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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	day_n	hour_n	minute_n	1,570	5	11.3251	5	false

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A10530	The grounde of artes teaching the perfect vvorke and practise of arithmetike, both in whole nu[m]bers and fractions, after a more easie ane exact sort, than hitherto hath bene set forth. Made by M. Robert Recorde, D. in Physick, and afterwards augmented by M. Iohn Dee. And now lately diligently corrected, [and] beautified with some new rules and necessarie additions: and further endowed with a thirde part, of rules of practize, abridged into a briefer methode than hitherto hath bene published: with diverse such necessary rules, as are incident to the trade of merchandize. Whereunto are also added diuers tables [and] instructions ... By Iohn Mellis of Southwark, scholemaster.; Ground of artes	Record, Robert, 1510?-1558.; Dee, John, 1527-1608.; Mellis, John, fl. 1588.	1582 (1582)	STC 20802; ESTC S102132	245,945	706

by the Stone in some places yet the very waightes of it are Cloues and Weys So that a Cloue containeth 8 pound and a Wey 32 Cloues which is 256 pound that is 12 score and 16 pound And so muche weigheth the Wey of Suffolke chéese And the like waight is or shoulde be the Barrell of Suffolke Butter The Wey of Essex Chéese containeth 16 score and 16 pound And so much is also the barrell of Essex Butter Measures for liquor Now of waights are made other measures both for graine and liquor For a pounde in waight maketh a Pinte in measure A Pinte Gallon Pottell Quarte so that 8 pound or 8 Pintes doe make a Gallon half a Gallon is named a Pottle and half a Pottel is called a Quarte which containeth two pintes Fyrkin Tertian Kilderkin Barrell Now aboue a Gallon the nexte measure is a Firken then a Tertian a Kilderkin or halfe Barrell and a Barrell And by those measures are solde commonly Ale Béere Wine and Oyle Butter and Soy● Salmon Herrings and Eeles But as these be vnlike things Ale measures so the measure of their vesselles doe differ for the measures of Ale are as followeth Of Ale the Fyrken the Kilderkē the Barrell conteineth 8 16 32 gallons Of Béer the Fyrken the Kilderken the Barrell conteineth 9 18 36 gallōs Sope measures both Firken Kilderken Sope measures and Barrell should be equall to al Ale measures Moreouer the Statutes do limitte the waight of euery of those thrée vessels being empty A Barrell Halfe Barrell A Firken to weigh empty 26 13 6 ½ pounds Herrings also be solde by the same measures that Ale and Sope be solde by Herring Herrings also are solde by the tale 120 to the hundred ten thousand to the laste Salmon Eeles haue a greater measure Salmon and Eeles Salmon Eeles the butte the barrell halfe bar the firken holdeth 84 42 21 10 ½ Gallons Howbeit some Statutes did limitte Eele vessels equall with Herring vessels VVine measures Nowe as for wine vesselles seldome are smaller than Hogges heads which are of 63 gallons euery Hogges head is two Barels yet there are many other wine vessels but of them all sée this table and marke the measures one to an other Of wine and oile the Rondlet the Barrell the hogges hed the Tertian the Pipe the Tonne holdeth ●8 ½ ●●1 ½ 63 84 126 252 Gallons Tertians But you shall marke that there be other kindes of Tertians for there be Tertians that is to say Thirdles of Pipes of hogges heads and of Barrels as wel of other things as of wine B●tte Also of Malueseys and S●cke c. the half Tonne is not called a Pipe but rather a Butte And thus much haue I thoughte méete to tell you at this time Scholer And is that alwayes true Maister I haue tolde you howe it shoulde be but howe it is I may not say howe they doe differ daily from their iust measure that Gagiers can tell you better than I. But I wil let this passe now and speake briefly of the other measures And as of waights there did spring the liquide measures whereof I spake laste so of the same springeth dry measures as Pecks Drie measures Bushels Quarters and suche like whereby are measured corne and like grains also salt lime coales and other like And this is the order and quantitie of them A Pecke is the measure of two Gallons A Pecke A Bushel containeth foure Peckes A Bushel A Quarter holdeth eight Bushels Quarter A Wey containeth sixe quarters These are the commō names measures VVey but in diuers places there be diuers sortes The bushel in many places is 2 bushels but then is the bushell there called a Strike Strike And in some places half a quarter is called a a Cornoke But these diuersities are to many to tel you briefly them al. And again sith they are against the law and Statutes I counte them vnméete to be vsed But now remaineth yet an other kinde of Measures Measure to meat lēgth breaden thicknes wherby men met length bredth and thicknesse and those are an Ynch a foote and such other whose names and quantities this table sheweth An ynch 3 Graines of barly in lēgth make an inch 12 Ynches make a foote Foote Yeard Elle Perch 3 Foote make a yearde 3 Foote and 9 ynches make an Elle 5 Yeards and a halfe make a Perch 1 Perche in breadth and 40 in length doe make a Rod of lande which some cal a roode some a yeard land and some a Farthendele Acre 2 Farthēdels make half an acre of groūd 4 Farthendels make an Acre More 40 Rods in length do make a furlōg 8 furlongs make a mile whiche conteyneth 320 Perches So that an English mile grounded vppon the Statute is in length 1760 yeardes 5280 foote and 63360 ynches Somewhat greater then the Italian mile 1000 paces and 5 foote to a pace Here might I tell you many things else touching measure and also howe to reduce strange measures to our measures but bycause it can not well bee done wythout the knowledge of Fractions whiche as yet you haue not learned I will let them passe til an other time when I shal instruct you in Geometrie wherein I should be enforced else to repeate the same often againe Scholer But yet sir of the partes of time I pray you tell me somewhat The partes of time A Day An houre VVeeke Moneth Yeare Maister You know that a naturall daye hath 24 houres and euery houre hath 60 minutes It néedeth not to tel you that 7 dayes make a wéeke and 4 wéekes make a commō moneth and 13 moneths make a yeare lacking 1 day certaine houres and minutes But of that I shall instruct you hereafter Here wil I make an end of Reduction for this time whiche thoughe it be counted no kind seueral of Arithmetike yet you sée it is no lesse néedefull to be knowen or easier to be done than of any of the other Scholer Mary sir it séemeth vnto mée much harder than any other sort for it requireth the knowledge of so many things but now sir when you sée time I am readie to learne forth for as much of Reductiō as you haue taught me I remember but and if I doe at any time forget I shall haue recourse to the tables which you haue set forth for me Maister So do you for it wil not be remembred without exercise And now according to promise here followeth the Table which I haue added to this Author for thy vtilitie intending at the latter ends of my Addition to this Booke to write of the ordinarie money vsed in moste partes of Christendome and their common values currant for traffique in those places with the manner of their exchaunges as also their vsuall waights and measures which I hope will be as gratefully taken of Gentlemen merchants

If 3 moneths suffise 40000 to howe manye will 8 moneths suffice To know this I multiplie the first number 3 into seconde 40000 it yieldeth 120000 which sum I diuide by 8 there wil be in the quotiēt 15000 which if I doe subtract from 40000 the remainer will declare that hée muste dismisse 15000 as this figure sheweth * Maist Nowe aunswere me to this question If 136 Masons in a moneth bée able to builde a Forte to preserue the Souldiers from the enemie And suche expedition requireth that I woulde haue the same finished in eighte dayes how manye workemen saye you is there to bée appointed Sch. As you taught me I set the numbers thus saying If 28 daies require 136 Masons what number of men by proportion will 8 dayes bring forth To know this I multiplie the first nūber 28 into 236 And it yieldeth me 2808 whiche I diuide by 8. And my quotiente is 476 which is the iust number of Masons that shall supplie this worke And now me think these questions are very easie Ma. Truly if you take delectation herein you shall finde this Art not onely easie but wonderfull pleasant profitable Now answere me this question so wil I make an end of this rule in whole nūbers hasting the sooner to broken nūbers For had you that vnderstanding of thē perfectly not only in this Rule but in all other the question in sight might haue ben 10 times more harder to absolue yet as easilie as soone wroughte as this Sc. Your words doth greatly encorage me to be studious to attaine whole numbers which me think are wōderfull But might I once attain to be a practicioner in brokē I should think my self a happy lad M. Now what say you to this If ●● carpenters in 2 dayes can make ●00 Staues estéeming they work but 12 howers a day And such néede requireth that 384 carpenters are set to the finishing of these 200 staues in what time say you wil they make thē vp Scholer I see here that I muste turne my ● daies into howers And so doing I sette my numbers thus Saying if 48 men are 24 houres 384 men will make an ende quickely For it is grounded vpon an olde Prouerbe many hands make quick spéede I multiplie 48 into 24 and it amounteth to 1152 whiche I diuide by 384 and my quotient is 3 houres which is my desire Note I take this for a note worthie the marking either in the Rule of thrée forwarde or backwarde when the two numbers art multiplied togither the Producte is of the same nature and denomination that the second number is of Maister Well sithe you perceiue nowe the vse of this Rule The double Rule I will shewe other which ensue of the same firste the double Rule which is so called because there is in it double working by which thing onely it differeth from this Sch. Then by an example I shal vnderstand it well ynough Ma. Of cariage So shall you and let this be the example If the cariage of 100 pound weight 30 miles doe cost 12 d how much will the cariage of 500 weight cost being caryed 100 miles Scholer I pray you shewe me the working of it M. You must make 2 workings of it the first thus If 100 pound weighte cost 12 d how much will 500 lb. cost Set your figure thus And multiplie 500 by 12 and therof amoūteth 6000 which if you diuide by 100 the quotiēt wil be 60 that is the price of 500 for 30 miles Thē begin the second worke saying if 30 miles cost 60 d how much wil 100 miles cost Set your figure thus Than multiplie a 100 by 60 wherof amoūteth 6000 which being diuided by 30 will yield 200 d Than you may say that so many penies shall cost the cariage of 500 pound waighte 100 miles after the rate of 12 pence for the 100 caried 30 miles Scholer Now I perceiue it also Mai. These and such other like questiōs are to be aunswered much quicker at one working by the Rule of 3 composed of fiue numbers whiche here I will not trouble you withall But at the ende of this Rule will shewe you the worke thereof not onlye of this and the nexte question but also I will there deliuer thrée or 4 other examples wishing you then to make a comparison the one with the other And so to vse which way you thinke good Sc. Sir I thanke you much for your curtesie and I long now til this rule be ended that I shall sée howe I maye behaue my selfe with that newe Rule of 5 numbers for that I haue euer since you taughte mée hetherto in the Golden Rule both forward and backward wroughte but with 3 numbers only Ma. Question of sovving Till we haue done with this lette vs go on forward and answere me to this question 30 bushels of wheat sowed yielded in one yeare 360 how manye will 80 bushels yield in 7 yeare Sc. First I saye that if 30 bushels will yield 360 in 1 yeare then 80 bushels will yield 960 in 1 yere Then for the seconde worke I say If one yeare yield 960 then 7 yeare will yielde 6720 as these two figures doe shew Question of Corn. But now sir if I set forth 30 bushels of corne to another man for 7 yeare agréeing so that he shall sow euerye yeare the whole encrease of the corne and I at the ende of those seuen yeares to haue the halfe of the whole increase I would know how many bushels will there amount to my part supposing the increase to be after the rate of the last question for 30 bushels in one yeare 360. Mai. In such a question you must haue so manye seuerall workinges as there be yeres as for example In the first yere ●0 bushels yield 360 then to knowe the yielding of the second yeare I must say If 30 yield 360 how many yieldeth 360 Work by your rule and you shal find 4320. Then say for the third yere if 30 yield 360 how manye will 4320 yielde you shall haue 51840 and so euery yeare multiplying the whole encrease by 360 and diuiding it by 30 the increase of the next yere wil amoūt as these 7 figures in the next page do orderly declare where I haue set 7 letters for the 7 yeres of which the first is set without art because that is the increase whiche you doe presuppose the last number of eche other doth shewe the increase of the yeare that it standeth for which the letters doe declare so that the increase of the seuen yeare is 1074954240 bushels how manye quarters that is and also how many wayes you may by Reduction soone finde Now with one question more I will proue you If 6 Mowers doe mowe 45 acres in 5 dayes how many mowers wil mow 300 acres in 6 dayes Sch. If 45 acres doe require 6 mowers then 300 acres requireth 40. Now agayn if 5 dayes require 40

mowers then 6 dayes néedeth but 33 mowers Mai. Why do you not make mention of the 2 that remaineth in the last diuision for the last part of the question is wroughte by the Backer rule where the first number 5 is multiplied into the seconde that is 40 whereof amounteth 200 whiche if you diuide by the thirde number 6 the quotiente will be 33 as you said but then will there remaine 2 which cannot wel be diuided into 6 parts how be it you may vnderstand by the sixt part of 2 the thirde parte of one mans work which you must put to the 33 or else you may say that 33 workemen wil ende all the 300 acres in 6 dayes saue two mens worke for one day or 2 dayes worke for one man But such brokē numbers called Fractions you shall hereafter more better perceiue whē I shal wholy instruct you of them Mai. Yet one question more of field matters I will propone and so I will make an end of this double Rule of 3. Sc. With all my hart sir I thank you and I wil dispatche it as soone as I can because would faine sée the order of the nexte Rule of 5 numbers Maist Then this is my question If 300 Pioners in 8 houres will cast a trenche of 200 Rods I demaund how manie Labourers wil be able with a like trēche in thrée houres to entrench a Camp of 3500 Rods. Sch. I thinke I am nowe in the Backe-house diche for I knowe not well whiche way to go about it And besides that trulie I think I shall neuer come to prefermente that way my grouth is so small Ma. You know not how God may raise you hereafter by seruice into the fauour of your Prince for the auaile of your Countrie Example Sir Francis Drake as worthy a man as euer England bred is not the tallest man and yet hath made the greatest aduēture for the honour of his Prince Countrie that euer English man did Sc. Sir I thanke you for your good encouragement my mind though I be little is as desirous of knowledge as any other I haue pondred now a little of it thus I set forthe the worke Saying if 200 Rod require 3400 300 men what shall 3400 Rod require I multiplie 3400 by 300 and it yieldeth 1020000 which I diuide by 200 and my quotient is 5100 men Then must I say for my second work if in 8 houres 5100 men be able to discharge it how many shall performe the same in 3 houres now if I should worke by the Golden Rule of proportion forwarde I should find a lesse nūber of men because 3 houres is lesse then 8 houres but because reasō teacheth me that the lesser the time is wherin the french must be made the more Laborers I ought to haue wherevpon I vse now the backer Rule as in example And I haue in my quotiēt 5000. So many Pioners must I haue to entrenche the camp in 3 houres Ma. You haue answered the question very artificiallie And truelie I commende you for your diligence and apte vnderstanding and now according to my promise I will in whole numbers giue you a little tast of the Rule of 3 compounded of 5 numbers The Rule of 3 compound of 5 numbers THis Rule of 3 composed is distinct for most néedefull questions into two seuerall parts or workinges And there belongeth vnto it alwayes 5 numbers wherof in this rule being the first part the seconde number and the fift are alwayes of one nature and like denomination which rule is to be wrought thus you must multiplie the first number by the seconde And that shal be your diuisor Then again multiplie the other thrée numbers the one by the other and their product shall be your diuidend And now according to my promise wée will first work the question of weighte and cariage whiche I deliuered you in the double rule of 3 to be absolued by this Rule which was this If the cariage of 100 lb. weight 30 miles coste 12 d what wil the carriage of 500 lb. weighte stande me in being carried 100 miles Then marke wel how these numbers stand multiplie 100 by 30 as thys figure sheweth And that number keepe for your diuisor Then multiplie the other 3. numbers the one by the other and they amount as you see to 600000 which you shall diuide by 3000 your quotiēt is 200 d Now you see it agréeth with the conclusion of the double Rule S. Sir I thanke you most hartely it is euen so Ma Yet note this for a generalitie in thys Rule Note loke what nature or denominatiō your middle number is and of the like denomination or nature is alwayes your quotient Scholer Well nowe and it please you by your patience I will sée howe I can ende the question then nexte following of 30 Bushels of Wheate sowed yéelded in one yeare 360 how many then will 80 bushels yéelde in seauen yeare and according to youre reasons I set my numbers thus which 201600 I diuide by 30 and my quotiente is 6720 bushels my desire M Yet one question more I will propound vnto you and so leaue this rule till it please God hereafter that I may make you worke it in broken numbers What comes the interest of 258 lb for fiue monethes after the rate of 8 pounde taken in the 100 lb for 12 monthes Sch Sir as this is a question of gaines So will I warelie worke this question in hope one day to reape someting for my paines and thus I propone it But I beseech you if it bée not well set downe to shewe me myne errour Ma. Procéede you haue done verye wel Sch. Then I doubt not by the grace of God but to ende it I multiplie 100 by 12 it yéeldeth 1200 and the 3 other numbers multiplied togither produceth 10 20 which I diuide by 1200 and my quotient is 8 poundes Thē according as you haue taught me heretofore I turne the 720 lb. that is left into shillings and diuiding it by my firste number my quotient is 12 s So I answeare that the lone of 258 lb for 5 monthes after the rate of 8 lb. in the 100 lb for a yere comes to 8 lb 12 s Mai. You say true I commende your diligence now beholde the manner of the second part of this rule M. In the second part of this rule of 3 composed the third number is like vnto the first And the rule is to be wrought as thus you shall now contrarie to the last rule multiplie the third number and the fourth togither and that product shal be your deuisor Then multiplie the fift by the seconde and the producte therof by the first and that is the number that shall be diuided For example I propond this question for a proofe of my last question of interest A Merchant hath receiued 8 lb 12 s for interest for 5 months terme which he receiued after the rate of 8 lb. in the 100 lb.

liste MVLTIPLICATION BVt nowe touchyng Multiplication you shall sette your numbers in two roomes as you did in those other kindes but 2 so that the multiplier be set in the first roome then shall you begin with the highest numbers of the seconde roome and multiplie them firste after this sort Take the ouermost line in your first working ☞ as if it were the lowest line setting on it some moueable marke as you list and looke how many counters be in him take them vp and for them sette downe the whole multiplier so many times as you tooke vp counters reckning I say that line for the Vnites And when you haue done with the highest number then come to the nexte lyne beneath and do euen so with it and so with the nexte till you haue done all And if there be anye number in a space then for it shall you take the multiplier 5 times and then muste you recken that line for the Vnites whiche is next beneath that space Or else after a shorter waye you shall take onelie halfe the multiplier but thē shal you take the line next aboue that space for the line of Vnites But in suche working if by chaunce your multirlyer be an odde number so that you can not take the halfe of it iustlye then muste you take the greater halfe and set downe that as if that it were the iuste halfe and further you shall sette one Counter in the space beneath that line which you recken for the line of Vnits or else onely remoue forwarde the same that is to be multiplied S. If you set forth an exāple hereto I think I shal perceiue you Maaster Take this example I woulde multiplie 1 5 4 2 by 2 6 5 therfore I set the numbers thus Then firste I beginne at the 1000 in the highest roome as if it were the first place and I take it vp setting downe for it so often that is once the multiplyer which is 365 thus as you sée here where for the one counter taken vp from the fourth line I haue set down other 6 which make the sum of the multiplier reckening that fourth line as if it were the first which thing I haue marked by the hand set at the beginning of the same Scholer I perceiue this well for in déede this sum that you haue set down is 265000 for so much doth amounte of 1000 multiplied by 365. Maister Which summes if you do adde togither into one summe you shall perceiue that it will be the same that appeareth of the other working before so that both sorts are to one intente but as the other is shorter so this is playner to reason for such as haue had smal exercise in this arte Notwithstāding you may adde them in your minde before you set them downe as in this example you might haue sayde 5 times 300 is 1500 and 5 times 60 is ●00 also 5 times 5 is 25 which all put togither doe make 1825 whiche you may at one time set downe if you list But now to go forth I must remoue the hande to the next counters whiche are in the second lyne and there must I take vp those 4 counters setting downe for them my multiplier 4 times seuerally or else I maye gather that whole sum in my mynde firste and then set it downe as to say 4 times 300 is 1200 4 times 60 are 240 and 4 times 5 make 20 that is in all 1460 that shall I set downe also as here you sée Then to ende this Multiplication I remoue the finger to the lowest line where are only 2 them do I take vp and in their stéede doe I set downe twice 365 that is 730 for which I set one in the space aboue the thirde line for 500 and 2 more in the thirde lyne with that one that is there alreadie and the rest in their order and so haue I ended the whole summe thus Whereby you sée that 1542 whiche is the number of yeares sith Christe his incarnation being multiplyed by 365 which is the number of dayes in one yeare doth amounte vnto 562830 The summe of the daies sith Christs incarnation which declareth the nūber of dayes sith Christes incarnation vnto the end of 1542 yeares beside 385 dayes and 12 houres for leape yeares Sc. Now will I prooue by an other example as this 40 labourers after 6 d the day for eche man haue wroughte 28 dayes I would know what their wages doth amoūt vnto Where in the firste place is the Multiplier that is 1 dayes wages for one man in the seconde space is set the nūber of the warkmē to be multiplied So appeareth the whole dayes wages to be 240 d that is 20 s So is the whole wages of 40 workemen for 28 days after 6 d eche daye for a man 6720 d that is 560 s or 28 pound Ma. Now if you would prooue Multiplication the surest way is by Diuision therefore will I ouerpasse it till I haue taughte you the arte of Diuision whiche you shall worke thus DIVISION FIrst set downe the diuisor for feare of forgetting and thē set the nūber that shal be diuided at the right side so farre from the Diuisor that the quotient may be set betwéene them as for example If 225 shéepe cost 45 lb. what did euerye shéepe cost To know this I shoulde diuide the whole summe that is 45 lb by 225 but that cannot be therefore must I firste reduce that 45 lb into a lesser denomination as into shillinges then I multiplie 45 by 20 and it is 900 that summe shall I diuide by the number of sheepe which is 225 these two numbers therefore I set thus Then begin I at the highest lyne of the diuident and séeke how often I maye haue the diuisour therein and that maye I doe foure times then saye I foure times 2 are 8 whithe if I take from 9 there resteth but 1 thus And because I founde the diuisor 4 times in the diuident I haue set as you sée 4 in the middle roome which is the place of the quotient but now must I take the rest of the diuisour as often out of the remayner therefore come I to the seconde line of the diuisor saying 2 foure times make 8 take 8 from 10 and there resteth 2 thus Then come I to the lowest number which is 5 and multiplie it 4 times so is it 20 that take I from 20 there remayneth nothing ☜ so that I sée my quotient to be 4 which are in valewe shillings for so was the diuident and therby I know that if 225 Shéepe did cost 45 lb euery shéepe cost 4 s Sch. This can I doe Example of vvages as you shall perceiue by this exāple If 100 soldiours do spēd euery moneth 68 lb what spendeth ech man First because I cannot diuide the 68 by 160 therefore I will turne the lb into pennies by multiplicatiō so shal there be 16320 d Now must I diuide

wrought euery day yéelding 25 d the totall is 600 d so that abating 480 out of 600 there resteth 120 and as you say it shoulde be but 65 therefore it is too much by 55 that must be sette on the right hand of the figure at the neather parte and ouer it on the same side 16 which is the seconde position thus And as I gather by your words it were al one if I did set 28 in steade of 12 and 24 in steade of 16. M. So were it But this shall you marke ☜ Note that of what nature so euer the two positions be of the same nature is the quotient Therefore when the positions in this question are 12 and 16 The profe of this rule which both being numbers of the playing dayes the quotiente shall declare the true numbers of playing dayes where as if the positions had bene 28 and 24 whyche are supposed to be the working dayes then woulde the quotient declare the true number of the working dayes not of playing dayes as it will doe nowe And therefore to continue the worke of this question and to find the true number of playing dayes I muste multiplie crosse wayes the firste position 12 by 55 that is the seconde erroure and the totall will be 660 then I multiplie 275 by 16 and it yéeldeth 4400. Now bicause the errours are like that is to saye both too much I muste subtracte 660 out of 4400 and so remaineth 3740 whiche is the diuidend Againe I must subtract the lesser errour 55 out of 275 that is the greater errour and there wil remaine 220 which shall be the diuisor then diuiding 3740 by 220 the quotient wil be 17. Wherefore I saye nowe constantlie that 17 is the true number of dayes that the Mason played and then it followeth that he wrought 23 dayes and so is the question answered Nowe for the order of triall of this worke there néedeth none other proofe but only thys to worke with this number according to the question and if it agrée then appeareth the number to be it that you would haue As here nowe séeing he wrought 23 daies and muste haue for euerie day 25 pence the whole sum commeth to 575. Then again séeing he played 17 dayes and muste abate 30 pence for eueriedaye the whole summe of the abatement will be 510 therefore I subtracte 510 out of 575 and there wil remaine 65 which maketh 5 s 5 d the cleare wages of the Mason for his worke according to the question Scholer Nowe I trust I vnderstand the worke and the rule so well and the better by thys proofe that I can be able to do the like And for a proofe I take the same question all saue the laste number where I will suppose that he hadde 10 s for his wages cléere And now to gesse at the number of the days that hée wrought I suppose first that he wrought 20 dayes then say I if he wrought 20 dayes his wages must be 500 d then did he play other 20 dayes for whych must be abated 600 d and then he leeseth 100 d And so am I at a staye for it is not like vnto your former worke Ma You shoulde haue required of me some question and not haue taken a question of your owne fantasying vntill you were more expert in this arte ☜ for so might you as well happen on an impossible question as on a possible but now to go forwarde consider that this number is too little by 220 séeing he should gaine by your supposition 120 d and in this positiō he léeseth 100 those both make 220 whiche you shall set downe for the first error with this signe betokening to little as here in this forme following doeth appeare And nowe for the rest go forwarde youre selfe once againe Scholer As my errour hath vttered my follie so it hath procured me better vnderstanding Nowe therefore considering this position not to solue the question I take an other supposing that he wroughte 30 dayes then for his wages he must be allowed 750 d and for the 10 dayes whyche hée wrought not he muste abate ●0● d and so remaineth cleare 450 d but it should be onely 120 d therfore is it to much by 330 whiche I sette downe in the figure with the former position and his erroure and the figure appeareth thus Nowe must I multiplie in crosse wayes 220 by 30 and it will be 66000. Then againe I multiplie 330 by 20 and it will be also 6600. Wherefore if I shall subtract the one out of the other there will remaine nothing to be the Diuidend Ma. In this you forget your selfe again for in as much as the signes in the errors be vnlike therefore must you worke by Addition adding togither those two totals to make the diuidend and also adding the two errours to make the diuisor And bycause you shall no more forgette this part of the rule take this briefe remembrance Vnlike require Addition And like desire Subtraction Sch. You meane that if the errours haue like signes then muste the diuidend and the diuisor be made by Subtraction as is taught before And if those signes be vnlike as in this laste example they be then muste I by Addition gather the Diuidend and the diuisor Therefore must I adde 6600 to 6600 and it will be 13200 whiche shall be the diuidend Then againe I adde 220 to 330 and it will be 5●0 whiche muste be the diuisor wherefore diuiding 13200 by 550 the quotient will be 24 whereby I knowe that the Mason wrought 24 dayes and then it followeth that he played 16 dayes M. Examine your worke whether it bée agréeable to the question or no. Sc For 24 dayes worke the wages muste be 600 d and for 16 dayes whiche the Mason wrought not there muste be abated 480 and then remaineth cleare to the Mason 220 pence as the question importeth wherefore it is euident that 24 is the true number of the dayes that he wrought Maister Althoughe you séeme nowe to vnderstande this worke yet to acquainte youre minde the better with the newe trade of this rule I thinke it good to propone to you fiue or sixe examples more before I make an end of it Sch. Sir I thanke you that you do so consider my commoditie and profit in knowlege for vndoubtedlie it is practise exercise that maketh men prompt expert in euerie kinde of knowledge Maister You say well so that they follow some certaine preceptes to gouerne and rule their practise by else maye practise procure custome of error and a repugnance to exactnesse of knowledge namelie as long as the error is not plainelie knowen to the vulgare sorte But to returne to our worke There is a seruant that hath boughte of the veluet and damaske for his maister 40 yeardes the veluet at 20 s a yeard and the Damaske at 12 s when he commeth home A question of vvares his maister demandeth of him

at Castili 350 Meruaides at L●sbone 360 Rats in Antwerpe 57 Deniers de Gros and at London 70 d sterling And contrariwise they do giue in the said Cities almoste as muche of their money to haue a Frēch Crown of the Marke at Lyons Thirdlye they doe giue at Lyons a 🜄 of the sunne to haue almost 93 Krentzers at Franckforde Auguste Norenberge or other Cities in Almaine Also at Lyons only they do pay the chaunge the 2 ● in gold and 1 ● in mony or else al in money in giuing 1 ½ for the hundreth Chaunges at Naples and other Townes Item at Naples they giue or deliuer almost 112 Duckets to receiue at Rome 100 Duckets of the chamber at the old value Through Luques and Florence they deliuer 100 Duckets Carlins to receiue there almost 86 🜄 of gold Through Palerme Messine one ducket of 5 Tary to receiue there almost 164 graines Throughe Milan one Ducket to receyue there almost 90 Soulx Throughe Geanes one Ducket to receyue there almost 65 soulx The whole sum to be paide within 10 dayes after the sighte of the bil of exchaunge Also at Naples they deliuer one Ducket to receiue in Antwerpe almost 67 d or Deniers de Gros. within 2 monthes At London almost 60 d sterling in ● months At Barselone almost 20 Soulx within 2 monthes At Valence almost 18 soulx wtin 2 monthes At Lisbone 333 Raies within 3 monthes and at the fayre at Castil almost 340 Merueydes at the same faire Chaunge of Venice to other places At Venice they deliuer 100 Duckets curraunte to receiue in Almayne almoste 140. Florenes at 60 Krentzers the péece At Lucques and Florence almost ●8 🜄 of gold in 10 dayes Likewise at Venice they deliuer a Ducket curraunt to receiue at Palerme and Messine almoste 21 Carlins at Milan almoste 93 Soulx At Geanes almost 62 soulx the whole at 10 dayes ende Of the Pair or Pari. As touching the exchaunge it is necessarie to vnderstande or knowe the Pair which the Italians call Pari which is no other thing than to make the money of the change of one Citie or towne to or with the money of an other by meanes whereof they doe finde the gaines or losse vpon the exchange Example Item hauing receiued letters of credite of one of Antwerpe that the 🜄 of the sunne is there worth 7 soulx The question is what the same is worth at London when the Pair or exchaunge goeth for 23 s Answer Saye if 23 giue but 20 what giueth 7 worke and finde 6 s 1 1 23 d and so muche is the 🜄 of the sunne worth at London The seuenteenth Chapter conteineth also a declaration of the diuersitie of the waightes and measures of moste places of Christendome for traffique At the ende of whiche discourse are two tables the one for waighte and the other for measure proportionate and reduced to an equalitie of our Englishe measure and waighte by the aide whereof the ingenious may easilye by the Rule of three conuerte the one into the other at their pleasure c. AT London and so all Englande throughe are vsed two kinds of waights and measures As the Troy waighte and the Haberdepoize from the Troy waighte is deriued the proportion and quantitie of all kinde of drye and liquid measures as Peckes Bushels quarters c. wherwith is bought and sold all kind of graine and other commodities mette by the Bushell And in liquid Ale Béere Wine Oile Butter Honie c. vppon these groundes and statutes is Bread made and solde by the Troy waight And so is golde siluer pearle pretious stones and Iewelles The least quantitie of this Troy waight is a graine 24 of these graines make a penny waight 20 penny waights an ounce and 12 ounces a pound 2 lb or 2 pintes of this waighte maketh a quarte And so ascending into bigger quantities is produced the Measures whereby are solde our other naturall sustenaunce vz. Ale or Béere with also other necessarie commodities as Butter Honny Herrings Eeles Sope c. Al which last before rehearsed though their Measures wherein they are contained be framed and deriued from the Troy waight yet are they in traffique with diuers commodities as Lead Tinne Flare Waxe with all other commodities both of this Realm of other Forraine Countries whatsoeuer bought solde by the Haberdepoise waight after 16 ounces to the pounde and 112 lb to the C. waight And vnto euerie C. is allowed 12 lb weight at the common beame From hence is also deriued the wey of Suffolke Chéese whyche containeth 32 Cloues 8 lb to a Cloue and weygheth in all 256 lb And also the barrell of Suffolke Butter is or shold be of like waight with the wey of chéese vz. 256 lb More 14 of these lb make a stone And 26 stone cōtaineth a sacke of english Wooll Forraine Woolles to wit French Spanish Estrich is also solde by the pound or C. waighte but most commonly by the Roue 25 lb to a Roue other commodities of tale are bought and sold by the C. fiue score to the C. Except headed ware to wit cattel nailes Fish whych are sold after sixe score to the C. Ther is also two other sorts of Measures to wit the Ell and the Yeard By the Ell is vsually mette linnen Cloth as Canuas c. And by the Yeard Silks wollen Cloths c. Antwerpe At Antwerpe are also 2 sorts of waights their golde siluer waight their common waight gold siluer is weighed by the Marke the Marke is 8 ounces the ounce 20 Esterlings and the Esterling 32 as our graines The Goldsmithes diuide that into smaller but not the Merchantes the proofe of Golde is made by Caractes whereof 24 maketh a Mark of fine Gold the Karact is 24 graines the proofe of the money is made by Deniers 12 deniers is 1 s fine that is a Marke of fine siluer the Denier also is diuided into 24 graines and the graine into 4 quarters Item 100 Markes in Antwerp Troy waighte maketh at Lions 103 Markes 2 ½ ounces and 20 graines 23 p̄ At Noremburg 103 Markes 2 ½ ounces 2 quints 3 Deniers at Franckford 105 Markes at Ausburge 104 Markes 3 ounces 1 quint At Venice 103 Markes 1 ounce 7 deniers 18 graines At London 66 lb. The Marke of Golde or Siluer at Antwerp Troy waight which is 8 ounces maketh 7 ½ ounces common waight with which all other merchandize is weighed So that the Troy waight is greater than the common waight by 6 ¼ in the C. By this waighte of Troy they also wey Muske Amber Perle c. All Silkes are bought at Antwerpe by the Bruges Ell whiche is greater than the common measure by which they retaile by 2 in the C. Their common Ell is ● 4 of our yeard and ⅖ of our Ell. Lions At Lions is vsed 3 sortes of waightes whereof the firste is the common Towne waight with whiche they wey all kinde of Spicerie and