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book_n	divers_a	follow_v	great_a	109	3	2.1245	3	false

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A74684	The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent.	Willsford, Thomas.	1660 (1660)	Wing W2876; Thomason E1748_1; Thomason E1748_2; ESTC R209647	103,352	283

and day of payment and likewise all such debts as are due to him for all Contracts whether by Paroll or Obligation in writing if without limitation of time are always due upon demand made An Inventory The Title entred the form of it is usually like a common Bill bearing date the year of our Lord with the moneth and day when the Owners estate was surveyed his name subscribed thereunto Upon the right hand or margent of each folio or page make 3 columnes to inscribe the pounds Sterling shillings and pence both of the Owners Cash or ready money with the Commodities as Lands Houses Rents Revenues Reversions Bonds Bills and Obligations c. according to their values or summes due also the Wares if any in his hands unsold with their quantities qualities and values in number weight and measure These entred and summ'd up take a rveiew of the engagements as whether in Factorage Company-accounts or intrusted for the use of others expecting his own share or part if any with all his proper debts as wares of others unsold ready mony in his hands accountable to others all Bills Bonds Obligations by promises of payment yet not satisfied all under the notion of debt-demanders decreasing the stock This Inventory is best reserved privately in the owners possession Thus having ballanc'd his estate the party may plainly discover what is his own and so commence a Trade without confusion imploying what stock he shall think convenient for any Adventure and divers Merchants do continually keep an Inventory but usually after this manner viz. A book in a large Folio every page hath 3 columns ruled in either margent denoting Pounds Shillings and Pence on the left-hand page his debts are inserted and on the right hand what is due unto him and from whom the money and wares with quantities and qualities inscribed between them and sundry other books they use the chiefest they use are these following The number and names of Books usually kept in great Merchants Accounts are these I. A Book for petty expences and daily disbursments of trivial summes of money kept like a Compendium of the Cash-book and these small accounts collected into one summe each week and moneth with a general total every year II. A Book of Letters or missive Characters received or sent upon publick or private business into forreign parts with the dates thereof and some breviate of the business III. A Copy-book of charges at home or Forreign accounts whether proper or for company by assignment for others or Factorage with abreviate of Receipts or Acquittances IV. A Book in Octavo of Memorandums to help the memory containing Bargains and Sales Promises Engagements by paroll or designed affairs in Commerce and Trade with the year moneth and day the parties names c. V. A Cash-book for inscribing the summes of mony in the Ca●heers posse●sion with all receipts and payments whereby to find what remaines in bank at any time and what debts are due one inscribed against the other VI. A Wast or Shop-book wherein are to be inserted all Wares Goods and Commodities arriv'd or shipt off received in or delivered out imported or exported and to whom with the year and day of the moneth every parcel distinguished by a line drawn betwixt them describe in the margent the mark of the said parcel with some note of reference to the Journal page and also the number weight and measure of each parcel with the quantities colour charges value or price of them VII Besides these there are Diurnals and books kept of Ship-accounts whether outward or homeward bound viz. daily occurrences Ship-expences charges and disbursements accidental c. VIII A book of Fraighcage Cargazones or bills of Lading Mariners wages and necessaries for them with divers other supernumerary Accounts not commonly kept by all Merchants nor yet convenient for this Treatise or my intended designe The scope here aimed at is a compendious form in keeping the Journall and leager-Leager-books by way of the Italian manner included by Debitor and Creditor with divers precedents in posting and entring the Commodities or Merchandises with the description of those books for to nominate all those which some particular Merchants Adventurers do keep would make a Catalogue in a poore Scholars Library and herein superfluous each book of them being but a relative Index unto the two last The Diary or Day-book ought to be in a large folio upon the front thereof write the year of our Lord and Saviour in numeral letters Arithmetical characters or both then the title of Journall noted with a capital letter as A B or C c. Thus made conspicuous the title of each page or parcel within the book is dated with the year moneth and day of any Wares Goods or Commodities bought sold exchang'd received in or delivered out every page on the right hand hath 3 columns in the margent expressing in money the value of the said Goods or Wares inscribed in pounds Sterling shillings and pence c. and upon the margent on the left hand one column for 1.2.3.4.5 c. as quotations to the Leagers page and folio Besides all this 't is convenient to enter the mark number weight and measure of the Commodities or Parcels the Debitors and Creditors names with the time place and manner of payment or what is convenient to be inserted in explaining the contract whether imported or exported Goods without blotting or interlining any thing X. The Leager is a collection of all the merchants books drawn together in a large folio charged upon some account in this order as the book is o●ened ●lace the Creditors upon the right hand page and all the Debitors on the left the pages number'd by 1.1.2.2 so as the Dr. and Cr. make but one folio u on either side in both margents there are also columnes which bound the matter inscribed in number various as the Merchants please or the multiplicity of their employments shall require whereof I will r●nder some precedents hereafter the words most frequently used in transporting or posting of Wares or Commodities from the Journall or Diary into the Leager-book are these In the first place on the Debitors side inscribe the word To after which let the Account immediately follow and on the Creditors part usually the first word is By preceding the name of that Account and note that every parcel is charg'd and discharg'd with the same summe and observe that most Accounts are best written in one line or so compendious as you can some men of very great Commerce and trading keep a Kalender Register or an Alphabeticall Index of the names of Men Wares Ships and Voyages with a mutuall reference of numbers to these and the Journal-pages where the Goods are e●●red according to Debitor and Creditor and this is alwayes annexed before the Leager either side or page of the Leager being noted with one and the same numbers The Definitions of Debitor and Creditor By Debitor or Debitors in Merchants

encreased or diminished by some common number from whence divers mechanical men do use and acknowledge it as a maxime in their trades in setting out Structures and regulating their works in perfect squares after this manner Take a long line as your occasion requires of which take 3 equall parts at pleasure then 4 such succeeding parts and from thence 5 so the line is now divided into 12 equal parts by 3 4 5. these parts extended wil inclose a right angled triangle as A. B. C rectangled at B. and proportional in all the parts as by the first Book 19 Prop. Trigon This right angle found you may describe a Parallelagram or a Quadrangle if you please as C.D.E.F. and A.B.D.E. or A.B.C.F. c. PROBLEME III. The three sides of any right lin'd Triangle being given to finde the superficial content thereof without knowing the Perpendicular The Theoreme From half the summe of the 3 sides subtract each particular side the total of their mutuall products encreased by half the summe of the 3 sides the quadrate root of that product will produce the superficial content Suppose a Triangle with all the three sides known or found by any true measure as admit in Feet and the dimensions these viz. 15 F. 20 F and 25 Feet the summe of them is 60 F the half 30 F. from whence subtract the particular sides the differences will be 5.10.15 these by multiplication continued will produce 750 that product again encreased by the summe of half the sides which here is 30 F. will produce 22500. the Quadrat root of it is 150. the number of square feet contained in the superficies of that Triangle required having here the superficial content of this Triangle by the first Probleme before you may easily find the Perpendicular for 150 feet is but half the long square made of the Basis and Perpendicular then 300 the whole square divided by 25 the Basis of this Triangle the quotient will be 12 feet for the Perpendiculars height and so in any long square the superficial content divided by the longest side will produce the shortest and divided by the lesser side will discover the greater If in multiplying or dividing any square figures or numbers that happen in fractions you must consider their sides for ½ multiplied by an unite will produce but ½ and ½ by ½ is but ¼ of that Square as by the first and second little Quadrats made of the line A. B. in the Scheme pag. 109. to which Book and Parag. I refer you and to my first Book of Trigon Prop. 31. The 3 sides of any plain Triangle given to finde the Perpendicular and in what part of the Basis 't will fall The Theorem Square the 3 given sides adde the 2 greater squares together and from that summe subtract the lesse h lf the remainder divide by the Basis or greater side the quotient will be the greater Segment As for example admit the 3 sides of a plain Triangle given 30 40. and 50. the Basis which the Perpendicular will divide into two Segments in this 32 and 18. making 2 right angled Triangles now with either of the two sides find the third as before which according to the state of the question will prove 24. the thing required PROBLEME IV. The dimension of any plain right angled Superficies and first of Board by square measure as a foot or 12 inches whose Quadrature contains 144 inches The Theorem The superficiall content of all rectangled figures are found by the multiplication of any two sides by one another that incloseth the right angle A foot is here allowed the integer by which board glasse c. is usually measured every one of these dimension● is divided into 12 equall parts called inches and are the next immediate fractions to that integer as by the Scheme pag. 103. Arith. does appear Now suppose a stock of board to be measured in number 20. each board is in length 18 feet in breadth 10 inches the length is in inches 216. which multiplied by 10 shews the superficial content to be 2160 inches that divided by 144 the number of square inches in one foot there will be found in each board 15 square feet and consequently in the 20 boards 300 feet the superficial content of the whole stock required if the boards be tapering as most stocks are the common custome is to take the breadth in the middle or the Arithmetical mean that is half the breadth from the summe of both ends as admit the breadth of the last stock had been 9 inches at the one end and 11 at the greater or 8 inches and 12. the summe had been 20 in either the half 10 inches as before Admit there were 24 panes of glasse propounded to be measured each pane containing in length 22 ½ inches in breadth 14 ½ inches and the superficial content is required in feet the breadth and length here given converted into half inches produceth 29 and 45 the square of them is 1305 half-squar'd inches in each pane which multiplied by 24 the number of panes the whole product is 31320. and since half the root or side of any insquar'd is bu● ¼ as by the demonstration of fractions pag. 109. divide 31320 by 4 the quotient will be 7830 square inches which divided by 144 the quotient will be then 54 ⅜ feet the true superficial content of all the glass required By Decimals Divers questions that fall in fractions may be readily performed by artificial number as thus the length of one pane here propounded is 1 foot 10 ½ inches the breadth 1 foot 2 ½ inches for these fractions see the first Section of the third Book and fifth Table Chapter 7. where you may finde the Decimall for 10 inches to 5 places .83333 and for the ½ inch or 5 10 this 04167 the summe of them .875 and for 2 ½ inches these .16667 and .04167 the total .20834 before these prefix their integers and then their numbers will stand thus 1.20834 and 1.875 the products of these are 22656375 which multiplied by the number of panes viz. 24 produceth 54.3753000 which is 54 3753 10000 feet and exceeds the former not 4 10000 and that by reason of the irrationall fractions which cannot be exactly true yet the greater number will have the lesser errour PROBLEME V. For boarding a Room There is a Gallery containing in length 271 feet in breadth 35 ½ feet how many feet of board will floor this room To find how many superficial feet this room contains will be discovered by the last Theorem for 271 feet multiplied by 35 ½ feet that is by 71 or more compendiously by encreasing 271 by 7 according to my former rule as in pag. 38. which will produce 19241 half feet and that divided by 2 as by the demonstration in fractions pag. 109. the true superficiall content will be 9620 ½ feet And here you are to consider in all such cases there will be losse in their breadths

once before attending the Press and now you with the regulation of Commerce and Trade accommodated to all ingenious capacities prescribed rules being equally necessary to all for those who know not how to buy will be ignorant how to sell or how to borrow that know not how to lend Besides these here are divers Geometricall Propositions appertaining to Manufactury Trades and some for the Surveyer Souldier Engineer and Accountants all of good use and convenient for the illustration of my former books of Arithmetick proportioned with Lines and Numbers composed more for speculation than practice and this designed more for practice then the Theory whereby none shall be deluded with words nor deviated with doubtfull directions in diversity of ambiguous Tracts or bewildred in Mazes out of which these Rules shall be your conduct if you please to accept them for a guide In witnesse whereof I give you here my hand by the subscription of Your benevolent Friend Thomas VVillsford To the Tyron of Merchants Accounts short Advertisements as to the Debitor and Creditor with some precautions to prevent mistakes for the right use of it THou hast here presented thee for thy practice what is really promised in the Title viz. Merchants Accounts epitomised yet is it so furnished with variety of usefull practicall and necessary Resolutions as may render it to be nothing deficient for thy initiation into the famous art of Accountantship by way of Debitor and Creditor here being both the Introductory part and Practicall so fitted to the meanest capacity that the more common Trades may hereby be informed to keep their Books Merchant like and an ordinary capacity may in a small time hereby learn a method whereby they may be rendred capable of keeping any accounts after the Italian manner This Book is so compleat that I thought it unnecessary to annex a Wast-book to the Journall it being compleat enough without by the reading of the Introductory part thou wilt be able of thy self to frame a wast-book whose office is nothing else but to set down at large and explain the time when we buy or sell the person of whom we bought or to whom we sold and what and in what nature whether for time or for ready money or exchange thereby to refer every particular parcel of Wares and Contracts to their proper places in the Journall there to be inserted their true Debitor and Creditor the use of which Book and all others necessary thou hast in the Introduction page 206 207 and what volume they ought to be of Now before you proceed to put any thing in practise you are desired to amend the Errata's committed in the printing of this Deb. Cr. some of them being occasioned by absence from the Press and the unusuall printing things of this nature the greatest being the misfolioing which are insufferable in books of this kind by reason of the several referrings the Journal Leager hath to each others true place or folio You shall find the second folio in order of the Leager to be by the printer numbred folio 1 the reason was because that stock which is there placed was in the originall copy in folio 1 but by reason in the printing it could not be brought into one folio it was put into one by it self bearing its originall folio by reason of its severall references to the Journall which in all places has it noted in fol. 1 the rest of the errours you have in the Errata following ERRATA THe pages 203 204 205 206 207 208 209. should be intitled An Introduction to Merchants Accounts p. 217. line 7. dele Creditor in fol. 1. of the Journall l. 7. dele to l. 3. in the 2. column it should be ● 1. fol. 4. in the first l. of the 4 last read or for our but that which is fol. 2. in the 6. fol. should be 6. in line 5. in the col of pence for 8. r. 4 d. l. 21. for 1659. r. 1658. l. 6. in the col of pence r. 8 d. that which is fol. 7. in order is f. 3. and for that 3 r. f. 7. in dito f. l. 19. just against A.B. in the col of l. s. d. insert 1 l. 2 s. 8 d. l. 22. just against Middlesex for 1 l. 2 s. 8 d. r. 12 l. l. 26. just against A.M. in the col of l. s. d. for 12 l. r. 200 l. f. 9. l. 1. for fo 1. for l. 6. for Vigmys r. Virginia f. 10. in the col of ls for 430 l. r. 304 l. l. 11. in the col of l. for 3 l. r. 4 l. In the Leager Fol. 4. Debitor side l. 3. in column 2. on the Debitor side to the left hand 7. dele 3. fol. 4. Cr. side col 2. to the left hand for 8. r. 9. in l. 4. f. 6. the totall and last summe of profit and losse on the Debitor side should be 588 l. 19 s. 4 d. f. 9. col 2. the Debitor side l. 1. dele 5. Reader ALthough the benefit of my Countrey and my owne Recreation hath put me upon the study and publishing of these Curiosities for the knowledge of these Arts wherein all things cannot be so plain but that there may be some need of the further assistance of an Artist I here make bold to acquaint thee with the perfections of Mr. Nathanael Sharp who writeth all the usuall hands writ in this Nation the Art of Arithmetick Integers and Fractions and Decimall Merchants Accounts also youth boorded and made fit either for Forreign or Domestick Employments He lives in Chain Alley in Crutchet-Friars To his Honoured VNCLE M. Thomas VVillsford c. WHat sacred Apathy confirms your breast And in loud storms rocks you to peaceful rest Calm Studies and the gentler Arts you ply No outward airs untunes your Harmony Resolv'd how bad or mad soe're we be Not to revolt from your lov'd Industry The great Archimedes ' mongst blood and rage Smoke and the cries of every sex and age Smil'd on the face of Horrour and was found Tracing his mistique figures on the ground Thus He and you seem to look down on Fate For 't is not Life but Time we ought to rate Which you improve to Miracle each sand Attests the labour of your head or hand While Arts Arcana and new Worlds you finde The blest discoveries of a trav'ling mind Nor are you to one Science onely known For ev'ry Muse all Phoebus is your own Edward Boteler AN INDEX TO THE FIRST BOOK Divided into three Parts PART I. OF Whole-sale and Retail without gain or loss or the contrary whether relating to the whole parcell or part or to any Interest per cent per ann as in page 1. to the 15. Propositions Equation of payment p. 19. prop. 16. Barter with the dirivation p. 20. pr. 17. 18. Tare Neat Tret and Cloff p. 22. pr. 19 20 21. Exchanges of forreign Coin Assurances and Returns of Money p. 27. pr. 22. to 28. Reduction of Weights

inches that multiplied by 4 will produce 154 square inches for the superficial content required but not exactly true Art being in all such cases defective as was said before 2. To find the superficial content of any Globe as thus multiply the Spheres diameter with the circumference of the same circle the product will be the thing required as in the last Example where 7 is diameter 22 will be the circumference the product of these is 154 as before 3. To measure the superficies of any Sphere multiply the square made of the circumference by 7 and divide the product by 22 the quotient will be your desire As for example admit the circumference propounded be 44 whose square is 1936 which multiplied by 7 produceth 13552 that divided by 22 the quotient will be 616 for the superficies desired in a quadruple proportion to the last 4. The superficial content of any Globe may be also thus found multiply the square made of the diameter by 22 and divide the product by 7 the quotient resolves the question as for example admit 14 the diameter given whose square is 196 which multiplied by 22 produceth 4312 that divided by 7 the quotient will be 616 as before all those 4 agreeing in one PROBLEME VIII The dimension of Globes and Spheres by their circumferences and diameters known and their solid contents found by any measure assigned and performed 3 several wayes 1. With the diameter or circumference by any one of the former rules find the convex superficies of the Globe of which take ⅓ part or ⅓ of the semidiameter those multiplied together will produce the solid content of the Globe as for example admit a sphere to be measured whose diameter is 7 inches the convex superficies will be found as before 154 inches the semidiameter of this circle is 3 ½ or 7 2 take ⅓ part of either as of the fraction here which will be 7 6 this multiplied by 154 produceth 179 ⅔ inches the solid content of this Globe required 2. The diameter of a Globe being given multiply the cube made of that diameter by 11 and divide the product by 21 the quotient is the solid content Example in the last question 7 was the diameter propounded whose cube is 343 that multiplied by 11 produceth 3773 and divided by 21 the quotient will prove 179 14 21 or ⅔ the solid content of this Globe 3. By the circumference of any Orbe find the solid content as thus take half the circumference and multiply it cubically and that cube by 49 then divide that product by 363 the quotient gives the solid content required Example 44 inches is a circumference given the half is 22 the cube of it will be 10648 which multiplied by 49 produceth 521752 this divided 363 the quotient will be 1437 ●21 363 or ⅓ and so many solid inches are contained in the Globe If more exactness or ampler satisfaction shall be required herein see Archimedes de dimensione circuli PROBEME IX The Diameter Weight and Magnitude of a Globe being given with the Diameter of another to finde the weight or solid content of that Orbe The Theorem All Globes and Spheres are in proportion one to another as be the cubicall bodies composed of their Diameters Suppose 7 inches were the Diameter of a Globe propounded and the solid content of it 179 ⅔ or 539 3 and the Diameter of another Orbe 14 inches whose solid content is required in the same parts the Cube of 7 is 343 and the Cube of 14 inches is 2744 the cubicall content of the first is given 539 3 which multiplied by 2744 produceth 1479016 3 and this divided by 343 the quotient will be 1437 343 1029 or ⅓ as in the Table does appeare and also in the former Probleme if the weight of the first had beene knowne and both their Diameters the weight of the second would have been discovered in the same manner as was the magnitude and if the Diameter of the one had been known with the weight or solid content of both the other would have been found in proportion of their Cubes as shall be illustrated by the following Propositions THE THIRD PART Consisting of Military Propositions PROPOSITION I. By the Diameter and weight of any Bullet known with the Diameter of another to find the second Bullets weight IT is a common received opinion that an iron bullet of 4 inches diameter will weigh 9 lb which if it be true and that all iron will weigh alike in equal magnitudes then this rule is a positive truth viz. as the cube of 4 is to 9 lb weight so shall the cube of any iron bullets diameter be proportionable to the weight thereof according to the last Theorem as for example an iron bullet whose diameter is 6 inches the cube of it 216 so the proportion is as 64 is to 9 lb. so will 216 be to 30 ⅜ lb as in the table is evident which ⅜ is 6 ounces PROPOSITION II. By knowing the weight of two bullets and diameter of one to find the other diameter For illustration of this Proposition I will reverse the last question viz. if a bullet of 9 lb weight shall contain 64 inches in the diameters cube then a bullet 30 ⅜ lb or 243 8 will require 216 inches whose cubique root is 6 inches for the bullets diameter these 2 examples are sufficient for any question of this kind but observe if by the diameter of the guns concave you would find what the bullet belonging unto it will weigh the diameter of it must be ¼ of an inch less then the diameter within the muzzle although it be not a taper bor'd gun To find what thickness they are in metal their Cylindars concaves with their bullets diameters Galaper Compasses are held the best for expediteness especially those that open with a quadrant divided proportionally in inches and to 1 10 commonly known to every Engineer as for proposals of this art there be divers books extant to which I refer you they belonging more to the practise then any Theory besides doubtful queries are made by them viz. as whether the quantitie of powder can be proportioned by Arithmetick to the weight of bullets or whether they move in a right line or circular or if a Canon be more fortified in metal upon one side then the other wherefore the gun discharged shall convey the bullet wide from the mark and the concaves cylindar incline to that side on which the metal is thickest because most resisted or wherefore a piece of great Artillary mounted at 18 or 20 degrees of the quadrant shall convey a shot the farthest and almost twice the level range also how good powder is known all which must be referred to experience This we know that the sulphur makes it quick to fire the Charcole maintains it and the Salt-peter turning into a windy exhalation by repercussion of the aire causeth such violent effects to amaze the world as if ambitious to imitate