you haue any good Geometricall instrument already sure also hast thou the vse thereof or if thou want heere art thou instructed to make the same according to thy affection for I seeke to tye none to my owne particular humor then might I haue referred them vnto my Geodeticall Staffe But happily some will say if there were sufficient instrumeÌ„ts before then what needeth these new inuentions would wee haue our owne wits more excellent then our predecessors Of such and such like I familiarly enquire if Antiquity bee onely Mistresse of this faculty if moderne wits may intimate or exhibite nought vnto the world if we must only beleeue what is set downe without contradiction should that bee so how farre had this age beene from the perfâ—ct Idea of the Art whose excellency turneth euery heart after the same as the Heliotropion after the Sun into what an intricate Laborinth of coÌ„fused errors had we run The most ancient Philosophers were as contrary in their sects as erronious in their opinioÌ„s till time brought in Truth truth Knowledge and Knowledge perfect Vnderstanding what a nuÌ„ber of sects had we as Catonians Peripatitians Academians and Epicurians Anaximander said the earth was like a columne Anaximenes flat Leucippus like a Drum Democrites like a platter till Thales demonstrated it to be round How grossely did they differ about the Tides some referring the cause to riuers falling from the mountaine Gaule entring the Atlantique sea as Tymeus Some to a rising of certaine waters as Plato Some to the Sunne drawing the winds vpon the Ocean which caused the Atlantique seas to swell as Heraclitus till Pytheas demonstrated the cause to bee in the increasing and decreasing of the Moone whereby Homer said I praise not my Ancesters for their knowledge but for that they desired knowledge But shaking off these old differeÌ„ces enquire of the commodity of the Compasses Sea-cards and new Maps of many other deuises engines that haue beene lately set forth more beneficial then any heretofore of which the old Philosophers Mathemâ—titians were ignorant of I think if they were liuing they would reioyce to see as amongst many I will remember Gâ—lâ—risius Astrâ—lâ—be the Mater wherof being excellent and a most Art-like proiectment resembling the true lineaments of the â—pheare and is now made perpetually famous with the Edition of the Rete by our ingenious countriman M. I. Blagraâ—e But my Pen shall not bee so much dismeasured to reproue ancient men to the end to draw the glory to them that be present Had we liued then we had knowne lesse then they and were they liuing now they would know more then we euery thing hath his time before it come to maturity neither doth nature alot like time to euery like action some things grow to perfection in a moment when others require a moneth The Beare bringeth forth in foure weekes when the Dolphin hath neere 40. when one fruite faileth another entreth into season we must first inuent next amend and lastly perfect the furtherance of which perfection it behoueth euery louer of the Science to cherish which is here freely offered vnto thy view though it might haue beene vndertaken I confesse by some one of more experience but he that most can least will and he that worst may holds the candle else the world must walke in darknesse There be many say the instruments be vncertaine and this or that is better but none seeketh to reforme the same contriue one that shall do best the professors themselues cry out at the erros but seeke no reformation of the fault so that it fareth with this as in the ciuill actions of the life euery man curseth excesse yet none liue temperately euery man praiseth patience yet none will suffer euery man blameth sloth yet none will take paines euery one exclaimeth on enuy yet none leaue emulating But to remit this and speake something of the application of Instruments He then that will be seene in the knowledge of Geometricall instruments must learne by contemplation to frame his proposition and by action to manage his instrument for I know diuers great Scholers deeply seene in the Theoricall part though in the actiue meere nouices which is a cause that such so learned were neuer able to correct and amend many defects For as meditation causeth ability to vnderstand so action bringeth dexterity to performe because the euent of the worke is illustrated by a precise obseruation as the life of the proposition is illuminated by a plaine demonstration for as points found lines lines surfoces and surfaces bodies so good instruments produce true obseruations true obseruations Symmetricall figures and the superficiall capacity of proposed platformes And as lines bound figures so hedges bound inclosures and angles in the field are created by the meting of hedges as they be in figures by the section of lines for you shall know that all instruments of what kinde soeuer if they cannot obserue the precise quantitity of the angle their worke is erroneneous for though some instruments expresse the quantity of angles as the Theodelitus c. and others regard not the quantitie producing angles Homogeneall as the Plaine Table yet if you faile in the one or the other your conclusion is error for it is as great an absurdity if the angle Homogeneall Mechanicall delineated vpon the Plaine Table Proue Heterogeneall and accord not Symmetrially to the respondent angles in the field as if with a graduated instrument you had falsly obserued the quaÌ„tity thereof and therefore it is childish vanity or at least selfe conceit to go about to prefer the Plaine Table before a large graduated instrument and I am perswaded all good Geometricians wil argue the same though I verily beleeue it is possible to separate fire from heate or the earth from the center at turne the obstinate will of the ignorant for vse and custome hath taken such roote in such that it will hardly be supplanted It sufficeth them plaine men to haue an Instrument for then they presume they bee Geometritians Euery horse is not Bucephalus yet he may be are one a iourney though hee bee long and lame in performing it and can hardly passe ouer a mountaine but let euery man vse his will and so I will mine heere in saying no more at this time onely wishing my selfe present to open any thing that the yong practizer shall doubt of From my Lodging this 9. of Aprill 1611. ARTHVR HOPTON The Author to the Reader concerning the Topographicall Glasse COme you whose eyes stand not in enuious head Whose tongue with Criticke humors is not fed And in this Glasse vnto your comfort view Such needfull workes that much may profit you The grounds of Art haue brought it forth for thee Which we haue suckt from famous Geometrie With Theorm's mixt and demonstrations rare Such as in hiddan Propositions are Heer 's no vaine shew illusions haue no place No spirit confind no hatefull painted face No eye-deceiuing
and one side giuen But if you would make experience of the height of hils onely by a leuell your best way is to finde out a third hill alike or néere a like distance from both the other hils so may you more truly iudge of both their heights and also of the difference thereof from the top of that hill euen as you bee directed by your line of leuell paralell to the Horizon CHAP. XXIIII To know if water will run vnto any appointed place IF you desire to know if water will be brought from any spring head vnto any appointed place you are first to consider how and in what you meane to bring it that is either by trenches and gutters or in pipes of lead or such like for those waters that will come in pipes of lead will not also come in gutters because the pipes may bring the water into a valley and so conuey the same againe vp ouer the top of any hill being not higher then the originall spring yea if it bee higher euen though you should fetch it at the bottome of an hill vpon the one side and bring it ouer the top of the said hill as low vpon the other side for if you once can set it running it will neuer ceasse vntill the pipes be burst or all the water spent the reason is because non potest esse vacuum in rerum natura And for a familiar example Take a number of quilles cut off at both ends and ioine them close together with waxe in a circular fashion and put the one end thereof into a vessel that hath water in the bottome let the other hang ouer the vessell brims the lower the better it sufficeth if so the one end of the quilles bee as lowe as the other Now if with your breath you draw the water into your mouth through these quilles and so take your mouth thence the water will run through the said quilles vntill all be spent in the vessel and this experience confirmes their opinion well that say Aqua ascendit quantum descendit But to know if water will come in pipes after the ordinary fashion to any appointed place you must first know that the ground whereupon the pipes lye must be lower at euery miles end by 4 ½ inches then it is at the spring head which considered plant your Glasse at the spring head so that the Diameter of the Demicircle lye paralell to the Horizon and equall in height to the head of the spring the two sights in the ends of of the Diameter looke through the same to the place whither the water should runne taking notice of what your eye apprehends through the sights for to that place will the water runne abating 4 ½ inches for euery mile the Tower is distant from you But say there be certaine hils betwixt the head of the spring and the place wherto the water should runne in such a case you must plant your Glasse at the head of the spring as before and looking through the sight note some marke in the next hill towards the place then go vnto that marke and if yet you cannot sée to the place obserue some other marke in an other hill and so foorth vntill from the last marke you may perceiue the appointed place in which make a note for abating as before the water will runne thereunto Example A is a place where water is found and the question is to know if it will be brought to the Tower at b which is distant from a 4 miles I plant my Instrument therefore at c so that the diameter p q lye paralell and also equall in heights to a the spring head then looking through q p towards b I cannot see the same by reason of a certaine hill that is betwixt me and b therefore I obserue a marke in that hill through the sight as at c where againe I plant my Glasse in some part of the hill so that the diameter of the semicircle lye paralell and in an equall heigth with the cundit head a the Instrument thus planted look againe through the sights towards the Tower and for that there is no other hill betwixt your sight and the same therefore through the sight espy some marke in the Tower as b which marke is iust leuell with the spring head a to which place the water may bee brought by pypes Note that some hold pipes of earth baked to be better then lead and some hold pipes of alderwood firre pine tree of such wood that hath rosen in it to be better then the former And if the ground lye reasonable leuell so that you conuey the water by trenches order the said trenches so by helpe of a plumbe that the water may haue currant 4 ½ inches at euery miles end then fill the gutter with pibble stones a foote or more deepe and vpon them throw earth so will the water run more cleere to the place appointed Note lastely that it is best if you bring your water by pipes What pipes bee best to beare water to let it come by many croked turnings and sometimes to fall directly downewards and then againe to rise by little and little by this meanes some thinke one may force the waters issue to be aboue the head of the spring so that in pipes you shall not need the foresaide abatement But now whereas in conueiance of waters by this way whether it be waters to houses or new riuers sometimes happely you shall meete with a deepe valley out of which you cannot get the water by ditches and to finde leuel ground you cannot without going a great compasse and hauing found it happely cannot haue liberty for to cut a trench through the same such a matter and such a difference I saw in bringing the new riuer from wards Ware to London for remedy whereof if the floud be great you must erect arches in manner of a bridg 1609 which may extend it selfe ouer the valley euen from the one banke to the other and if the water be but for a house postes may serue to beare the same the like must you do if you meete with a riuer brooke or such like M. L. doth teach you how to solder your pipes of earth or wood that is with vnquenched lime and hogs-grease or with rosen and white of egges or with lime white of egges and fylings of Iron CHAP. XXV To take the quantity of any stationary angle by the Topographicall Glasse YOu must put the Index with the sight vpon the Diameter in the Planisphere where the degr doe take beginning noting that a stationary angle is such an angle that hath no respect to the néedle but to the station The Instrument then duly planted vpon his Staffe you shall mooue the Planisphere the Index fixed as before vntill you espy through the sight the one marke vpon your left hand and for hedges vntill the Index lye paralell with the hedge the Instrument so resting
Chapter I deduct 20. from 43. so haue I 23. remaining by which your line stationary a c 129. yards must be augmented so haue I 2967. which I part by 60. so is my quotient 49 2 6 9 6 yardes the length of b z. And if your station were at d and the one section made at n falling out in the right side o s and the other at w in the left side s p and you required to deliuer the said distance b z then must you work according vnto the 3. difference of this Chapter I did prosecute the first difference with an exaÌ„ple for that neither of the sections will be made in the right parts vnlesse you stand neerer to the base of the altitude then the length of the altitude it selfe that is vnlesse the altitude bee greater then your distance from the base Otherwise Get the three angles of the triangle b d c thus obserue the angle b d a which take from 90. for that b a d is a right angle so haue you a b d then take the angle b d c which adde to a b d taking the totall from 180 so haue you the angle b c d by the 7.60 of the Geodeticall Staffe chap. 1. p. 21. This had get the line c a or a d then protract as in the 28. chapter or work as in the 32. chapter Comp. 3. in the end thereof or as in my 7. booke of Trigonometria CHAP. XXIII To know how much one Hill or Mountaine doth exceed an other in height THis matter is not so easily performed as many ordinarily thinke it to be for to seeks how much one hill is higher then another is not to stand vpon the top of one of the hils and by your Instrument finde whether the other bee higher or lower then the leuell of your eye as in the 19. Chapter and so to iudge him higher or lower then the hill you be one But hee that will know how much one hill doth excéede another in height must finde how much both of the summities of each hil is distant from the center of the earth or at least how much either of their perpendicular altitudes excéede the Semidiameter of the earth for the lesser of this excesse taken from the greater leaueth the difference of the mountaines perpendicular altitude For you must imagine what hill soeuer you stand vpon beholding another adiacent mountaine 20. or 30. miles distant which albeit that hill you behold be equall in height with that whereon you stand yet shal he not séeme so nor fall out to be so being proued with an Instrument or line of leuell for that where you stand is alwaies the vppermost place the other hill being situate as it were vpon the side of the earth which we may proue by a Philosophical Axiome Omne graue fertur deorsum ad centrum vbi quiescit insomuch that if you trauell about the earth with a line and plumbe at the end thereof the plumbe will alwaies point towards the center so that the excesse of any mountaines altitude aboue the superficiall conuexity of the earth is altered in respect of our sight according to the position of the place and therefore when you bee asked concerning the height of two hils you must know whether they meane in respect of the position of the hils according to the apprehension of your sight or in respect of the swelling of the same aboue the true conuexity of the earth for you must vnderstand that the earth is imagined to be round as a globe and so by some it is thought that it was at the first creation and that these mountaines and hils were since made at Noahs flood by the raging of the water which forced stones trées and earth vpon diuers heapes and thereby did irregulate the globous body of the earth the which albeit being compared to the Spheares in in the heauens by the consent of most Philosophers is but as a point hauing no sensible magnitude yet to vs that inhabite vpon the superficies of the same the very hils haue an apparant and great magnitude eleuating themselues aboue the true circuit of the earth and as these hills are much aboue the true superficies of the earths circular conuexily so is it not to be doubted but that many valleyes fall within and lower then the said circular conuexity so that sometimes we may bee distant more then the earths semidiameter from the center as being vpon a mountaine and sometimes lesse as in some kinde of déepe valley all which you shall bée taught to â—â—nde and proue by the ensuing demonstration To performe what is said before you must ascend vnto the top of one of the proposed hils which let bee b let the other hill bee c and you desired to tell which of the top of the hilles is the higher that is whether b or c be furthest distant from a the center of the earth Being therefore at b by some Instrument described in this booke get the angle c b a 87 degrées then must you go to the hill c and there againe get the angle b c a 74. degrées and so adding these two angles together you haue 161. which taken from 180. leaueth 19. the angle c a b made at the center of the earth Hauing these thrée angles get their signes and finally the distance of the two hils c b so haue you a line known and thrée angles knowne and thereby as you be often taught get the side a c and a b which note for looke which is the greater and that hill may you conclude the higher which heere is c a. Now to get the height of b or c aboue the true circular conuexity of the earth subtract 34364 11. from the liue b a so haue you the height of the hill b d foure score doe so to c a so for example sake haue you the height of the hill c e seuen score aboue the true circular conuexity of the earth If you seeke how much the one hill is higher then the other then take b d 4 from c e 7 so haue you thrée score and so much is the hill c e higher then b d. And here it is apparent that if you stand at b and by a line of leuell looke towards c your sight will run to f aboue c so that the lower hill by this meanes will séeme the higher for you must note that euery line of leuell doth make right angles with the perpendicular and euery perpendicular pointeth to the center of the earth as you may perceiue in the figure for b a is a perpendicular making right angles with f b the line of â—euell On the other side standing at c you shall sée the line of leuell c g run farre aboue b and by this meanes you may seeke the altitude and difference of altitudes of hils which otherwise is difficult to be found This chapter may finely be performed by your staffe for that you haue thrée angles
come vnto the 26 day I end with the number of 12 whereby I conclude the sunne was in the 12 degree of Scorpio So of any other here the losse of a day doth nothing hinder CHAP. XLII To finde the houre of the Night by the Tpographicall Glasse and to know the time of high water and also the place of the Sunne or Moone SEe in any ordinarie Sunne diall what of the clocke the shadow of the Moone yeeldeth then turne the Index that is marked with f vnto the said houre in the Planispheare which so resting seeke the age of the Moone in the circle whereto the Index is fixed for the houre line in the innermost circle in the Planispheare passing by the said age of the Moone is the true houre of the night So likewise doth the houre line and the foresaid Index shewe vpon what point of the compasse the Sunne and Moone then be and the number of points included betwixt the said houre line and Index acquaints you with the distance of the Sunne and Moone which the circle in the Peripher expresseth in degrées and minutes which is more then was proposed To know the tides or high water by the Topographicall Glasse Seeke as hereafter what Rombe or Wind maketh a full sea at the proposed place and then learne the age of the Moone these two things had put the Index where 29 ½ standeth vpon the said Rombe or Wind found which resting seeke the age o the moone in the mooueable circle for the houre in the inward circle of the Planispheare answering thereunto acquaints you with the houre of the full sea in the proposed place and for your practise and ease behold the table of tides ensuing The moone south or north maketh a full sea at Lands end south and by east at the Gore end south south west betwéene holy Island and Tynemouth south west and north west betwéene Tynemouth and Flambrough head south west and by west betwéen Flamb and Bridlington in the Bay west south west betwéene Bridligton and Laurenas east west betweene Laur. and Cromer south east betwéene Cromer and Yarmouth rode to Laystow north rode south east and by south betweene Layst rode and Orfordenas south south east between Orf. Orewell woods south by east between Naase the Ware head of Colnes south south west at Grauesend south west at Lon. bridge south and by east at Portsmouth east and west at Waymouth west and by South along the coasts vp to Bristow and the coast of Ireland from Waterford to Kynsale if you desire more you may haue it of any skilfull Mariner or in the tables of the Regiment of the sea One thing note that it floweth sooner by one point of the compasse in the Spring tides then it doth in any of the quarters of the moone especially if the Riuer haue any indrafte and distance from the Sea A note of additions to the Planispheare in the Glasse To the Planispheare in this Topographicall Glasse you may also adde the Celestiall Zodiacke and another circle of the daies of the moneth inclusiuely the same or such like that are placed vpon the Horizon in Sandersons Globes by which you may gather the signe and neere the degr that the Sunne and Moone be in and if you doe but note the aspects in the Rundle of the moones age in their proper places you may thereby find what aspect the sunne and moone haue one to the other at any time Or thus you may find what signe the moone is in place the Index marked with f vpon a in the Planispheare where the degrees doe take beginning then count the age of the moone in her proper circle vnder which in the Planispheare make a marke to which marke turne the foresaid Index f noting the degree cut in the circumference for that is the distance of the sunne and moon which parted by 30 the quotient yeelds the number of signes and the remainder the degrées so that knowing the place of the sunne by any ordinarie Almanacke hereby haue you also the place of the moone by adding the distance of the sunne moone vnto the place of the sunne in the Almanacke as in March after the 10 day the signe is in Aries and by the rules before I find her distant from the sunne 60 degrees or 2 signes Therefore the moons must be in Taurus the deg are knowne by the deg that the sunne is in and by the deg cut by the Indexes as before Finally if in this vtter circle you character the aspects then also may you find the aspects betwixt the sunne and moone Many things Astronomicall might I open in the vse of this Glasse which for breuities sake I am forced to omit At this time I will conclude the vse of the Topographicall Glasse hoping I haue said sufficient to open the whole vse therof which containes matter sit for a great volume THE DESCRIPTION AND vse of the Plaine Table containing all such propositions as are most fit and familiar to be wrought thereon setting aside others as pertinent to curious demonstrations rather then apt to produce exactnesse and truth CHAP. XLIII To vse the Topographicall Glasse as the Plaine Table To alter the Topographicall Glasse to a plain Table YOu must take the circular sight boxe needle and all things of the foreside the Planisphere of the Glasse and so set the socket that is vpon the backside vpon the foreside the instrument so doth the backeside beeing a foure square plaine board stand vpwards next must you couer this smooth board with a sheet of white paper which fasten thereunto with mouth Glewe or you may haue folding Rulers as the plaine table it selfe to performe the same Lastly haue a Ruler with Sights as in the next Chapter to stand vpon this plaine Superficies and to the one side of the board in the thicknesse thereof with screw pins fixe the néedle and boxe in such order that the South line I meane not the line of variation make right angles with the side of the said board so haue you finished CHAP. XLIIII Of the Plaine Table with a description thereof and the parts thereunto belonging The Plaine Table THe Plaine Table or Geometricall Table is a right angled aequilater paralelogram made of a board of halfe an inch in thickenesse whose equall sides containe 9 or 12 inches the superficies whereof is made smooth and plaine some vse to make him represēt an Oblong al is one Some for ease in cariage vse to make this square board to consist of thrée péeces which they vse to ioyne together with certaine ledges such as bee at the end of Table boards as you may gather by the figure The edges of this table round about be abated with certaine square channels to the thicknesse of halfe the board according as you may gather by the shadowed lines about the table The ribs or for rulers of the Plaine Table 2 The peeces of this table being set
all the angles thereof To get a plat at many stations by the doctrine of the last Chapter FIrst set vp markes in euery angle of the field as in the last Chapter of this Booke then place your instrument in some place of the field and from thence draw lines from as many angles as you can see that are together and those lines measure and set the measured distances vpon the lines on the instrument from point to point drawe lines to represent so much of the hedge then appoint out some place for your second station whereunto measure and then drawe a station line setting the measured distance theron after this remooue your Table to that second station and there fixing it as it was at the first station which you shall obserue with your néedle as in the second proposition of the sixt booke before is taught Then from the center of your second station drawe lines to all the rest of the angles of the field which haue not lines drawne to them before or at least so many of them as you can see and measure the lines as at the first station this done choose a third station if before you could not see all the angles as you did a second stil obseruing that your néedle stand as at the first station and if at this third station you cannot sée all the angles yet vnmeasured you must againe choose a fourth station and the fift if néed require and thus proceed till you haue taken all the angles of the field and at last obseruing the measuring into euery angle as also the rules before taught you shall produce a figure proportionall and equall in angles to the plat or field presented which was the thing required to bee done The field is f g h i k l m n o p q r s wherein I plant my Instrument at a whence I cause the angles s f g h i and no more therefore I finish all those angles as in the last chapter and then find out another station as b where I plant my instrument as at a in all respects whence againe I may thence sée the angles k l m n and so procéed in the same order with those angles drawn to the second station b as I did at the first station a but for that at this second station I cannot yet sée all the angles in the field therefore I am forced to séeke a third station as c and there obserue the angles of o p q r which be all the angles which I protract and limit vpon the paper as before and you must note that the line a b and b c must be measured as well as a h and a i with all the rest and note that the néedle cut 40 deg at a and so must it doe at b and c and as many more stations as you should be occasioned to make for note generall causa breuitatis The South end of the Needle cuts like degrees in the card at euery station as at the first station This Chapter is remembred lib. 6. Geodetia Chap. 7. defi 5. CHAP. LIII To drawe the plat of a field by once placing the Instrument in an angle of the field and measuring round about the field because happly you cannot trauerse the same by reason of waters and such like impediments To plat by measuring about the field and yet but once placing the Table FIrst set vp the markes of euery angle then plant your table in such an angle from whence you may sée all the angles in the field then make a point on your table in a conuenient place to represent the pricke of your first station from whence drawe lines into each angle then measure first the hedges which are on the containing sides of that angle in which your table standeth and set those measures by the scale on that line which representeth it then measure the next hodge vnto it and take so many measures on the scale and set one of the féete of your compasse in the last made pricke and with the other foote strike an arch through the next line to it and note the interception thereof and from the pricke last made thereunto drawe a line which shall represent the second hedge and in this order measure about the field and strike an arch from line to line as in the first so shall you produce a figure proportionall to the field The figure is a b c d e f g the angle where the instrument is planted is a whence I drawe lines into euery angle as a b a c a d a e a f and a g then I measure the line a b and lay it downe then I measure the line b c and note where it intersects with a c as at c then I measure c d and note where it intersects with d so I go round about the field and produce a figure proportionall to the figure proposed CHAP. LIIII To take the plat of a field by the rule of the last Chapter where all the angles cannot be seene from one angle FIrst angle out the field then plant your table in one angle as in the last Chapter and from that angle get as great a part of the field as you can in order as in the last Chapter then plant your Table againe in an angle where your last measures ended in like fort situated as at the first station which you shall doe by setting the néedle on the same degrées it cut at the first station or looking backe as hath béene before taught from whence take all the rest of the field if you can there sée all the rest of the angles if not you may make a station or two more as occasion shall serue And so worke till you haue wholly inclosed the field so shall you make a figure on the table proportionall to the plat of the field with angles equall thereunto This Chapter differeth litle from the last onely you must performe that at many stations that there you did at one This agréeth with the 7 Chapter def 4. Geodetia CHAP. LV. To drawe the plat of a peece of ground by 2 stations and measuring but one line where all the angles of the field may be seene from both the places FIrst goe round about the field and set vp markes in euery angle thereof A plat of two stations then choose out your 2 stations something neere the middle of the field a good distance one from another in such sort that they lie not both in a straight line to any of the angles of the field but so that they may make as great angles with euery angle of the field as may be for the greater regard you haue in the choosing out your two stations the better will your lines intercept one from another Wherefore hauing thus made choyse of your stations the worke is performed As in the 31 Chapt. as you may gather by the demonstration C d f g h i k is the Peripher
fortified a Campe that C. Martius who had béene seuen times Consull of Rome right skilfully that when Sylla surnamed Foelix saw it said that the rest in comparison of him were blinde béetles knowing neither how to build or incampe When therefore you minde to build a house with your Scale and compasse lay downe the ground plat according vnto your proportion ordering your sellerage larder and all houses of office in as necessary forme as to you shall séeme most conuenient appointing places for great staires priuate staires houses of office chimnies c. that shall be most requisite for vse and least annoying or defacing the house or any of the principall lights chambers or roomes then according to your ground plat drawe the forefront or face side backe-side ends and gabell ends with all returnes iutteyes soyle péeces windowes c. euen as you determine to haue it made but draw it not as commonly these Painters do proportions of houses by the eye but lay it downe by your Scale and compasse that by the application thereof at any time you may know how many foote or inches any returne any gable end any story or window is in length or bredth which you shall be taught to do haply in some other place thus vpon seuerall papers set out euery seuerall part of your house whereby your selfe or the architector may informe the mechanical Carpenter of the length of euery seuerall péece of timber all things else required about the house as the number of boords for flooring and dooring the quantity of glasse and tile with the quantity of séeling rough casting pauing other such like whereby you may giue order to the Glasier for the bredth and length of your glasse to the Tiler for tile to the Plaisterer for lime to the Sawyer for boords procéeding no one thing staying for the finishing of another thereby proportion your house according to your purse Now for the addition of more delight vnto your house vpon the South side thereof set out a faire square garden beautified with bowers walkes and such like as your gardener can best deuise adioyning vnto which let there be a fine orchard planted with trées but if your clymate be hote as Spaine c. plant your garden in the North but for England the South is best vnlesse for some trées that naturally desire the shade let there be no oxe-stall dormant and filthy water stable or other thing that may bréed noysome smelles néere vnto your gaâ—den make the alleys drie for which I could teach you diuers deuises which here is no place for and plant the trées in your orchard after a Chequer forme that standing at any trée all the rest be in right line with you which forme is called a Quinqunx within your house make your staires large not with these monnell posts but with foure steps and a halfe pace a faire light answering to euery halfe pace Let the chambers be of a conuenient height ouer head and sufficient light albeit the chamber you lodge in would not be ouer light not yet a ground chamber inclining rather to cold then heat for by meanes of heat in sléepe we may procure a swoune because the heate of the body beeing become internall and cold externall this inclosing heat and that cold will striue let the place therefore be temperate and frée from noyse for sleepe is a a cessation of the common senses which béeing occupied troubled with noyse hindereth sléepe moreouer kéepe the beames of the moone from your bed for it is hurtfull to the sight to haue the moone shine vpon your eyes sléeping Touching the plats and formes of houses some affect the quadrant building with a square court inclosed in the middest like to the Colledges or as the Royall Exchange which indéed in respect of the columnes and arches making the vnder walkes is more stately againe some affect the Romane H. some other formes but that must bee partly referred vnto the pleasure of him that bestoweth the cost and for my part I intend not at this time to lay forth the diuersitie of plats and how they should be taken or laid downe by scale and compasse for that haply I shall open the same in another péece of worke more proper CHAP. XCVI Of the sinking of a Well and of the conueying of water in pipes IF you desire to find a place where digging a pit you may also find water fit to maintaine a well or pumpe you must ss Iean Liebault writeth earely in the morning your face into the East looke close by the ground if then you espy any vapour like to a little cloud rise out of the ground there if you dig is water to be found or if such vapoâ—rs rise in a dry and faire season also if you dig trenches foure or fiue foote déepe throwing therein wooll that is cleane and dry couering the same with leaues hearbes or such like if then this wool hauing lyen for a certaine space still remaine dry there is no water thereabouts to be found but if it be little wet or greatly wet there is little or great store of water to be found according as the wool was in wetnesse Also water is to be found vnder these insuing herbes Yarrow or Nose bleed Veruaine wild peniroyall Venus haire Cammomill Dogs tooth foxtaile trifoly Cinkefoile Millefoile Coliander or as some say where aboundance of gréene Ferne doth plentifully grow or as L. saith where any other gréene hearbs naturally flourish and abound without setting Your springs thus found they of longest continuance be which are in a gray or red grauelly rocke or ground in a blackish sandy clayie or red stony ground especially being mixed with stones and grauell Now for the pipes for the conueyance of water lead is good earth is better but wood of fir Alder or pine or such other wood that hath rosen in it is best such they vse now in conueying of waters to houses from the new water mil in Westminster they must be bored through with long agores first with a lesse one theÌ„ with a bigger any boughes or knotty péeces wil serue so they bée large when the poles so bored haue not ground to lye straight vpon but lye vneuen rising and falling there be crooked péeces of wood like elbowes prouided of purpose which are also bored through being let a foote at either end into the other two poles it ioyneth together so are all the poles that be ioyned one to another made to go into the end of one another a foote or more in manner as they péece bag-pipes or such like the hole in the end of the one pole receiuing the hollow end of the other pole into the same being alwaies for a foote déepe wider then the rest of the bore which you must ioyne together with good cement as you be taught before to do CHAP. XCVII A briefe discourse how to draw the platforme of any kind of building or any other thing
any altitude is leuell with your eye c. 19. p. 58 To search out lengths in heights c. 20. p. 59 To reduce parts of the right side the Geometricall quadrant into parts proportionall of the left side c. 21.61 To find lengths in heights by the Geometricall quadrant in the Glasse c. 22. ibid. To know how much one hill is higher then another 23.64 To know if water will run to the appointed place c. 24.67 To take the quantitie of any stationary angle c. 25.70 To make a protractor scale c. 26. ibid. To protract an angle and lay downe the ends c. 27. p. 71 To obserue an angle of position and protract it c. 28.73 To take the plat of a great chāpion c. c. 29. p. 74 To plat meadows plain fields pastures c. c. 30.75 To reduce lines hypothenusall into lines horizontal 31.76 Cōpendious forms of working by the Geod staffe 32.77 To square lands and to reduce irregular formes to regular c. 33.80 To search the perpendicular in any triangle c. 34.81 To reduce many plats or obseruations into one map 35.82 To diuide an Empire kingdom or continēt into Prou. 36.85 Reasons why the suns altitude hath bin hitherto falsly obserued 37.87 Paralaxes of the sunne ib. 88. A table of the sunnes paralaxe ib. 90 Correcting the taking of the starres altitude 38.91 To take the altitude or Almicanther of the sunne or any starre and to find their Azimuth 39.92 To take the amplitude of sun or starre 40.93 To get the houre of the day the houre of sunne rising or setting by the Topographical Glasse 41. ib. To find the houre of the night likewise hie water 42.64 Additions to the planisphere in the Glasse ib. 95 To vse the Topographicall Glasse as the Plaine table 43.97 A description of the plaine table 44.98 Absurdities vsed of many who affect the plain table 45.102 Things belonging to the vse of the plaine table c. 46.104 To take any horizontall distance by the plaine table c. 47. ib. Part of the distance of any thing giuen to find the rest ch 48. p. 107 To take the distances of two townes c. c. 49. p. 108 To find the horizontall distance from you by a newe way c. 50. p. 110 To draw the plat of a peece of ground at one station where all the angles of the field may be seene 51.112 To drawe the plat of any field where you can not see all the angles c. 52. p. 113 To drawe the plat of a field by once placing the instrument in an angle of the field and measuring the field round about c. 53. p. 115 To take the plat of a field by the rule of the foregoing Chapter where all the angles cannot be seene from one angle c. 54.116 To draw the plat of a peece of ground by two stations and measuring but one line c. 55.117 To draw the plat of a field by many stations and yet measure but one line in all c. 56. p. 118 To drawe the plat of a peece of wood-ground which for thicknesse one cannot set an instrument in c. 57.120 To drawe the plat of a field by setting his instrument in euery angle yet measuring but one line c. 58. p. 122 To take the plat of any champion field by the plaine table yet neuer change paper c. 59. p. 123 What chapter is fittest to vse in platting of ground what instrument to vse c. 60.124 A description of the circumferentor and the parts thereof c. 61. p. 126 Of the Sights longer shorter c. ib. p. 127 The Circumferētor his appellation and things generally to bee considered therein c. 62. p. 129. To take the Almincanther and Azimuth of the sun 63.130 To know in what part of the horizon any thing seene lieth c. 64. p. 131 To finde the houre of the day by sight of the sun c. 65. p. ib. To find the houre of sun rising and setting c. 66. p. 132 To find the amplitude of rising sun or starres c. 67. p. ib. Of the opposite degrees and how to find them c. 68.133 To find the quantitie of an angle c. 69. p. 134 To take the distance of any marke by the old Circumferentor c. 70. ib. To performe the last Chapter by protracting the Circumferentor ch 71. p. 135 To take an Altitude onely by the Circumferentor 72.136 To take the plat of a peece of ground by the old or new Circumferentor c. 73. p. 137 To take a plat at one station by the circumferentor 74.139 Degrees of a field being taken to finde the closing of the plat ch 75. p. Ibid. To reduce hypothenusall lines into horizontall c. 76. p. 141 To performe the same by a Quadrant ch 77. p. 142 To take Altitudes by such a Quadrant ch 78. p. 143 To take the declination of a wall chap. 79. p. ib. Suruey of a Mannor ib. p. 144 To make a Map and sea Carde ibid. p. 146. To discouer the true plat of a parke forrest c. c. 80. p. 148 To cast the contents of a parke chap. 81.153 To plat any field by intersectiō of lines c. 82. p. 159 To seeke the distance of a Turret c. 83. p. 158 To finde the length of any hypothenusal c. 84. p. 160 To finde the distance of two Towers c. 85. p. 162. To finde the distance of any thing from you 86. p. 165 To know whether a ship come to you or goe from you chap. 87. p. 167 A ship pursuing another when it will ouertake the former chap. 88. p. Ibid. How to take the platforme of a house Castle c. 89. p. 168 To discouer how Mines and Trenches run ch 90. p. 169 To place barrels of powder vnder Castles c. ch 91. p. 170 Whether a mine bee aboue or vnder the Horizon chap. 92 p. 171 To know which way it declineth ch 93. ibid. To build and situate a Cittie ch 94. p. 173 To build and situate a Mannor chap. 95. p. 174 To sinke a wel and conuey water pipes c. 96. p. 177 To draw the plat of a building or other thing not seene ch 97. p. 179 To make an excellent ruler for reducing plats chap. 98. p. 180 To burne any thing farre off with the Sunne beames ch 99. p. 182 To make a Glasse to discerne any small thing halfe a mile off as to reade a letter c. c. 100. p. ibid. How to buy annueties or money due afterwards ch 101 p. 183 The measuring of Solids and Plaines THe best time to fell Timber and to season boords chap. 1.186 To measure solid timber 2.187 To find the square of any tree growing 3.188 To find the square of a tree vnsquared 4.189 To find the square of a squared peece 5.190 To find the square of any flat peece 6.191 To find the square of a peece like a diamond 7.192 To find the square of peeces of 3 5 6 7 or 8 sides looke the 8 and 9 chap. p. 193 To find how much timber will make a foot square 10.195 To measure all sort of timber 11.196 Of surfaces and solide figures 12.197 Measuring contents superficiall and solide 13.200 To measure the aire or any plaine surface 14.202 FINIS You may haue any of the Instruments in this booke made of wood in Hosier lane neere Smithfield in London by Iohn Tomson The Glasse is made in brasse in blacke Horse-ally neere Flecetebridge by Elias Allin