from the point F to raise a Perpendicular F G Then from the point B which is the fire to draw another Parallel to the base until that it divide F G at the point H and this point H shall be the foot of the light as if the Torch were lying by reason that its fire remaineth always at the point B. For to finde this foot of light at the Board above we must from the point G draw a Parallel to the base as G I and from the point B to make a Perpendicule to G I which shall give the point K which shall be the point of the foot of the light as if the Torch were turned upside down For to finde it on the other side of the Hall we must make the same Order as on the side C and we shall have the point L. For to finde the foot of the light at the bottom of the Hall we must from the point H draw to the point of sight O until that we divide the Perpendicule E at the point M then from this point M to make a Parallel to the base which shall divide the Torch at the point N this point shall be the foot of the light for the bottom of the Hall The foot of the Candle is found by the same Order as that of the Torch taking the midst of the foot of the Candlestick for the foot of the light but when it is a Pâ—ated Candlestick or an Arm set against a wall it must be that the Arm or the Branch of the Candlestick determine the line or shall be the foot of the light For example in the Plate
P we must by the branch Q draw a Perpendicular to the base as R S then from the fire T to make a small Parallel to the base which shall divide R S at the point V which shall be the foot of the light for this side the point X shall be it for the board below the point Y for the board above and Z for the bottom of the Hall or Chamber For the Lamp it is the place where it is fastned which determineth its foot as here * from which place they draw a Parallel to the base unto the first Ray and altogether the same as at the Torch and at the Candlâ— For to find the shadows by a Torch on all the sides of a Chamber THe shadows taken from the Sun draw always towards the Earth by reason that this Star communicateth not its brightness except it be above our Horizon and by consequence elevated above all the objects which causeth that their shadow always descendeth But it is not so with the Torch nor with the Candle or with the Lamp the which one may set above or below or on the side of the objects which rendreth their shadows on all parts as we have said The Figure aforegoing will help to find the shadows of the Objects set on every side of a Chamber for having found the Foot of the Light as I have newly spoken there is no more difficulty seeing that this is all the same order as the Cube of the 141 F O whither we may have recourse but that we go not to search so far I shall say that for to have the shadow of the Table upon the which the Torch is passed we must from the point A the foot of the Torch draw Rays by all the feet of the Table C then from the point of the light B draw lines by the corners from upon the Table I until that they divide the Rays C at the points O which shall be the bounds of the shadow of the Table The shadow of the piece D shall be found drawing from the point A by all the Angles of the plane unto the Angle of the Wall E and from this Angle to raise them Perpendicularly Then from the point of the light B to draw lines by the top of this piece D by observing the Angles correspondent to the lines of the plane and we shall have the shadow F of the figure or of the piece D. The shadows of all the other pieces shall be found by the same order Wherefore I shall quote only the foot of the light seeing that the fire shall be always the point B. For to find the shadow of the piece G the point L is the foot of the light For to find the shadow of the piece N the point H is the foot of the light For to find the shadows of the pieces I and M the point K is the foot of the light The second Figure HAving found the foot of the light on all the sides of the Chamber as I have said in the foregoing leaf one may have the shadows of the objects in what place soever they be by the order that I have given For by example having found the foot of the light Q and its fire P. We must for to have the shadow of the piece R draw Rays from the point Q which pass by the plane of the peice R and to continue them infinitely but because that they meet with the bottom of the Chamber or the Wall T we must at the meeting of the Angle S elevate all these lines Then from the point P draw other lines by the top of the same piece R which shall go to divide those of the plane and to mark the place of the shadow upon each of them taking care that the Angles have reference to the lines drawn on the plane This order is so general and universal that he which shall well understand only how to take the shadow of a Cube shall find no difficulty to find the shadow of any object whatsoever it be Wherefore having given this order of the Cube at the 141 fol and this above which is altogether the same I believe I have sufficiently instructed how to give all the shadows without being obliged to use repetitions in all the other figures which follow where I shall only quote the point for the foot of the light For to find the shadow of the piece V the point X is the foot of the light For to find the shadow of the piece Y the point Z is the foot of the light For to find the shadow of the piece ✚ the point is the foot of the light and P the fire or the light for all the pieces of this second figure 2 Figure The shadow by a Torch of a Pyramide upright and another upside down THIS Pyramide upright giveth its shadow by a Torch as if it were by the Sun by reason that in the one and the other there is but one line only upon the which they determine a point â—n which is for the point of the Pyramide For example having made the Plane B C D E and drawn two Diagonals for to finde the midst of the Plane F we must raise a Perpendicule F A then to draw from these four points B C D E to the point A and the Pyramide shall be framed for to finde its shadow we must from the foot of the light G draw one line only passing by the point F and prolong it infinitely Then from the fire or light of the Torch H draw another line by the top of the Pyramide A and continue it until that it divide G F at the point I which shall be the bound for the shadow of the Pyramide which shall be finished drawing C to I and E to I for this Triangle C I E shall be the shadow of the Pyramide A. For to have the shadow of this Pyramide over-turn'd we must cause Perpendiculars to fall from the square above and to frame the Plane below thereby as we have said at that of the Sun fol. 138. this Plane being framed we must from the foot of the light G draw lines by all these Angles Then from the point H which is the fire draw also others by the Angles of the square above which dividing those of the Plane shall mark the place of the shadow as we have said in other Orders of the Torch The shadow of a Cross HAving set a Cross in the shadows of the Sun it seemed to me necessary also to set one in the shadow of a Torch to the end that by that and by this we might know the difference of the one from the other The Order is seen enough seeing that we have already taught at the 137 fol to finde the Plane and that the rest is as in other Orders of the Torch For to finde the shadow of Round Objects by a Torch HAving made the fore-going figure it came into my mind that one
might be in trouble if there should be Bowles Cups Viols Flagons or other round pieces which have Ordinarily more breadth above then below of the which we would have the shadow by a Torch by reason that such pieces seem more difficult then the squares although that in effect it be all the same Order there being nothing but to reduce the square into round so as I have taught in the fol. 19. 20. 28. 29 and 86 Where we shall see all the Orders for to set the Planes of round pieces into Perspective the which being known all the rest is very easy to understand I have said already at fol. 138 how we must finde the Plane of a Bowle and by this Plane to have justly the greatness of the shadow by the Sun But as this of the Torch is different from that I believed it to be necessary to set that also down here by reason that it doth facilitate the Order of all the other Rounds For the shadow of this Bowle I say then that having made its Roundness with a Compass which is the the Circle A and draw his Diameter B C that we must under this Circle make a line Parallel to B C which toucheth the Circle at the point H then from the ends of the Diameter B C to Cause Perpendiculars to fall upon this line underneath as B D and C E of the which points D E we shall frame the ordinary way the Plane D E F G whereof the diameter F G shall divide this D E at the point H This Plane D E F G shall serve for to finde shadow of this Bowle A. For after having drawn from the Foot of the Light I lines which touch this plane on the one side and other as are the lines I K and I L And also another line passing by the midst of the plane H which shall be the line I H M. We must afterwards draw other lines from the Light of the Candle N which touching the Bowle shall go to divide these lines of the Plane as from the point N to draw a line which toucheth the Bowle between A and B and divideth the line I H at the point M which shall be the end of the shadow for to have the beginning of this shadow we must from the same point N draw another line which toucheth the fore-part of the Bowle and divideth also the line I H at the point Q this distance Q M shall be the length of the shadow for its bredth we must also from the point N draw two lines by the ends of the Diameter of the Bowle Z Z and they shall divide the lines I K at the point R and this I L at the point S. Wherfore if R S be the bredth of the shadow and Q M the length we have only to joyn these fower letters of Crooked lines which shall give an Ovall for the shadrw of the Bowle A I have a little Extended my self for to facilitate the shadow of this Bowle by reason that I believe this only Order sufficient for to finde the shadow of other Rounds as of the Figure V the which having two breadths unequall ought to have a Plane of two Circles And that below X which hath three differences obligeth to make a Plane of three Circles The one for the Neck of the Viol or Flagon the other for its Belly and the other for the foot all these Planes are made as of the Bowle I believe that it not necessary to use Repeâ—itions The figure being able to teach of it self Of the shadow upon many Planes Parallels THE first Plane that is the Ground where the Chair A is placed the second Plane is the upper part of the Table which is Parallel to the first Plane and either above or below the Table it might also have one or two or more of these Planes upon which we shall finde the foot of the light for to finde the shadows of the Object which should be there For example the foot of the light it is C and the fire B from these points C B we must draw lines by the under-part and the upper of the Object D for to have its shadow E upon the Table E. But to have the shadow of the Chair A which is upon the Ground we must find upon the same ground the foot of the light which is upon the Table the point C the Order following teacheth this We must from the point of distance which is here out of the Paper draw a line by the foot of the Table F then from the corner upon the Table G to make a Perpendicular G to fall which shall divide the line F at the point H and from this point H to draw a Parallel H I which is equal to the upper part of the Table and which ought to facilitate to finde that which we seek for having from the point of sight K drawn a Ray passing by the foot of the light C unto the end of the Table L we must from this point L let fall a Perpendicular upon H I which shall give the point M from which point M we must draw a Ray to the point of sight K and upon this Ray M K must be the point of the foot of the light which shall be found easily making a Perpendicular to fall from the point C the which dividing the Ray M K shall give the point N for the foot of the light This point N being found there is no more difficulty to finde the shadow of this Chair A because that it is all the same Order as of other Objects which we have seen in the leaves aforegoing that is to say that we must from the foot of the light N draw lines by all the Angles of the Plane of this Chair and from the light B to draw other lines by the upper part of the same Chair which divide those of the Plane and shall mark where the shadow ought to go the figure will make it known that all is to be ordered as I have said elsewhere The second Figure I Do not set down this second Figure for that I have any particular thing nor different from that above But only to refresh the Memory of that which I have said in the beginning that all the Objects cast their shadows diversly and according as they are set about the light as we see that which is upon the Table giveth its shadow according as it is enlightned that is to say directly either on the right or on the left that which is found by the ordinary Orders of the foot of the light P and of its fire or light O the most part of these Objects are broader above then below wherefore we must make their Planes as I have said in those folio's where I have spoken of the like figures The shadow of boarded Floores by a Torch I Have not set this figure in the shadows taken from the Sun by reason that this light is above
all the Objects that are in the World and by consequence cannot give a shadow which supposeth the Light or the Light-some-body under the Object One might object to me that Experience causeth it to be seen every day that when the Rays of the Sun enter within an Hall or a Chamber the shadow of the Floores and of other things cease not to appear To which I answer that then this shadow or these shadows is not or are not of the Sun but caused by the great Brightness of the Sun and such shadows might not be given by Parallels as those of the Sun but by Rays from one and the same Center as those of a Torch taking the Window where the Sun passeth or the place where it giveth for the point of the light and to do for such shadow as I am saying of the shadow of a Torch The Orders aforegoing which oblige to make Planes and to draw lines by all the Angles for to finde the bound of the shadows would be too long for this and the great Number of lines which one must draw there would make this figure very difficult by reason of the Number of Beames and Joysts which there are met with the which made me seek the Means to abridge it for to make is easie in the practise without going forth of Rules and Maximes of Art Having made the floore in Perspective as it is taught in the 55th or 57 fol. And placed the Candle the Torch or the Lampe in what place we would We must search by the means of the foot of the light the place where the fire ought to to be or to speak more truly the which we shall use in stead of the fire for from this point to lines which pass under the Object and mark out the bound of the shadows For to have this point of fire the light being at B we must from the foot of the light C draw a Parallel to the Base D E untill that it cut the Ray E F at the point G from this point G we must elevate a Perpendicule G L. Then from the fire of the Torch B draw a Parallel to D E which shall divide the Perpendicular G L at the point L and this point L shall serve for the point of fire which shall give the place and the length of the shadow For Example having to finde the shadow of the Beame A we must from the point L make a line to pass under the Angle which is towards us as H and see where this line L H shall divide the first Joyst at the point I for this shall be the place where the shadow of the Beame endeth from this point I we must draw a parallel I K and marke upon the Joysts the place of the shadow O for the shadow of the space of the Joysts ir will be found by drawing also a line from the point L by the Angle of the first Joyst M which shall divide the Angle of the Hollow at the point N from this point N making a Parallel N P we shall have all the shadow marked Q for the Beame A. For to finde the shadow of Joysts besides that of the Beame we must only draw a line of fire B by the Angle S untill that it divide the Bottome of the Floore at the point T do the same to all the other Joysts and you shall finde the shadow longer at the farther distance from the fire Having marked upon one Beame all the points T we must from the point of sight R draw lines by each of these points and we shall have justly between all the other Beams the shadow of the Joysts as is to be seen at the points V. The figure below is the same with that above with this difference that this is shadowed and that the former is not by reason that the shadow would have hindred to see the letters and the small lines There is more in this the shadow of the Iawmbs of this Gate which must be taken from the foot of the light as is to be seen in X and Y. For to finde the shadow by the foot of the light IF the Objects be Perpendiculars to the base and more elevated then the fire of the Candle A. We ought only to draw lines from the foot of this light B by the Angles most advanced of the Objects as are C D of the Screen and from the Angle of the wall E the which lines B C B D and B E shall make the place of the shadow at the meeting of the Angles which the Shuts of the Screen make with the floor and also the return of the wall at the points G from which points G we must elevate Perpendiculars at the base G R which shall finish the shadows which the Candlestick A giveth The reason of this is that the line A B is parallel to the lines C H D I K and E L the which maketh that in what part soever the fire be upon the line A B whether on high or in the midst or all below it shall give always the like shadow We must observe that this Order is not good but in Pieces which are more elevated then the fire as these here for when those shew the upper part as the Object M. we must use the Orders aforegoing by drawing lines from the points of the feet and of the fire of the light Of the Shadow doubled WHEN two lights meet in the same subject or object it is of necessity that two shadows meet there because that each day or each light produceth its own with proportion I say with proportion for if these Fires lights be equal at the same distance It is certain that the shadows shall be equal but if there be the least disproportion as if the one of these lights be a little greater then the other or that these fires be a little greater then the other or that these fires although equal be more or less advanced the one then tho other from the object these shadows shall be different for example the object O being enlightned with two Candles the one near P the other farther off Q it is most assured that the shadow of the Candle P shall be much stronger then that of the Candle Q as is to be seen in the figure The Orders of these shadows are no other then those that I have given as well so the Sun as the Torch For the Shadow of Figures by a Torch IT is to be believed that my counsel will be followed that one should not turn over the leaf for to learn the order which followeth before they understand and remember well that which went before Wherefore supposing that one understands well the order that I have given at 139 fol. for to find the shadow by the Sun for all the figures of such postures as they may be I have nothing to say for these seeing that the line below which I make to serve for the plane and all
its Ornaments as is A B of which having taken the bredth and made a square Plane in the ordinary way and from this square to elevate from all the Angles Perpendiculars we shall frame the body or solid part of the Pilaster Then we must only take that which projects it self from the body for example the base of the Pilaster C and transport its measures as in D E. for to set it in Perspective round about the Pilaster we must from the point of distance F draw a line Diagonal which passeth forth of the square to the point E unto G it is no matter for the length Then from the point A to make a Ray passing to the lower part of the Projector H and at the point where this Ray shall divide the Diagonal at I it shall be the advancement of the whole base the same Ray A H shall give the Projector of the bottom by dividing the other Diagonal at the point K Then for the Projector before we must from the point I draw a Parallel to the base until that it divide the Diagonal which shall give the other Corner of the Projector before at the point L then drawing lines of the height of the Base unto these points as are M to L from D to I from N to K you shall have the bredth and the hight of all the Base The Capitall is made of the same fashion Here is for the first figures above Those below shall Cause the rest to be known and shall avoid Confusion For the Pilasters O we must observe that above P where the line D H bereth all the sections of the base Wherefore from the point of sight A we must draw Rays the which passing by the divisions of D H must marke them upon the lines D I and N K And drawing Parallels from the points of D I to M L there will be no more then to give the Turnings about or wheelings as the shape of the Colum. When you shall meet with squares or Flat-bands either above or below they are made by Perpendicular As for to make the Plinth you must raise Perpendiculars from the Points L I K the from the point of sight A to pass by the Corner of the Plinth Q it will give the height upon the Perpendicules I and K. Then L must be equall to L. I beleeve that this Instruction for the Base will suffice for to make the Capitall being the same Order This last Pilaster R is only for to cause one to be seen without being mingled with lines We have broken them for to make the Bases and Capitall to be seen not having had space Enough for to make them appeare whole A great Cornish above the Horizon in Perspective IT is the same Order with that which we have explained but as it is somewhat difficult by the multitude of lines I thought it convenient to set it down again here for to avoid confusion I say then that having taken the pourfill of the Projector and the Cornish that one would make we must set it at the place where one would make it as C which is the pourfill is at the corner of the Wall A B for to find the height which it ought to have and to make those below seen we must from the point of sight D draw a Ray passing by the end of the pourfill E as is D F then to make a line Diagonal from the point of distance H passing by the corner of the Wall B and to continue it until that it divide the Ray D E at the point F from which you shall draw the line F G which must be the Angle in Perspective for to receive all the measures F G the corner of the other end of the Wall K L is drawn from the other distance I as being the other Diagonal In the figure marked 2. we shall see that all the figures which are upon the line M N must be transported by visual Rays from the point of sight D upon the line N O for to draw Parallels to the Horizon from all these points which shall give the whole Cornish perfect But before we pass any further we must mark as I have already said that all the flat-bands and squares are made by Perpendiculars For example for to make this great square of the Cornish having made the Wave or Ogee and the filet under the filet which must be the height of the square we must abase the Perpendicule P Q. Then for to know where it must be divided for to make the under part be seen we must draw from the point of distance I by the point above the quarter of the round R unto the Perpendicule P Q. and you shall have that which you seek That which I have said of the great square must be understood of little ones as are small mouldings the filets c because that they must all make that below to be seen The third figure sheweth that having found all the points and drawn Rays upon this line from the Angle S T we must there trace out or shape the mouldings out proportionally I mean that when these shall project themselves as this here doth because that its point of distance is near we must help the mouldings that is to say a little bend down the quarter of the Round set up the Ogee enlarge the filets and mark at one end the same that at the other as at V X the same that at S T after that there is no more but to draw parallels to the base and all shall be done The fourth figure sheweth the Cornish wholly made I have drawn parallels from all the points of the line of the Angle Y Z I have made an end of the Wall to pass upon the Cornish for to give to understand that one hath liberty for to make it throughout and that our rule is general for to make it where they would For to find the under parts of the Great Projectors FOR to find the Projector of the Crown of the Body or of the Wall A We must from the Corner of the quarter of the round B make as small line of the length that one would have that it come forth as is B C then from the point of sight D to draw a Ray E passing by the end of the Measure C. After that you make a Diagonall from the distance F and make it to pass by the quarter of the Round B and the section that it shall make at the Ray D E at the point G that shall be the under part aswell of the bottome as of the side as is B H the which one may see more cleerly in the opposit in the body marked K The Projector of the Body or Wall marked L is made as the first marked A There is only this difference that the Body L hath the Projector M N greater by one half then that above B C for to Shew that by the same Order one