not corrant by the Statutes of this Realme An other cause is by reason they are so vncertaine that they be neuer long at one rate And againe they are so different in so many places that it were matter inough for a great booke to speake sufficientlie of them all Howebeit yet because you shall not bée altogither ignoraunt of them I will shewe you the valewes of some that are moste in vse and first of Fraunce Frenche coines The most common money are Deniers Soulx and Franks 12 Deniers make 1 s 20 soulx make 1 Frank so that as you see these thrée kindes are like in the rate to penies shillinges and pounds with vs but that this is the difference that their Denier is but the 9 part of our pennie and so their soulx commonly called sowses go 9 to our shilling and 9 of their Frankes to an Englishe pounde of money So that 3 of their Franks make a noble And by those 3 may you practise how to reduce French mony into English mony And as for the rest of their coynes I will omit till an other time when I intend to shewe you the rate of sundry other kindes of mony But now as for the coynes of Flaunders they be so chaungeable Flaunde is Coynes that you must know theÌ„ from time to time els you cannot reduce them into our money certainely But yet that you may haue an example of their mony to exercise you withall you shall take those that be most common as Stiuers both single and double Grotes Flemmish Carolus and Gyldens A Flemish Grose is a litle aboue 3 farthings English A single stiuer is 1 d ob q. The double Stiuer is â— d q The siluer Carolus single 2 d q q. c. The double stiuer Carolus is 4 d ob q q. Then is there also the Carolus GyldeÌ„ which is worth 20 Stiuers And the Flemish noble is worth 3 Carolus Gildens and 12 Styuers Touching Danske mony they haue their soulx wherof 20 is a Liuer which is 2 s sterling They haue also their Grashe whereof 30 makes a Gylderne which is foure s sterling They haue also Dollors and their common or olde Dollor is 35 Grashe new Dollors they haue whiche be diuers some valued at 24 Grashe some at 26 and some at 30 and thus much I thought good to adde to the Author touching Danske mony But I will let them passe now exhorting you to practise to reduce those kinds into English money according as I haue sette forthe here following 2100 deniers make 240 d or 20 s 3240 deniers make 360 d or 30 s 8352 deniers make 928 d or 2 lb 17 s 4 d 2160 soulx make 240 shillings and so of other theâ— in â—ilie rate But if you wil reduce Flemmish money iustly you muste reduce it first into the smallest parte of Englishe money that is in that come as for example If I would reduce 368 double stiuers into English money considering that a double Stiuer containeth 131 d q you shall firste looke howe many q bee in the double Stiuer and you shall finde them 12 therefore multiply the summe of the stiuers by 13 and then haue you their valew in farthings which is 4784. Nowe if you diuide that by 4 then will there appeare the number of pence but better it were to diuide it by 48 for so manye farthings are in 1 shilling and then will the quotient declare the summe of the shillings Likewise if you would reduce any summe of single styuers into Englishe money you must multiply the summe first by 13 then haue you a certaine summe which summe if you diuide by 8 then wil amount the summe of pence or if you diuide it by 96 the summe of shillings will appeare But this marke in al diuision when ye do reduce to bring one denomination into an other ☜ if there be any remayner after the diuision that must be named by the denomination of the grosse summe that was diuided as for example I woulde bring 254 q into pence therefore I do diuide that 254 by 4 for so many farthings make 1 penny and the quotient is 63 whiche is the summe of the pence and then remaineth yet 2 whiche are farthings still as one maye proue by diuiding And this must be marked in all Diuision namely when it is done for Reduction Yet two words more added to the Author CoÌ„cerning Spanish mony wherof the most common mony are Cornados Marueides Ryalls and Duckets 6 Cornados make a Marueide 34 Marueids maketh one Ryall and 11 Rialls maketh one Duckate so the Ducket containeth 374 Marueids which to reduce into sterling mony English 34 Cornados maketh our penny or 5 Marueides 4 Cornados c. VVeights Thus muche haue I sayde of Mony nowe will I shew you in like sorte the distinction of weyghts after the statutes of Englande where the leaste portion of weight is commoÌ„ly a grayne meaning a grayne of Corne or wheate A Graine dry and gathered out of the middle of the eare A Penny of Troy Of these graynes in time passed â—2 wayed iust 1 peny of Troy and then was but 10 pennies in an Ounce An Ounce But nowe are there 46 pennies in an Ounce so that there are not fully 14 graynes in one penny But now of Ounces after Troy rate which is the standard of Englande 12 doe make 1 pound Haberdepoise vveights But commonly there is vsed another weight called Haberdepoise in which 16 ounces make a pounde Therfore when you would reduce ounces into poundes you must coÌ„sider whether your weyghts be troy weighte or Haberdepoise and if it bée Troy weyght you must diuide your ounces by 12 to bring them to pounds but if it bée Haberdepoise you must diuide them by 16. Now againe there bée greater weights which are called an hundred halfe a hundred A hundred vvaâ—ght a quarterne and also a halfe quarterne c. Scholler Why so there may be reckened 20 pounde 40 pounde 200 pounde and such innumerable Maister All these are numbers of weyght but they haue not common weights made to their rate as the other haue And agayne these that I did name are not iust in number as they séeme by their name for an hundred is not iust 100 but is 112 pounde And so the halfe hundred is 56 the quarter 28 and the halfe quarter 14. And these be the common weights vsed in most things that are solde by weight Howbeit there are in some things other nams as in wool VVoolâ— vveights Todde Stone· 28 pouÌ„d is not called a quarterne but a Todde and 14 pounde is not named half a quarterne but a Stone and the 7 pound halfe a Stone Other names bycause they differ in many places and agrée in few I let them passe Sacke But a Sacke of Wooll by the Statutes is limited to be 26 Stone Cheese vvaights Now in chéese though it be solde by the hundreth and
and all their proofs and some newe formes of workings c. Reduction with diuers declarations of Coines Waights and Measures of sundrie formes newly added with a newe Table containing most part of the golde Coines throughout Christendome with the true waight and valuation of them in currant money English c. Progression both Arithmeticall and Geometricall with diuers sundrie questions touching the same The Golden Rule of thrée and the Backer Rule of thrée with diuers questions therevnto belonging newly added augmēted The double Rule of Proportion The Rule of thrée composed of 5 numbers The Rule of Felowship both with time and without time Vnto all these are added their proofes The second Dialogue containeth The first 5 kindes of Arithmetike wroughte by Counters The common kindes of casting of accomptes after the Merchants fashiō Auditors also Numbring by the hande newly added The Contents of the second parte touching Fractions What a Fraction is Numeration in Fractiōs The order of working fractions with diuers familiar questiōs proponed for the perfit vnderstanding proof of ech of thē Multiplication Diuision Reduction of diuers fractions into one denomination in 3 varieties Fractions of Fractions Improper Fractions Fractions to the smallest denomination with easie rules how to conuert thē thervnto Fractions in other partes of things with a Table demōstratiue of their proportiōs Fraction and how it may bée turned into any other Fraction or into what Denomination you liste Againe of Multiplication Duplation Diuision Mediation Addition Subtraction The Golden Rule with diuers questions and their proofes The Backer Rule A question of Loane The statute of Assise of Breade and Ale recognised and applied to this time with newe tables therevnto annexed The Statute of Measuring of ground with a table thereof faithfully calculated and corrected Questions of Societie with the reason of the Rules and proofes of their workes To finde thrée numbers in any proportion The Rule of Alligation with diuers questions and the proofes of their workes with many varieties of such solutions The rule of Falshode or false Position with diuers questions and their proofes The Contents of the third Addition to this Booke The first Chapter entreteth of Rules of Breuity and Practise after a briefer Methode than euer yet was published in the English tong The second Chapter treateth of the briefer Reduction of diuers Measures as Elles Yeards Braces c. by Rules of Practise The third Chapter entreateth of the Rule of thrée in Broken numbers after the trade of Merchaunts somthing differing from Master Records order which is comprehended in 3 Rules The fourth Chapiter entreateth of Losse and Gaine in the trade of Merchandize The fifth Chapter entreateth of Losse Gain in the trade of Merchandize vppon time c. with necessarie questions therein wrought by the double Rule of thrée or the Rule of 3 composed The sixth Chapter entreateth of Rules of payment and of the necessariest Rules that appertaineth to buying and selling c. The seauenth Chapter entreateth of Buying and Selling in the Trade of Merchandize wherein is taken part ready mony and diuers dayes of payments giuen for the rest and what is won or loste in the 100 lb forbearance for 12 moneths c. The eight Chapter entreateth of Tares and alowances in the trade of Merchandize sold by waight and of their Losses and Gaines therein c. The ninth Chapter entreteth of Lengths and Breadths of Arras and other Clothes with diuers questions incident therevnto The tenth Chapter entreateth of reducing of Pawnes of Geanes into English yeards The eleauenth Chapter entreateth of Rules of Loane and Interest with diuers questions incident therevnto The twelfth Chapiter entreateth of the making of Factors The thirtéenth Chapiter entreateth of Rules of Barter or Exchange of Merchandize wherein is taken parte ware part readie money with their proofes and diuers other necessarie questions therevnto belonging The fourtéenth Chapter entreateth of exchanging of mony from one place to an other with diuers necessarie questions incident therevnto The fiftéeeth Chapter entreateth of sixe sundrie formes of practise for the Reduction of English Flemish and French money and howe eche of them may easily be broughte to others money sterling The sixteenth Chapter containeth a brief note of the ordinarie Coines of moste places of Christendome for traffique and the manner of their exchaunging from one Citie or towne to an other which knowen the Italians call Pary whereby they finde the gaine or losse vpon the Exchange The seauentéenth Chapiter containeth also a Declaration of the diuersitie of the waights and measures of moste places of Christendome for traffique at the ende wherof are two Tables the one for waight and the other for measure proportionated to an equalitie vnto our Englishe measure and waight wherby the ingenious practitioner may easily reduce the waight and measure of eche Countrey into other The eightéenth Chapiter entreateth of diuers Sportes and Pastimes done by Number FINIS A Collection of suche Tables as are contained in this Treatise A large Table of Numeration A Table of Multiplication A Table of Diuision A Table of the money currant in this Realm when the Author first published this booke A Table of all the vsuall siluer Coines nowe currant in this Realm newly added A Table of all the golde Coines in this realm with all the most vsuall Golde Coines thoroughout Christendome with their seuerall waights of Pence and Graines and what they are worth in currant mony Englishe Certaine Tables or Notes of the contentes of Ale Béere Wine Butter Sope Salmō Eeles c. both what suche vessels ought to containe by the Statute and what those vesselles emptie ought to wey A Table of the quantitie of drie measures as Peckes Bushels Quarters Weyes c. A Table of the proportion of measure touching Lengths or breadths to wit from the inche to the foote and so to the yeard the Ell with their partes the perch the rod the furlong the myle c. A Table made by Progression Arithmetical whyche contayneth a double table of Multiplication A Table of the Arte of Numbring by the hande A Table or demonstration of a figure or measure for the perfect vnderstanding of Fractions of Fractions A Table of the contents of the Statute for the assise of the waight of bread From 1 s the quarter to 20 s faithfully corrected and amended A necessarie Table of the Statute of measuring of grounde vpon the breadth giuen what length it ought to containe faithfully corrected according to the equitie of the statute wherein the Author declareth how necessarie this worthie Art of Arithmetike is vnto Gentlemen Students of the lawe and suche other as are desirous of infallible trueth Briefe Tables of the ready reducing of Englishe French and Flemish money eache into others common currant monies A briefe Table or collection of the common vsuall monies of moste places of Christendome for traffique the maner of their paymentes or exchaunging from one
they are lesser then pounds and many of them are contained in one of the other as so likewyse of other thinges whatsoeuer thing is compared to other if it be greater and containeth many of them it is a grosser denomination but if it bée lesser so that manye of them are in the other then are they called subtile denominations whereby you may perceaue that one denomination may be called a grosse denomination and also a subtile that is to say a great and small in diuers comparisons For shillinges compared to poundes are a Subtile or small denomination but compared to pennies they are a grosse or greate denomination Scho. Nowe I vnderstande the name I pray you teache me the vse Mai. The vse is easily learned if you remeÌ„ber what you haue learned before For if you will reduce any summe of a grosse denomination To reduce grosse denominatioÌ„s to subtile into a summe of a smaller or subtiller denomination you must consider howe many of that subtiler denomination doe make one of the grosser denomination and by that number or numerator doe you multiplie the other summe as if you woulde reduce 20 poundes into shillinges you must consider that in a pound are included 20 shillings therfore multiplie the one 20 by the other 20 and there will amounte 400 whereby you may knowe that in 20 pounde are contained 400 shillinges Likewise if you would reduce 30 shillinges into pennies considering that in 1. shilling are 12 pennies you must multiplie 30 by 12 and it will be 360 whereby you find that in 30 shillings are contained 360 pennies And thus may you reduce any grosse denomination into a more subtiller by multiplication if you know how many of the lesser doe make the greater of which thing I will anone giue you a bréefe table for the most accustomed kinds of money weights measures and tyme and such like whereby you maye knowe howe often eche subtile denomination is contained in the Grosser when you shall néede it for the foresayde kinde of Reduction And also the same shall serue you if you would reduce any summe of a subtiler denomination To reduce subtile denominatioÌ„ to grosse into a summe of a grosser denomination For in suche Reduction you must consider as in the other forme howe manye of the smaller doe make the greater and by that number must you diuide the other summe and the quotient will declare howe many of the greater denomination are comprehended in that summe as for example If you woulde know how many shillinges are contayned in 3240 pence consider that 12 pennies doe make 1 shilling you must diuide that 3240 by 12 and your quotient wil be 270 wherby you know that so many shillinges are in 3240 pennies But and you would knowe farther how many pounds are in those 270 shillinges séing that euery pound contayneth 20 shillinges diuide that 270 by 30 and it will be 13 and 10 remaining wherby you may know that in 3240 pennies or 270 shillings are 13 poundes and 10 shillings For euermore the remainer muste be named by the name or denomination of the summe that was diuided which in this place were shillinges ☞ And thus maye you doe with any other kindes of denominations Wherefore to the intent that you maye haue a lighte knowledge in the common Coines weights measures and such other I haue prepared here a briefe table whiche shall suffise to you at this time til hereafter at more conueniente opportunitie I maye instruct you more exactlie in the same Note gentle Reader these valewes of Englishe comes as they were when this Authour first published his Booke But in our time namelie An. 1582 they are much diuerse Therefore something to pleasure thee in this purpose I haue for thy benefit at the end of Reduction set downe and annexed a Table not onlie of our coines but also of the most parte of Christendome with their iust waighte and values currant in this Realme of England as by the same shall plainlie appeare A Table for English coines An 1540. A Soueraine Half a Soueraine A Roiall Halfe a Roiall A quarter Roiall An old Noble Halfe an old Noble An Angell Halfe an Angell A George Noble Half a George Noble A quarter Noble Englishe Coines A Croune Halfe a Crowne A Croune A Grote A harpe Grote A peÌ„nie of 2 pence A dandie pratte A pennie An half pennie A Farthing The valew of English Coynes The value of English Coines A Soueraine is the greatest english coin and containeth 2 Roials or 3 Angels eyther 9 halfe Crounes or 4 Crounes and an halfe that is to say 22 s 6 d Half a Souerain is equall with a Royall A Royall containeth an Angell and a halfe that is to say 11 s â— d Halfe a Royal containeth 5 s 7 d ob A quarter of a Royall containeth 2 s 9 d ob q An old Noble called an Henrie is worth 2 Crounes or a Noble and half that is 10 s Halfe an old Noble is worth 5 s An Angell containeth a Croune and halfe or 3 halfe Crownes that is 7 s 6 d Half an Angell is worth 3 s 9 d A Noble called a George is worth 6 s 8 d Half a Noble is worth 3 s 4 d A quarter of a Noble which in the old Statute is called a Farthing containeth 20 d A Crowne containeth 5 s and the halfe Croun 2 s 6 d Howbeit there is an other Croun of 4 s 6 d which is knowne by the rose side for the Rose hath no Crowne ouer it as in the other Crowne but it is enuironed on the 4 quarters with 4 floure deluces whereby you may best know it But I will returne to speake of the value of the coynes for I intend not now to describe the formes of them Now of gold are there no more common coynes In siluer the greatest is a Grote whiche containeth 4 pennies TheÌ„ is there another Grote called an Harp which goeth for 3 d Then next is a pennie of 2 d And then a Dandiprat worth 3 halfe pence Nexte it a pennie then half a pennie and last and least of all a Farthing whose coine is on the one side a crosse on the other side a purculles This I tell you because I sée manye that cannot know a farthing from a small halfe penie Now haue I tolde you all the Englishe coynes both of gold and siluer but yet of the thrée most coÌ„mon valewers of money spake I nothing that is to say of pounds Marks and shillinges whiche though they haue no Coynes yet is there no name more in vse then they of whiche the shilling contayneth 12 pennies or 3 grotes and the pound 2 old Nobles 3 George Nobles or 4 Crownes that is to saye 20 s A Marke two George Nobles that is 13 s 4 d Here would I now expresse the valewes of sundrie other coines of diuers countries but for three causes I now refrauâ—e The first and chiefest is because they are
and other my Countreymen in generall as I of good will sette forth the same A Table of the names and valuatioÌ„ of the most vsuall Gold coines throughout Christendome with their seuerall waight of Pence and Grains and what they are worth of currant mony Englishe The names and titles of the gold The vveight PeÌ„ny Grains The valevve Shil Pence Royall 4 23 15 0 Halfe Royall 2 11 8 6 Olde Noble 4 9 13 4 Halfe old Noble 2 4 6 8 Angell 3 7 10 0 Halfe Angel 1 15 5 0 Salute 2 5 6 4 2. parts of Salute 1 11 4 2 George Noble 3 0 9 0 half George noble 1 12 4 6 First crown K. H. 2 9 6 4 Base crown K H. 2 0 5 0 Great Soueraine 10 0 30 0 Souera K. H best 0 0 10 8 Edward Souera 3 14 10 0 Souera K.E. 3 14 10 0 Vnichorne of Scot 2 10 6 6 Elizab. Soueraine 3 14 10 0 Elizab. crowne 1 19 5 0 Scottish crowne 2 5 6 0 French Noble 4 16 13 4 Al the sorts of Frenche crownes 2 5 6 0 Old French cro 2 5 6 0 Flaunders Rider 2 6 6 6 Gelders Rider 2 2 3 6 Phillips Royal 3 10 10 0 Phillips crowne 2 5 5 0 Collyn Gilden 2 2 4 8 New Andr Gyld 2 3 5 0 Flanders noble 4 10 12  Flem. Angel best 3 6 9  Fland. real or Key 3 10 10  Carolles Gylden 1 21 3 6 Flanders Royal 2 6 5  Saxon Gylden 2 2 4 8 Flanders crowne 2 5 6  Phillips Gylde 2 3 4 2 Golden Lyon 2 16 7 8 3. parts of gol Ly.  21 2 5 2.3 parts gol Ly. 1 19 4 11 Dauids Gylden 2 2 â— Â Horne Gylden 1 12 4 11 Old Andre Gyld 2 4 4 10 Crusado long cros 2 6 6  Crus short cros 2 6 6 2 Myl rayes 4 20 13 4 Half Mill rayes 2 10 6 8 Portigu 1. ounce 2 16 3 lb. 8 s  Portigu 1. ounce 2 18   Golden Castilio 2 23 8 10 Ducket of Castile     Ducket of Arags 2 6 6 6 Hungarie Ducket 2 7 6 4 Double Pistolate 4 8 11 8 Single Pistolate 2 4 5 10 Ducket of Valens 2 6   Ducket of Floren. 2 5 6 4 Double Ducate 4 11 13  Single Ducket 2 6 6 6 Dou. duc of Rome 4 13 12 8 Of siluer coines currant in this Realme The Edward Crowne of 5 s The Edward halfe crowne of 2 s 6 d The Edward shilling halfe shilling and the 3 d Philip and Maries shilling and half shilling The Marie groat and Marie 2 d Quéene Elizabeths shillings 6 d 4 d 3 d 2 d 1 d 3. ob and 3 q It is to be vnderstoode gentle Reader that whereas the waight is called by the name of a penny Note it is not meant a penny of siluer money but a penny of Goldsmithes waight which is 24 Barly cornes drie And xx of these pence make an ounce and twelue of these ounces make a pouÌ„d Troy So that if a man haue not the waight where with to wey any péece that may come to his hand hée may do it with the Barly graines or cornes being drie and taken out of the middle of the eare Nowe to Progression PROGRESSION ALthoughe vntill this day the most parte of writers haue defined Progression as a coÌ„pendious kinde of Addition yet truelye it is not so for progression as the verie nature of the worde doth informe any man is a going forwarde and proceeding in numbers and that regularlie and orderlie whose place is aptlye chosen to be verie â—eare or rather next after the exposition of the four principal partes of Arithmetike for in it after a moste easie manner are all the foure former partes exercised and practised and not onelye Addition as customablie is done Whiche custome hathe bene the cause why it hathe so speciallye bene named a kinde of Addition and defined to bée a quicke and briefe Addition of diuerse summes procéeding by some certayne and reasonable order You shall also vnderstande that there are infinite kinds of progressions but for you as yet two are sufficiente to be exercised in of which the one I cal Arithmeticall and the other Geometricall Arithmetical progression Arithmetical progression is a rehearsing or placing downe of manye numbers number after number in such sort that betwéene euerie two nexte numbers rehearsed or placed downe the difference diuersitie or excesse be equal and alike Scho. Syr I thanke you for that you haue both opened vnto me what Progression is truly and also why it is here placed But I pray you with an example make plaine your definition Ma. Examples can not want séeing al reasonable creatures naturallie vse the order of one kind of Arithmetical progression whiche therefore is also named Naturall when so euer they distinctlie doe counte or number any multitude one by one saying 1.2.3.4.5.6 wherby the procéeding from number to number and euerie one surmounting and excéeding his fellow next before by a like quantity which here is 1 declareth the same to be Arithmeticall progression And for the more plainnesse I set it down in this maner Sc. This is most euideÌ„t And I thinke that I am able to tel you now of any progression Arithmetical propounded what is that common excesse or difference wherby it procéedeth if this order be kept in it M. What say you of 3.6.9.12.15 Sc. They excéede eche other by 3. And that may I set down in such euident order as you did your example of Natural progression in this wise Maister And doe you not also nowe perceiue that the whole table of Multiplication maye be made by the order of progression Arithmetical either if you wil begin at the first number of any of them on the left hande and so procéede right ouerthwarte or at any of the first numbers of the vpper rowe and goe directly downward Sch. I pray you let me consider the thing a little and I wil answere you 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 By this triall I perceiue it nowe verie well for the common excesse or difference betwéene any two next is continually as much as the firste number of euerie rowe either from the lefte hande ouerthwarte taken or from any of the vppermost ouerthwart rows downward Ma. Nowe then if of any suche progression you woulde spéedelie knowe the totall summe muche quicklier thaÌ„ by common additions rules To knovv the total sum of an Arithmeticall progression first tell howe many numbers
pence the price of the lb of flax for the thirde number TheÌ„ Multiply and diuide and you shal find 9 â—8 5â— d And for so much shal he sel the pound of flaxe in barter 6. Rule Two are willing to exchaunge merchaundise the one hathe Norwiche Grograines at 35 shillings the péece redie money And in barter he will haue 30 shillings and he will haue the ¼ parte of his ouer price in readie money The other hath Norwich Stockings at 40 shillings the Doosen to sell for readie money But in as much as the first Merchaunts Grograins are no better he woulde deliuer them so to ballance the barter that he may gaine after 10 lb in the 100 lb The question is now how he shall sell his hose the doosen in barter Answere Say if 100 giue 110 what shall 40 s giue which is the iuste price of the dozen of stockings multiplie and diuide and you shall finde 44 s Then take the ¼ of 30 s whiche is 7 s 6 d And subtracte it from 25 s and also from 30 s And there will remaine 17 s 6 and 22 s 6 d for the two firste numbers in the Rule of thrée and 44 s which is the iust price with his gaine in the dozen of stockings for the thirde number Then multiplie and diuide and you shall finde 56 s 6 6 7 and for so muche he is to sell his dozen of stockings in barter 7. Rule Two Merchantes will chaunge theyr merchandise one with the other the one hath 720 Elles of Cambricke at 5 s the Ell to sell for readie money but in barter he requireth 6 s 8 d And yet notwithstanding hée loseth by it after 10 lb vppon the 100 lb wherevppon he requireth the ½ of his ouer price in readye money And the other Merchant hauing skill ynoughe to make the barter equal deliuereth English Saffron at 30 s the lb The question is now what his Saffron coste the pounde in readie money Answer You muste firste séeke what is lost vpon the 100 lb which to do you may say if you please if 100 lb loose 10 what shal 6 â…” s loose worke and you shall finde â…” shillings or eight pence whiche muste be rebated from 6 s 8 d So resteth 6 shillings still or you may say if 100 lb giue me but 90 lb what shal 6 s 8 d giue Worke this waye either and you shall finde also as before directly in your quotient 6 s your desire Then are you next to cast vp what the 720 elles of CaÌ„brick commeth to at 6 s 8 d the ell and you shall finde 240 pounde the ½ whereof the Cambricke Merchaunt wil haue in readie money which is 120 pound nextly you muste caste what the Cambrick coÌ„meth to after his losse in the 100 lb whiche as you founde is but 6 s an ell and you shal find 216 lb now must you subtract his readie money which is 120 lb out of 240 lb also of 216 lb. And there wil remaine 120 lb 96 lb for your two first numbers in the Rule of thrée and 30 s the ouerprice of your Saffron for the third nuÌ„ber Then multiply and diuide and you shal find 24 s and so muche didde hys Saffron coste in readie money Two Merchants barter the one hath 50 Clothes to put away for readie mony at 11 lb the Cloth and in barter putteth them awaye for 12 lb taking Hollande Cloth at 20 d the Flemmish Ell whych was worth no more but 18 d The question is nowe what Holland payeth for the Cloth and what he winneth or looseth by the bargaine Aunsweare 50 Clothes at 11 lb the Cloth commeth to 550 lb and put away at 12 the péece maketh 600 lb Then to finde what Holland payeth for the Cloth Say by the Rule of thrée direct if 20 d buy 1 Ell what 600 lb worke and you shall finde 7200 Elles Nowe to finde the estate of his gaine or losse you must séeke what his 7200 Elles commeth to at 18 d the Ell worke by the Rule of Proportion direct and you shal finde 540 lb which is not so muche as his Clothes were worth in readie mony by 10 lb and so much lost the first Merchant by his exchange A Venetian hath in London 100 péeces of Silke to put away for ready mony at 3 lb the péece But in Barter he delyuereth theÌ„ for 4 lb the péece taking woolles of a Felmonger at 7 lb 10 s the C. waight which was worth no more but 6 lb the C. in ready money The question is now what woolles payeth for the Silkes and whiche of them winneth or looseth by the barter Answer 100 péeces of Silkes at 3 lb is 300 lb and at 4 lb is 400 lb Then to find what woolles payeth for the Silke Saye by the rule of thrée direct If 7 ½ d buy me 1 C. waight what 400 lb worke and finde 53 â…” C. waight of wooll Nowe to finde the estate of their gaine or losse caste vppe his wooll at 6 lb the C. for so muche they were worth readie mony and you shal find 320 lb which is 20 lb more than the Silkes were to be solde for in readie money wherevppon the Venetian gained 20 lb by the Barter A Merchant hathe 53 â…“ C. waight of wooll at 6 lb the C. to sel for ready monyâ— but in barter he will haue 7 lb 10 s and an other doeth barter wyth hym for Silkes which are worth 3 pounds a péece ready money The question is now how he ought to deliuer his Silkes the péece in barter and howe manye payeth for the woolles Answere Say by the Rule of Proportion or the rule of thrée direct If 6 lb for a C. waight readie money yéelde me 7 lb 10 s what will 2 lb yéelde which is the iust price of a péece of Silke in barter To make the Trucke equall worke and find 3 lb 15 s the price of a péece of Silke in barter then saye if 3 lb 15 s require 1 péece of Silke how many péeces of Silke are bought wyth 400 lb whiche is the valewe of the 53 ½ C. waight of wooll at 7 lb 10 s worke by the Rule of thrée direct and you shall finde 106 péeces of Silke and â…” of a péece and so many péeces of Silke payeth for the woolles and neither partie hath aduantage of other Two Merchants wil change merchaÌ„dize the one with the other The one of theÌ„ hath béere at 6 s 8 d the Barrell to sell for ready money but in barter he will sell the barrell for 8 s and yet he wil gaine moreouer after 10 lb vpon the 100 lb and the other hath white Spanish wooll at 20 s the Roue to sell for ready mony the questioÌ„ is now how he shal sell the Roue of wooll in barter Answere Saye if 6 â…” s whiche is the iuste price of the barrell of Béere be solde in barter for 8 s for how much shal 20 s whiche
is the iuste price of the Roue of wooll bée solde in barter worke by the Rule of thrée direct and you shall finde 24 s Then for because the firste Merchant will gaine after 10 lb vpon the 100 lb he maketh of his 100 lb 110 lb And therefore say by the Rule of thrée if the second Merchant of 110 lb doe make but 100 lb howe much shall he make of 24 s Multiply and diuide and you shall finde 21 s 9 d 9 11 of a penny And for so much shal he sel the Roue of wooll in barter Two Merchants wil change their coÌ„modities the one with the other The one of them hath white Paper at 4 s the resme to sell for ready mony And in barter he will doe it away for 5 s and yet he wil gaine moreouer after the rate of 10 lb vpon the 100 lb and the other hath Mace at 14 s 6 d the pound waight to sel in barter Now I demaund what the pouÌ„d did coste in readie money Answere Say if 5 s whiche is the ouer price of the paper in barter be come of 4 s the iuste price of howe muche shall come 14 s ½ which is the surprice of the pound of Mace in barter Multiplie and diuide and you shall find 11 s 10 d Then for because the first Merchant of Paper will gaine after the rate of 10 vpon the 100 Say if 100 do giue 110 what shall 11 â…š s giue worke and you shal finde 13 s 0 d â…• and so muche didde the pounde of Mace coste in readie money The fourteenth Chapter entreateth of Exchaunging of money from one place to an other EXchaunge is no other thing then to take or receiue money in one Citie to render or pay the valewe thereof in an other Citie or else to giue mony in one place and receiue the value thereof in an other at terme of certaine dayes moneths or fayres according to the diuersitie of the place But this practise chiefly consisteth in the knowledge of the Mony or Coines in diuers places of which for thy benefite after a few examples giuen to the Introduction to thys worke I wil set down by certaine notes of diuersitie of the common and vsuall Coines in most places of Christendome for trafique And first I will beginne at Antwerpe where they vse to make their Accomptes by Deniers de gros that is to say by pence FleÌ„mish whereof 12 doe make 1 s Flemmish and 20 s doe make 1 lb de Gros. Item a Merchaunte deliuered at Antwerpe 400 poundes Flemmishe to receyue in London 20 s sterling for euerie 23 s 4 d Flemmishe The question is nowe howe muche sterling money is to be receyued at London for the saide 400 pounds Flemmish Answere Saye by the Rule of thrée if 23 â…“ Flemmishe giue 20 s sterling what 400 poundes Flemmishe worke and you shall finde 342 lb 17 s 1 5 7 d and so muche sterling shal I receiue in London for the 400 lb Flemmishe Otherwise also wrought by Rules of Practise in taking the 1 7 of the Flemmish money deliuered and abating the same from the principall the rest is Englishe money sterling as before A Merchant at London deliuereth 200 pound sterling for Antwerpe at 23 s 5 d Flemmishe the pounde sterling The question is how muche he muste receiue at Antwerpe Answer Say by the Rule of thrée if 1 lb sterling giue 23 s 5 d FleÌ„mish what 200 lb sterling worke and you shall finde 234 lb 3 s 4 d So many pounds Fleshmish shall he receiue at Antwerp for the said 200 lb sterling Otherwise also by Practise In LondoÌ„ 200 lb sterling is deliuered by exchange for Antwerpe at 23 s 9 d Flemmishe the lb sterling The question is what rate the Flemmishe money ought to be retourned to gaine 4 lb vppon the 100 lb sterling at London Answer First say by the rule of 3 direct if 1 lb sterling giue 23 2 4 Flemmishe what 200 lb sterling Multiplie and diuide and you shall finde 237 lb 10 s The whiche to returne to gaine 8 lb sterling in London Say by the Backer Rule if 200 lb sterling require the exchaÌ„ge 23 s 9 d Flemmish what the exchange to make 208 lb styrling worke by the Rule and finde 22 s 10 d 1 26 d Flemmish the effect in the question required If I take vppe money at Antwerpe after 19 s 4 d Flemmish to pay for the same at London 20 s sterling and when the day of payment is come I am forced to returne the same mony againe in LondoÌ„ to pay my Bill of Exchange So that for 20 s whiche I take vppe here at London I muste paye 19 s 6 d at Antwerpe I demaunde whether I do winne or lose and howe muche in or vpon the 100 lb of money Answer Say by the rule of thrée If 19 ½ giue 19 â…“ what will 100 lb giue Multiplie and diuide and you shall finde 99 lb 2 s 106 117 whiche being abated from 100 lb there will remaine 9 s 11 117 and so muche do I lose vppon the 100 lb of money If I take vp at London 20 s sterling to pay at Antwerpe 22 s 4 d and when the daye of payment is come my Factor is constrained to take vp money againe at Antwerpe wherewith to pay the foresaide summe and there he doeth receiue 23 s 4 d Flemish forthwith I muste pay 20 s at London the question is now whether I do winne or loose and howe muche vpon the 100 lb of money after that rate Answere Say by the rule of Proportion if 22 â…“ s giue 23 â…“ s what will 100 lb giue Multiplie and diuide and you shall find 104 lb 9 111 201 s from the which abate 100 lb and there will remaine 4 lb 9 5â—1 201 s and so much is there gained vpon the 100 lb of money In Antwerpe is deliuered 200 lb Flemish by exchaunge for London at 20 s sterling for euerie 23 s 4 d Flemmishe The question is at what rate the same is to be returned to gaine 5 lb vpoÌ„ the 100 lb Flemish in Antwerp Answere First say by the rule of thrée if 23 â…“ Flemish giue 20 s what shall 200 lb giue worke and you shall finde 171 lb 8 s 6 6 7 d Then say againe by the Rule of thrée direct if 171 lb 8 s 6 6 7 sterling giue me 210 lb Flemishe what shall 20 s sterling giue worke and you shall find 24 s 6 d Flemish And at the same rate ought the same to be returned at Antwerpe to gaine 10 lb vppon the 100 Flemish A Merchaunt of Antwerpe deliuereth 234 lb 3 s 4 d Flemish to receiue at London 200 lb sterling the question is nowe how the Exchange goeth after this rate Answere Say by the Rule of 3 direct if 200 giue 20 what giueth 234 â…™ Multiplie and diuide and you shall find 23 s 5 d and for so muche goeth the Exchaunge Item the Exchange from
London into France is not like as it is in Flanders but is deliuered by the French Crowne whiche is worth 50 soulx Turnois the péece Wherevpon also you muste note that in France they make their accoÌ„pts by Franckes Soulx and Deniers Tournois whereof 12 Deniers maketh 1 Soulx Tournois and 20 soulx maketh 1 lb Tournois whiche they call a Liure or Franc. But the Merchauntes to make their accompts do vse French crowns whiche is currant among them for 51 soulx Tournois But by exchange it is otherwise for it is deliuered but for 50 Soulx Tournois the Crowne or as the taker vp of the money can agrée with the deliuerer And note that this 🜄 Caracter representeth the Crowne by exchaunge and is euer 50 soulx Tournois or French money A Merchaunt deliuereth in London 240 lb sterling after 5 s 6 d sterling the Crowne to receiue at Paris 50 soulx Tournois for euerie Crown I demaund howe muche Tournois or French mony payeth the billes for the said 240 lb sterling Answere Saye by the Rule of thrée if 5 ½ s sterling giue me 50 s Tournois what shall 240 lb sterling giue Reduce the pounds into shillings then multiplie and diuide and you shal finde 2181 Liuers 16 soulx 4 Deniers and 4 11 Tournois and so much paieth the bils at Paris for the said 240 lb sterling A Merchant deliuereth in RoaÌ„ or elsewhere in Fraunce 1430 lb or Francks the whiche Francke or lb is 20 soulx or pound Tournois to receiue in London 6 s 4 d sterling for euery 🜄 of 50 soulxe Tournois The question is howe much sterling mony I ought to receiue at London for my 1430 pound Turnois Answere Say if 2 ½ lb giue me 6 â…“ what wil 1430 giue me worke and you shall find 3622 s â…” sterling which maketh 181 lb 2 s 8 d and so much money is to be receiued at London for the saide 1430 Liuers Tournois after 6 s 4 d for euery crown of 50 soulxe In London is deliuered 200 lb sterling by exchange for Paris at 5 s 9 d the 🜄 of 50 soulx Touâ—nois the question is at what price the saide Crowne is to bée returned to gaine 6 lb vppon the 100 lb sterling at London Answere Firste say by the Rule of thrée direct if 5 ¾ sterling giue 50 soulx Turnois what shall 200 lb sterling giue worke and you shall finde 1739 Franckes or Liuers 2 soulx 14 2â— Then the which to returne and gaine â— lb vpon the 100 lb in London Saye by the Rule of three direct if 17â—9 Francks 2 soulx 14 23 yeelde 1 lb. what the 🜄 of 50 soulx worke and finde 6 s 1 d 7 50 the effect required in the question A Merchant deliuered in London 160 lb sterling to receiue in Biskaie for euerie 5 s 6 d 1 Duckate of 374 Marueides the question is howe many Marueides I ought to receiue at Biskate Answere Say if 5 ½ s sterling giue 374 Marueides what shall 100 lb sterling giue Multiplie and diuide and you shall finde 217000 Marueides and so many I oughte to receiue at Biskie for my 160 lb sterling A Merchant deliuereth in Bayon 20000 Marueides to receiue in London 5 s 8 d sterling for euery Duckate of 374 Marueides the question is now howe muche sterling money payeth the Billes of Exchange for the saide 20000 Marueides Answere Say if 374 Marueides make 1 Duckate what 20000 Marueides Multiplie and diuide and finde 106 Duckates 178 187. Then saye againe if 1 Duckate giue 5 2 â— s what giueth 106 178 187 Duckates worke and finde 30 lb 6 s and 34 56â— s whiche is worth â—â—â— 561 partes of a penny Otherwise it is wrought more briefer at one working as in the laste question before in considering that 5 s 8 d containeth 1 Duckate or 374 Marueides Therefore say by the rule of 3 if 374 Marueides giue 5 â…” s what 40000 Marueides worke and you shal also finde in your quotients 30 lb 6 s 34 561 and so many pound sterling is to be receiued for the 40000. Duckats In London 200 lb deliuered by Exchange for Vigo 374 Marueids the Duckate of 5 s 10 d sterling maketh 256457 1 7 Marueides the whiche io returne and gaine 10 lb vpon the 100 lb in London Saye by the rule of thrée directe if 220 lb require 256457 1 â— Marueides what 5 s 10 d worke and finde 340 Merueides prises of euerie Duckate in returne which is the effecte in the question required These may séeme sufficient for enstructions NOtwithstanding for thy further aide and benefite hereafter followeth 6 speciall and moste briefe Rules of Practise for English French and Flemmish money 1 teacheth how to turne Flemish to English sterling 2 teacheth how to turn English sterling to Flemish 3 teacheth how to turne Flemmish to French 4 teacheth how to turne French into Flemmish 5 teacheth how to turne sterling into French 6 teacheth lastly how to turne French into sterling The fifteenth Chapter entreateth of the saide 6 Rules of breuitie and of valuation of English Flemish and French money and how ech of them may easilie bee brought to others value How brieflie to reduce lb s and d Flemish into lb s and d Englishe Sterling IT is to be noted that 7 pound Flemish maketh but 6 lb. sterling 7 s Flemishe maketh 6 s sterl and 7 d flem. 6 d sterl So that 7 yéeldeth but 6. Wherin is euideÌ„t that there is lost 1 7 if it may be so called when it is reduced into English money Wherefore to know how much 233 lb. 13 s 4 d flemish maketh English you must subtract from it 1 7 beginning with the pounds c. and that whiche resteth after this subtraction is the sum required so that 233 lb 13 s 3 d flem. maketh 200 lb 5 s 8 4 7 d sterling Example An other Example To reduce lb s and d ster into lb s d flem. Note that a lb sterling maketh 1 lb 3 s 4 d flem. that is 1 lb â…™ 1 s ster maketh 1 s â…™ flem. and 1 ster maketh 1 â…™ Flem. So that there is gained if it may so be called â…™ of the summe being thus reduced to Flem. For of 6 6 is made 7 6 which is 1 whole and â…™ Then to knowe how much 237 lb 7 s 6 d ster maketh Flem. subtract from your ster the â…™ of the whole summe and adde it to the same summe and it maketh 276 lb 18 s 9 d whiche is the summe required Example An other example Ye shal note that the equalitie of Flemish and French mony is this that is to say the lb Flemish maketh 7 lb â…• French or Turnois 1 s Flemish maketh 7 s â…• French a great Flemish maketh 7 d â…• French Wherefore to knowe howe muche 143 lb 4 s 9 d Flemish maketh French Ye must multiplie the whole number twice by 6 beginning at d and so forwarde and the product of your second
acquainted wyth thys Goldon Rule I haue here proponed 6 questions and their aunsweres whiche I thinke moste conueniente and méete to preferre the desirous to perfecte vnderstanding The firste foure are all braunches of one Question sproong out of the beste trée for a young learner to taste of that groweth in this Grounde of Artes for that no manner of Question in the Rule of 3 what so euer it bée can be proponed but it muste be comprehended vnder the reason or style of one of these foure The Questions be these If 15 elles of Cloth coste 7 lb. 10 s what comes 27 elles too at that price Aunsweare 13 lb. 10 s If 27 elles coste 13 lb. 10 s what are 15 elles worth Answere 7 lb. 10 s If 27 elles coste 13 lb. 10 s howe manye elles shal I haue for 7 lb. 10 s Answere 15 elles If I sell 15 elles for 7 lb. 10 s howe manye elles are to be deliuered for 13 lb. 10 s Answere 27 elles If 8 pound of any thing cost 16 s 6 d what money is to be receiued for 49 pounde Answere 2 lb 4 s 11 d If 4 lb. of anye thing coste 17 d what money wil 8765 pound of that commoditie cost Answere 155 lb. 4 s 3 d farthing Of all which questions I omitte the work of purpose you shoulde whet your wit there by at conuenient leasure to climb ech branch and gather the fruite of them And doe minde nowe before we make ad ende of this Rule to giue you some Instructions of the Backer Rule of 3. whose order is quite contrarye to thys that you haue learned For in thys Rule hitherto euermore looke how muche the thirde number is greater than the firste so muche the fourthe number is greater then the seconde And contrarye wayes loke howe much the firste summe is greater then the thirde if it doe chaunce so so much is the second summe greater then the fourth But in this Rule there is a contrary order as this That the greater the third summe is aboue the first the lesser the fourth sum is beneth the seconde and this rule therfore you may call the Backer rule The backer rule as in example If I haue boughte 20 yardes of cloth Question of buying cloth of 2 yards breadth and woulde buy canuas of 3 yards brode to line it withall howe manye yards should I néede Sc. Why there is none so broade Mai. I doe not care for that I doe put this example only for your easie vnderstanding For if I should put the example in other measures it would be harder to vnderstand But nowe to the matter If you woulde know this question set your numbers as you did before but you shall multiplie now the first number by the seconde and that ariseth thereof you shall diuide by the third which thing if you doe here I meane if you multiplie 30 by 2 it will be 60 which summe if you diuide by 3 there will appeare 20 whereby I knowe that if 30 yardes of cloth of two yardes broade should be lined with canuas of thrée yardes broade 20 yards of canuas woulde suffice as this figure sheweth And nowe because yée found fault at my example how say you perceaue you this Sc. Yes sir I suppose Mai. Then aunswere me to this questioÌ„ how many elles of canuas of elle breadth will serue to line 20 yards of Saye of thrée quarters brode Sc. In good faith sir I cannot tell for I know not how to bring the summes to like denominations Maister Then wil I tel you sith there is mention here of quarters and againe euerye one of the measures both elles and yardes may be parted into quarters do you parte them so both in the breadth and length and then put forth the question by quarters Scholer Then I shall say thus Howe manye quarters of canuas of fiue quarters broade wil line 80 quarters of 3 quarters brode Mayster Now aunswere to the question Sc. First I wil set them downe in their forme thus for 5 is ioyned with the question and is therefore the third number then is 3 the number of the same denomination I meane because they be both referred to breadth Now I multiplie 80 by 3 and it is 240 which I diuide by 5 and it yieldeth 48. Then saye I that 48 quarters of 5 quarters broad will suffice to line 80 quarters of 3 quarters brode Ma. Turne the quarters againe into elles and yardes Sch. Then I say that 9 elles and thrée quarters of a yarde of elle broade will serue to lyne 20 yardes of thrée quarters brode as this figure sheweth * M. Now what say you to this questioÌ„ I lent my friend 400 lb for 7 months now how much money ought he to leÌ„d me again for 12 moneths to recompence my curtesie shewed him Can you aunswere to this Sc. Yes sir I suppose for I wil set down my nuÌ„bers thus where I multiplie 7 into 400 and it maketh 2800 whiche I diuide by 12 and it yieldeth 233 lb and there is 4 lb. remaining of my Diuision what shall I doe therewith Mai. Turne that same 4 lb into s and then diuide it by 12 as you did before Sc. Well sir it shall be done so haue I 6 s for my quotient and yet remaineth 8 s vpon my diuision Ma. You must also reduce 8 s into pence which maketh 96 and diuide that also by your first diuisor Sc. So haue I done and I finde 8 pence for my quotient and nothing is left Ma. This must you alwayes doe when any thing remaineth vppon your diuision whether it be mony weight measure or any kind of thing whatsoeuer This rule is so profitable for all estates of men that for this rule onlie if there were no more but it all men were bound highly to estéeme Arithmetike By this Rule maye a Captaine in warre worke many things as Maister Digges in his Stratiaticos doth notably declare Onlie nowe in this my simple addition for a taste and incouragemeÌ„t I wil enlarge the Author with a questioÌ„ or ij more wishing you euerie my couÌ„triemen or GentlemeÌ„ whatsoeuer that by nature be anye thing giuen to Millitarie affaires to be familier and wel acquainted with this Exceliente Arte the whiche he shall finde not onely at the Sea but also in the Campe and Fielde seruices aboundantly to aide him either in fortificatioÌ„ or in paying of Souldiors wages how differente soeuer their paye be Charges of Ordinaunce pouder shot Munition and instrumentes whatsoeuer but now to the question If it should chaunce a Captaine whiche hath 40000 souldiers Question of prouision touching aâ—aâ—â—ate to be so inclosed with his enemie that he could haue no fresh purueiance of vittailes and that the vittailes which he hath would serue that armie but only 3 moneths how many men should hée dimisse to make the vittaile to suffise the residue 8 moneths Sc. As you taught me I set the nuÌ„bers thus saying
coÌ„panioÌ„s bought 2000 shéepe and paide for them 241 lb. 13 s 4. d of which sum one paide 101 lb Question of Sheepe 10 s The second paid 82 lb. 17 s 10 d And the third paide 57 lb 5 s 6 d How many shéepe must each of them haue Answere The first shal haue 840. The second 686. And the third 474. And that must you worke thus Solution Firste considering that your money is of diuerse denominations you shall by Reduction bring it all into the smallest denomination whiche is in it that is to saye pence and so will the total sum bée 58000. pence Now if you turne eache mans mony into pennies also the firste mannes summe will be 24360 pence The second mans summe 19894. pence And the third mans mony wil be 13746. pence Now to know how many shéepe euery maÌ„ shal haue let the whole sum of money that is 58000. pence in the first place in the secoÌ„d place set the number of shéepe and then orderly in the thirde place set eache mans money and then multiplying the thirde and the seconde summes togither and diuiding that that amounteth by the firste there will appeare the number of shéepe that eche man ought to haue as these thrée figures do shewe Scholer Why doe you set the mony in the first place séeing in the question you saye 2000 sheepe cost 58000 d not thus 58000 d cost 2000 sheepe Mayster You remember I taught you at the beginning of this Goulden rule that the firste and thirde numbers must bée of one name and of like thyngs and euermore the number that the question is asked of must bée sette in the third place Now is the question playnely this If foure men bought 2000 sheepe for 58000 pence howe many sheepe shall each man haue But seing in this question there ought more respect to be had to the summe of mony than to the summe of the persons for in the suÌ„mes of mony is there proportion toward the sheepe and not in the number of persons therefore must wée turne the question thus If 18000 pence bought 2000 shéepe how many did 24360 s buy Agayne how many did 19894 d buy how many bought 13746 pens Scholler I perciue it reasonable and so shall I doe in all like questions Mayster Euen so But for easinesse of the work marke this Note When soeuer the first and second numbers haue ciphers in the first places you may bothe in the multiplication and in the diuision leaue out those ciphers so that you leaue out like manye out of bothe summes as in this question the first number 58000 hath thrée ciphers and so hath the seconde that is 2000 therefore caste awaye their ciphers and so will the first number bée 58 and the second 2 set them in their places and worke according to the rule and you shal perceiue that it wil be al one sauing that this is the shorter and easier way as these thrée figures do shew And this you sée is both easier and also the more certaine waye to know the answere to this question S. Truth it is as you say but sir me séemeth I might aske a further question here not onlie how manye shéepe eche man should haue but also what euerie shéepe cost Maister That question doeth not onelye belong to this rule but may also be discussed by Diuision especiallie if the questions number be one onelie as thus Diuide the totall summe 58000 pence by 2000 or 58 by 2 omitting the ciphers and the quotient wil be 29 pence that is 2â— s 5 d howbeit by this rule you maye doe it and beste when the number of the question doth excéede 1 as if I shoulde aske this question 2000 shéepâ— coste 58000 d ☜ howe muche did 20 coste Then shal I set my figure thus And doing after the rule there wil amouÌ„te 580 pence that is 2 lb 8 s 4 d the price of one score But if you wil vse that easie waye that I did teach you you may change the firste and seconde number thus Thus doe you perceiue the vse of the rule without time The rule of felovvâ—hâ—p vvith time And that you may as welâ— perceiue the same with diuersitie of time I propose this example Foure Merchants made a common stocke Question of a banke whiche at the yeares ende was encreased to 35145 lb. Nowe to knowe what shall be ech mans portion of gaines you muste know eache mans stock and time of continuance The first man of these foure laide in 669. lb which hée did take from the stock agayne at the end of 10. moneths The second man layd in 810. lb. for 8. moneths The thirde layde in 900. lb. for 7. moneths And the fourth layd in 1040. lb. for 12. moneths This question shall you examin as you did the other before sauing that where as in the third place of the figure you did set eche mans summe alone ☞ here you shall set the same béeing multiplyed by the number of their time likewise in the firste place of the figure you shal set that number which amouÌ„teth of their whole summes so multiplyed by their time added into one whole summe as thus The first mans summe is 669 lb. which I multiplye by 10. that was the number of his time and it maketh 6690. The second mans summe 810. lb. multiplyed by 8 which was his time make 6480. The third mans sum 900. lb. multiplied by 7 for that was his time yeldeth 6300. The fourth mans summe was 1040 lb and his time 12. multiply the one by the other and and it will be 12480. These foure summes thus multiplyed by their time must be set orderly in the third place of the figure and in the first place must bée set the whole summe of all foure whiche is 31950 and the gaine must be in the second place which is â—5145 Now to end the question I say firste If 31950 did get 35145 what did 6690 get Answere 7359 lb as by this figure appeareth Likewise the second man had to his part 7128 lb the third must haue 6930 lb And the fourth maÌ„ shal haue for his part 13728 lb as these figures doe partly declare Scholer This I like verye well but what proofe is there of this worke Mai. The same that I taughte you for the other Howbeit Another proofe there is vsed both for this worke and the other also this manner of proofe to adde all the portions togither and if they agrée to the whole summe then seemeth it well done but this is no sure rule Sch. Yet will I prooue it in this example The foure parcels are these which if I adde togither there will amount 35145 and that was the whole summe so is this rule true here Maister And so will it be still when the worke is truely done Note the imperfection of this kinde of proofe But if you lift to sée it prooued false take 10000 lb from the
at two seueral payments aforesaid To gain therby after the rate of 10 lb vpon the 100 lb in 12 monthes Briefe Rules for our hundreth waight here at London which is after 11â— lb for the C. Item who that multiplyeth the pence that one pound waight is worth by 7 diuideth the product by 15 shal finde how many pouÌ„ds in money the 112 pounde waighte is worth And contrariwise he that multiplieth the poundes that 112 lb waight is worth by 1â— And diuideth the product by 7 shall finde howe manye pence the pounde waighte is worth Example At 10 d the pound waight what is 112 lb waight worth Answer Multiplye 10 by 7 and thereof commeth 70 the which diuide by 15 and you shal finde 4 â…” lb. And thus the 112 lb is worth 4 lb 13 4 d after the rate of 10 d the lb aforesayde At 6 lb the 112 lb waight what is one lb worth Answer Multiplye 6 lb by 15 and thereof commeth 90 the which diuide by 7 And you shal finde 12 d 6 7 So muche is one pounde worth when the 112 lb did cost 6 poundes The eight Chapter entreateth of tares and allowances of merchandise solde by waight and of losses and gaines therin c. AT 16 lb the 100 suttle what shall 895 lb suttle be worth in giuing 4 lb waight vpon euerie 100 for treate Answer Adde 4 vnto 100 and you shall haue 104. Then saye by the Rule of thrée if 104 be worth 10 lb what are 895 lb worthe Multiply and diuide and you shal finde 237 lb â—13-10 2 13 d And so much shal the 895 lb waight be worth Item at 3 s 4 d the pound waight what shal 754 ½ be worth in giuing 4 lb waight vpon euerie 100 for treate Answer Sée first by the Rule of thrée what the 100 pound is worth saying if 1 cost 3 â…“ s what 100 multiplie and diuide and you shal finde 16 lb 2 â— Then adde 4 vnto 100 and they are 104 Then say again by the rule of thrée if 104 be solde for 16 â…” for howe muche shall 754 ½ be solde for Multiplye and diuide and you shal finde 120 lb 18-3 1â— 53 d And for so much shal the 754 ½ be sold for at 3 s 4 d the pound in giuing 4 vpon the 100. Item if 100 lb be worth 36 s 8 d what shal 860 lb be worth in rebating 4 pounde vpon euerie 100 for tare and cloffe Answer Multiplye 860 by 4 and thereof commeth 3440 the which diuide by 100 and you shal haue 34 2 â— lb abate 34 â…– from 800 and there wil remaine 825 â…— Then saye by the rule of thrée If 100 lb cost 36 â…” s what wil 825 â…– cost after that rate Multiplie and diuide and you shal finde 13-15 â…• s And so muche shall the 800 cost in rebating 4 pound vpon euerie 100 for tare and cloffe Item whether doeth he lose more that giueth 4 lb vpon the 100 or he that rebateth 4 lb vpon the 100 Answer First note that he that giueth 4 lb vpoÌ„ 100 giueth 104 for 100 And he which rebateth 4 lb vpon the 100 giueth the 100 for 96 Therefore say by the Rule of thrée if 104 be deliuered for 100 for how much shall the 100 be deliuered multiplye and diuide and you shal finde 96 2 12 and he which rebateth 4 in the 100 maketh but 96 of 100 so that he looseth 4 in the 100 And the other which giueth 4 vpon the 100 looseth but 3 â— 1 1 â— vpon the 100 Thus you may sée that he which rebateth 4 in the 100 looseth more by 11 12 in the 100 lb. than the other whiche gaue 4 vpon the 100 for tare and cloffe If 100 lb of any thing coste me 22 s 4 d The question is howe I shall sel the lb to gaine after the rate of 10 lb vpon the 100 pound Answer Saie by the rule of 3 if 100 lb giue 110 lb. what shall 23 ½ s giue multiply diuide and you shal finde 1 lb 17 60 Then saye againe if 100 lb be worth 1 17 60 lb what is one pound worth multiplye and diuide and you shal finde 3 d 6 75 And so muche is the pounde worthe in gayning 10 pounde vpon the 100 pounde Item a Grocer hath bought C waighte of a commoditie for 6 lb 10 s The question is now to know how many pouÌ„ds ther of he shal sel for 33 s 4 d to gaine 20 shillings in the C. waight Answer Adde 20 s vnto 6 lb 10 s and they make 7 lb 10 s Then say if 7 ½ yéeld me 112 lb what shal 1 â…” lb yéeld multiplie and diuide and you shal finde 24 lb 8 9. And so many pound ought he to sel to gaine 20 shillings in his C. waight If one pounde waight cost 3 s 4 d and I sel the same againe for 4 s what is gained in 100 pound Aunswer You may saye if 3 â…“ s giue 4 s what will 100 lb giue But then when you haue sound you must subtract the product out of 100 lb the rest is your neate gaine Or else to produce the neate gaine in your worke at the firste Then subtract the iust price out of the ouer price as I taught before in the firste beginning of losse and gain And your conclusion shal be al one multiply diuide by which of the two wayes you thinke good and you shal find that he gaineth 16 lb 13 s 4 d in the 100 pound Item if the pound waight which cost 4 s be sold again for 3 s 4 d I demaund what is lost in the 100 lb of mony Answer Say if 4 s loose â…” what shal 100 lb loose Multiplie and diuide and you shal find 25 lb and so much is lost vppon the 100 lb of money Item if C waight of any commoditie cost 45 lb And the buyer repenting would loose 5 lb in the 100 lb of money I demauÌ„d how the pound may be solde his losse to be neither more nor lesse than after the rate aforesaide of 5 by the hundreth Answer By the Rule of thrée if 100 lb loose 5 lb what shal 45 lb léese Work and you shal finde 2 ½ lb which rebated from the principal 45 resteth 42 lb 15 s Lastly say if 112 lb yéeld but 42-15 s what 1 pound multiply diuide and you shal find 7 s 7 d 17 28. And so much is the pound worth after that losse A Grocer hath bought 2 péeces of reasoÌ„s waying 175 ½ lb 182 ¼ lb 191 lb tare for eache fraile 2 ¼ lb at 25 ½ s the C waight The question is what they amounte too in money I answere 6 lb 8 s â— 40. A Grocer hath bought 3 sacks of Almonds waying 267 ½ lb tare 2 lb 257 ½ lb tare 2 ½ lb 252 lb tare 3 lb at 2 s 10 ½ the pounde what amount they too in money I answere 110 lb 11-7 â…› d The ninth Chapter
other hath Holland at 5 s 6. d the ell readie money The question is nowe at what price he ought to deliliuer the ell in barter to saue him selfe harmelesse Answer Saye by the Rule of thrée direct if 2 â…“ s readie money giue 3 s in barter what shal 5 ½ s giue in barter you shal finde 7 1 14 s and at that price oughte the seconde Merchaunte to sell hys Hollande in barter The proofe Two barter the one hath Holland at 5 s 6 d in the ell to sell for readie money And in barter he will haue 7 1 14 s the other hath Pepper at 2 s 4 d the lb to sel for readie money The question is now howe he ought to sel it in barter Answer Say by the Rule of thrée direct if 5 ½ redie mony giue 7 1 14 s in barter what ought 2 â…“ s to take in barter multiplie and diuide and you shal finde 3 shillings your desire 3. Rule Two barter the one hath cloth of Arras at 30 shillings the ell readie money but in barter hée will haue 35 ½ shillings And the other hath white wines which he deliuered in barter for 16 lb for a Tunne The question is now what his wines cost the Tunne in readie money Answer Say by the rule of thrée direct if 35 ½ s in barter giue but 30 readie money what did 16 lb in barter cost Work and you shal finde 13 lb 10 â—â— â—â— s and so much cost his wines for a Tunne readie money The proofe Two barter merchandise for merchandise The one hath wines white at 13 lb 10 10 â—1 s the Tunne to sell for readie mony But in barter he deliuered it for 16 lb. The other to make his matche good and saue himselfe harmelesse deliuereth Arras at 35 ½ s the ell The question is nowe what an ell of his Arras coste in readye money Answer Saye by the Rule of thrée directe if 16 lb in barter giue but 13 10 30 71 s in redie money what shal 35 ½ s yéelde in barter worke and you shall finde 30 shillings your desire 4. Rule Two barter the one hath Carsies at 14 lb the péece readie money But in barter he wil haue 18 lb. And yet he wil haue the â…“ part of his ouerprice in readie money And the other hath Ginger at 8 groats the puund to sel for readie money The question is how he ought to deliuer the Ginger by the lb in barter to saue himselfe harmelesse and make the barter equal Answer Item for the working of thys question and suche other the like you muste vnderstande if the partie ouerselling his wares require to haue also some portion in readye money as c. Then shall you rebate the same demaunded part whatsoeuer it be from the ouer price And also from the iuste price And those two numbers that shal remaine after the subtraction is made shall be the two first numbers in the Rule of thrée And the iuste price of the same merchandise shall be the thirde number whiche by the operation of the Rule of thrée directe shall yeelde you a true solution howe and at what price you shal ouersel that your merchandise to saue your selfe harmelesse and make the barter equal Example Take the â…“ of eightéene which is the ouerprice of his cloth which â…“ of eightéen is sixe whiche as appeareth here in the margent you must subtract from 18 there resteth 12. And also abate it from 14 which is the iuste price of the cloth and there remaineth 8 which 8 and 12 are the two firste numbers in the Rule of thrée Then take 8 groates or 2 â— 1 shillings for the third nuÌ„ber Then say by the Rule of thrée directe if 8 s giue 12 s what shall 2 â…” s giue Multiply and diuide and you shal finde 4 s And for so much shal the second MerchaÌ„t sel his Ginger or his commoditie in barter to ballaunce the same equal The proofe Two barter the one hath Fine Carsies at 14 lb the péece readie money But in barter he will haue 18 lb. And yet he will haue the â…“ part of his ouerprice in readie mony And the other hath Ginger whiche he hauing cunning ynough to make the barter equal deliuered for 4 s the pounde The question is nowe what his Ginger cost him in readie mony Answer After you haue made the subtraction abating 6 the â…“ part of 18 both froÌ„ 18 and 14 as before was taught you then wil there remain 8 and 12 for your two first numbers in the Rule of thrée Then say if twelue giue but eighte what shall come of 4 the ouerprice of the pounde of Ginger Multiplye and diuide and you shall finde 2 s 8 d your desire Two Merchaunts barter Merchandise for merchaundise the one hath Denshire whits at 7 lb 13 s 4 d the péece readie money but in barter he doth them awaye for 8 lb 3 s 4 d And yet he wil haue the â…“ parte of his ouerprice in readie money And the other hath Cottens at 3 lb the peece readie money The question is now at what price he oughte to sel or exchange his Cottens in barter to saue him selfe harmelesse and make the barter equal Answer First séeke â…“ parte of 8 lb 3 s 4 d whiche is 2 lb 14 5 â…“ d which rebated from 8 3 4 d there resteth as appeareth by the example aboue saide 5 8 10 2 2 d which â…“ of 8 3 4 d also rebated from 7 13 4 d there resteth 4 18 10 â…” the two firste numbers in the Rule of thrée And the 3 lb which is the neate price of the péece of Cotten is the thirde number Then saye by the Rule of thrée derect as was taught before if 4 18 10 â…” d giue 5-8 10 â…” d what shall 3 lb giue multiple and deuide and you shall finde 3 lb 6 s 1 91 292 d the iuste price that he ought to deliuer his Cottens in barter 5. Rule Two Merchauntes wil chaunge Merchaundise for Merchandise the one hath Carsies at 40 s the péece to sell for ready monie And in barter hée will sell them for 56 s 8 d and he will gayne after 10 lb vpon the 100 lb And yet he will haue the ½ of his ouerprice in ready monie The other hath Flaxe at 2 d the pound readie monie The question is nowe howe he shall sell the pound of his Flaxe in barter Answer Sée firste at 10 lb vppon the 100 lb what the 56 â…” s commeth to in saying by the Rule of thrée direct if 100 lb giue 110 lb what 55 â…” multiplie and deuide and you shall finde 3 lb 2 s 4 d of whiche the â— 2 that he demaundeth in ready monie is 1 lb 11 s 2 d the same 31 s 2 d abated from 40 s and also from 56 s 8 d there will remayne 8 shillings 10 pence and 25 shillings 6 pence for the two first numbers in the Rule of thrée And 3
multiplication diuide by 5 so that worke is finished Or multiplie the saide summe by 7 and take out of it ⅕ adding it to the producte of your multiplication by 7 and that is your number required So that as well by the one as by the other 143 lb 4 s 9 d Flemish maketh 1031 lb 6 s 2 d ⅖ French or Tournois Example An other Example Another example or thus A briefe Reduction of lb s and d French into lb s and d Flemish Multiply 233 lb 8 s 4 d fr. by 5 and diuide the product twice by 6 that is the saide number by 6 and the product againe by 6 and the quotient of this seconde diuision is the thing required So that 233 lb 8 s 4 d fren maketh 32 lb 8 s 4 d 5 9 flemish Example Another To reduce lb s and d Sterling into lb s and d French or Tournois The lb ster maketh 8 lb 8 s french that is to say 8 lb ⅖ the s maketh 8 s ⅖ and the peny 8 d ⅖ frenche Wherefore to know what 231 lb 13 s 4 d ster maketh french ye must multiply your whole sum by 42 that is by 7 and the product of it by 6 and diuide thys second product by 5 and that is the sum required Otherwise multiply the sum ster by 8 and adde twice to the product ⅖ and it shall produce the sum required So that both waies 231 lb 13 s 4 d ster maketh 1946 lb french As here vnder followeth The same otherwise An other Example The same To reduce lb s and d fren into lb s d ster To know how much 1256 lb 12 s 6 d fren maketh in sterling money multiplie the sum by 5 and diuide the producte by 7 and 6 at twice and the last quotient shal be the thing required that is to say 1256 lb 12 s 6 d maketh 149 lb 11 s 11 d 4 7 sterling Example An other Example Note that when any money is giuen by exchange at London for Roan at 71 d ½ or rather 71 1 7 for the crown of 50 s french there is neyther gaine nor losse for it is one mony for an other accompting 8 lb 8 s French for 1 lb sterling So the Gyuer loseth the time of payment which is about 15 dayes hée that taketh it hath gaine of the same They of Rean that putte sorth or take money by exchange for London ought to haue like consideration Item when any man giueth at London 64 d ⅓ or rather 64 d 2 7 to haue at one of the Faires of Lions a crowne de Marc he that so giueth his mony loseth the time and he that taketh it gaineth the same for 62 d 2 7 is equall in value to 45 s French He that putteth or taketh money at Lions for London ought to consider the same Item when anye deliuer in Antwerpe 75 d to receiue at Lions a crown of Marcke hée that putteth it foorth looseth the tyme and hée that taketh it gaineth the same For 75 groates Flemish is equall in valewe to 45 s French Thus for this time I make an ende of the practise of exchaunge and the enstructions therevnto belonging and according to my promise gratify such as are desirous to know the common coynes vsed for traffique among Merchauntes in these Cities following Here followeth a briefe declaration of their monies and the recknings and accompts of them The sixteenth Chapter contayneth a declaration of the valuation and diuersitie of coines of most places of Christendome for traffique And the manner of exchaunge in those places from one citie or towne to an other whiche knowne is righte necessarie for Merchauntes by meanes whereof they doe finde the gaine or losse vpon the exchaunge ITem for as much as the greatest diuersitie of money of exchaunge is at Lions Therefore I will beginne duely of the money of that place At Lyons they vse Franckes Soulxes and Deniers Tournois a Francke maketh 20 Soulx and one Soulx 12 Deniers But the Merchants to kéepe their bookes of accompts doe vse French Crownes of the marke at 45 Soulx the péece and doe diuide it into 20 s 1 s and 12 d Item a Marke of golde 65 🜄 of the Marke whiche serueth for exchaunge And diuide it into 8 ounces The ounce into 24 pēce or Deniers the Denier into 24 graines And so the sum or whole by imagination or gesse Also at Lyons there are 4 fayres in a yere at the which they do commonlye exchaunge whiche are from thrée monthes to thrée monthes At Geanes they vse the Soulx on Ducket maketh lb. 3. At Naples they vse Duckets Tarie and Graines The Ducket maketh 5 Taris one tarie 20 graines but they take 6 Duckets whiche maketh thirtie taries for the ounce A Ducket maketh 10 Carlins a Carlin 10 graines so that 2 Carlins make a Tarie and 100 graines make a Ducket At Rome they vse Duckets of the Chamber one Ducket is worthe 12 Guylis and a Guili 10 Soulx At Venice they vse Duckets Curraunts at 124 Soulx a peece or 24 Deniers one Denier maketh 32 picolis At Falerine and Messine they write after ounce tary graynes and 1 ounce is worth 6 Duckets or 30 taris and 1 tary is twenty graines and 1 graine 6 picolis One Ducket is also worth 24 Carlins At Milan they vse lb. s d of Duckettes imperials and 🜄 of exchaunge is worthe 4 lb. At Lucques Florence and Aucone they vse the 🜄 of gold in gold the French Crowne is worth lb. 7 but at Buloigne lb. 3.10 s At Barselon they vse the soulx the Ducket of exchaunge is worth 22 soulx At Valence and Saragosse they vse the Liuer Soulx and Denier the Frenche crowne of exchange is worth 20 soulx and 1 soulx is 12 Deniers At the Fayres of Castill they vse the Meruaidies the Ducket is worth 375 Meruaidies At Lisbone they vse the Raies one Ducket of exchaunge is worth 400 rayes At Noremburge Franckford and Auguste in Germanie they vse the Krentzers whereof 60 make a Floryn At Antwerpe they vse lb. s and d de Gros and they exchaunge into the Denier de Gros. To wit our English peny At London they vse the 1 lb sterling and 1 d sterling and they exchaunge in 1 d sterling The exchaunge of Lyons at sundrie places Item at Lyons there is exchaunge in thrée sorts at the cities and townes following Firste they deliuer at Lyons one Marke to haue or receiue at Naples almoste 41 ½ Duckets at Venice 70 Duckets corrant at Rome 63 Duckets of the Chamber Luques and Florence 65 🜄 of Gold at Milan 82 🜄 And contrariwise at the saide Cities aforesaide they doe giue so muche of money to haue a marke at Lyons Secondlie they giue at Lisbone one 🜄 of Marke of 45 soulx Turnois a péece to haue at Gennes almost 68 Soulx At Palerme and Messine almoste 24 Carlins at Barselone 22 soulx at Valence or Saragosse 20 soulx At the fayre