books is understood the account that oweth or stands charged and the word Creditor or Creditors signifies the discharge So all things received or the Receiver is alwayes made Debitor the things delivered or the Deliverer is the Creditor all which are compendiously comâ—rised by some Accountants according to these following breviats And thus stands all Bills Bonds Obligations of things lent or promises to lend or cause to be lent or paid included in the same predicament with the two former whether simple or mixt the foundation of this structure What Debitor and Creditor contains in summe unfolded in the Merchants books viz. All Goods Men Money Voyages Ships Cargazones Bills of Exchanges Wares or Commodities c. with Profit and Loss are contracted into two kinds viz. Debitor and Creditor and those contained in these Predicaments under 12 Species whether proper for Company Factorage Domestick or Forraign or mixt with the other two How these are comprehended under the notion of Debitors or made so by Commerce and Trade I. Lands Rents Revenues Money Wares or Commodities either in possession or shipt away to forreign parts with all those who are engag'd to pay or deliver must be inscrib'd in the Merchants Books Debitors to the Owners to their Cash or Stock II. Whosoever receiveth or the Goods received whether Money or Merchandizes upon their own proper account for Factorage or Company wâ—ite them oâ— the Wares Debitors III. If a man delivers Wares or payes money Bills or Exchanges upon the account of another that party upon whose account t is paid becomes Debitor IV. A man who delivers an Assignation in payment whether his own or not but for the use of another then the party upon whose account 't was delivered is made Debitor V. Money received that was taken up at Interest then is Cash commonly written for the Principall Debitor but the Lone or Profit and Loss for the Interest money is made Debitor VI. An Adventurer or any other for him that sends merchandizes unto a forreign place or Region whether proper or for any Company consign'd to a Factor or Resident there the Voyage or Ship is written Debitor VII A Merchant that insures any wares and receives the money presently then is the Insurer or Cash written Debitor but in case the Insurance be not immediatly paid then is the party for whom they were insured Debitor for the Insurance reckoning VIII Upon advice that any Goods insured for Proper or Company-account and those shipt to sea were cast away in part or all the Insurer or Insurance reckoning is Debitor but if otherwise then Profit and Losse are subscribed Debitors IX Upon Returns or Advice from a Factor that the shipt wares were received whether for Proper or Company-account enter the Factor there resident Debitor X. A Factor that drawes an Echange upon the Merchant Company himself or others to the party or parties uâ—on whoâ—e account it was drawn inse t Debitor and the like upon Exchanges remitted the acceptor who must discharge it is Debitor XI A Merchant or Company that loses by the sale of Wares by Bank-routs Exchanges Insurances Interests Gratuities or whatsoever proves a detriment in Commerce and Trade to all or any of these subscâ—ibe profit and loss Debitor XII In balancing of Accounts if there be money or wares in the house unsold or in the possession of their Partners and Correspondents who have not rendred satisfaction then must People and Cash bâ—th in the old and new books be written Debitors Creditors in Merchants Accounts are generally but reconversions from Debitors discharg'd or the Principall included briefly in these 12 Species I. Stock or Cash for wares unsold Creditor and the people to whom any one is indebted whose names are distinctly to be specified under the notion or by the subscription of Creditor II. What things soever a Merchant delivers or engages to be delivered whether for Proper Factorage or Company-account in money or wares either the goods delivered or the party promised is Creditor III. Any man that delivers money Wares Exchanges or Assignations upon anothers account that party or parties upon whose account 't is received muâ—t be subscribed Câ—editor IV. A Merchant borrowes money at interest which being received the party who delivers it or the lender is Creditor for the Principall and enter the Lone reckoning or profit and loss for the interest money Creditor V. A man having a Principall of anothers in his possession the time of payment expired and yet detained the owner of the principall is for the interest of that time onely to be written Creditor VI. A Merchant receives advice from his Factor of the sent Goods received and sold or not enter then Voyage to such a place consign'd to his correspondent Creditor VII Any Wares or Adventures safely arriv'd the insurance not paid but customes and charges defraid inscribe one of these viz. Cash Charges the Insurer Insurance reckoning or Profit and Loss Creditors VIII Goods or Commodities insured for Proper or Company-account shiâ—t to sea and by misfortunes cast away as by letters from the Factor or Resident appears subscribe Voyage to the place consign'd to such a man for Proper or Company account Creditor IX A Meâ—chant from his Factor or Resident receives Returns in money or merchanâ—izes in lieu of the Wares received and sold whether for Proper or Company account the Factor or Correspondent that caused these goods to be delivered is Creditor X. An Exchange drawn by a Merchant upon his Factor for his Proper Company or any others account or remitted then the party or parties for whose account it is drawn charg'd sent or remitted make Creditor the correspondent Debitor XI A Merchant or Company that gaines by Gratuities the sale of Wares Exchanges Insurances Interests or what things are beneficiall in Commerce and Trade to all or any these subscribe Profit and Loss Creditor XII In balancing of Books Factors Partners and all others unsatisfied if Fortune hath favour'd the Merchant Stock and the People will be in the old and new books Creditor To shun mistakes betwixt Debitor and Creditor and not to be prolix I prescribe these rules and instructions more compendiously then others have delivered them yet those I have seen in some copies epitomiz'd like the good works of this Age easily to be remembred without over-fraighting the Readers memory which for the assistance of young men I will render in this breviat a transcription of others presented to your view in two tables one balancing the other The Debitors or whatsoever oweth are 1 What Goods we have 2 Who receives any thing 3 All Wares that we buy 4 The men to whom we sell 5 Those for whom we buy 6 Those for whom we pay 7 The men who are to pay 8 Goods that are insured 9 Those for whom we insure 10 Voyages where we send 11 Goods on which is gained 12 Profit and Losse The Creditors or what is to receive are 1 From whence it ariseth 2 Who delivers any
and Measures p. 35. pr. 29. to 32. Factorage p. 39. pr. 33. to 36. Cambio Maritimo Sea-hazard or Bottom-ree p. 44. pr. 37. PART II. Definitions and Etymologies of Usury and Interest-money p 47. Simple Interest in Forbearance where the Principall Interest and Time are of whole or mixt denominations p. 50. pr. 38. to 45. Discount or rebate of money for any Interest or Time p. 59. pr. 46 47. Tables of forbearance and discount in compound Interest calculated by Decimall Arithmetick from 1 day to 25 years inclusive at 6 l. per cent per ann p. 64 65 66. The construction of Decimall Tables p. 67. in forbearance and discount of Money Rents Pensions Annuities and Reversions with the purchase of them to p. 78. The application of these Tables p. 79. quest 1. to qu. 21. PART III. Rules of Practise by memory and the assistance of one Table p. 103. 105. The description and use of this Table in 9 Examples p. 107. A Julian Kalendar for the receipt and payment of money or other businesse as to find what day of the week any day of the moneth shall fall upon for 11 succeeding years p. 112. A Gregorian Kalendar for the receipt or payment of money beyond sea where that account is received p. 114. The Contents of the second Book divided into five parts PART I. The dimension of all plain or right-lin'd Triangles pag. 117. Problem 1 2 3. The dimension of Board Glass Hangings Wainscot Pavements Land c. p. 122. pr. 4 5 6. Reduction of any squared Superficies from a greater to a lesse and the contrary p. 129. pr. 7. How to make the Carpenters Ruler for the dimension of any Superficies measured by the foot or yard square p. 136. pr. 8. To find the content of a Square including any Circle propounded p. 134. pr. 9. The Diameter of any Circle known to find the greatest circumscribed Quadrangle p. 135. pr. 10. To find the nearest Quadrature of a Circle p. 137. pr. 11. The dimension of solid bodies p. 139. prob 12. to pr. 14. A Demonstration in the commensuration of tapering Timber p. 147. To divide the Carpenters Ruler for the measuring of solid bodies p. 151. PART II. The dimension of round and concave Measures p. 155. prob 1. The gaging or measuring of Casks from the Runlet to the Tun either of Wine or Beer p. 158. pr. 2. By the diameter of any Circle to find the Circumference p. 160. pr. 3. With the diameters of two Circles and the circumference of the one how to find the other or the contrary p. 161. pr. 4. With the diameter and superficies of one Circle to find the content of any other the diameter being known p. 161. pro. 5. With the superficiall content of two Circles given and one Diameter to find the other p. 162. pr. 6. To find the convex superficies of any Sphere or Globe whose diameter or circumference is known and that four severall wayes p. 163. pr. 7. By the diameter or circumference of any Sphere or Globe known to find the solid content 3 severall wayes p. 194. pr. 8. With the diameter and weight of any sphere or Globe to find the weight of any other whole diameter is known p. 166. pr. 9. PART III. With the diameters of 2 Bullets known with the weight of one to discover the other p. 169. proposit 1. By the weight of 2 Bullets known and diâ—meter of the one to find the other p. 70. prop. 2. Compendious Rules for martialling of Souldiers in all right angled forms of battels with their definitions p. 172. prop. 3 4 5 6. The incamping of Souldiers in their severall quarters p. 176. pr. 7. The height of any Wall or Tower being known to find the length of a scaling Ladder p. 177. pr. 8. To find the height of any Wall or Tower that is accessible p. 178. To find the distance to any Fort or place though not accessible p. 179. pr. 10 11 12. In a City Castle or Fort to be beleaguer'd how to proportion the Men and Victuals Guns and the Powder whereby to make the Works tenentable for any time limitted p. 182. pr. 13. to pr. 16. Generall Rules and Observations of experienced Engineers and Gunners p. 189. PART IV. The form of keeping Merchants Books of Account after the Italian manner in form of Debitor and Creditor p. 233 Architectonice or the art of Building as an Introduction to young Surveyors of the Estimates Valuations and Contracts from p. 1. to p. 5. The manner in taking of a survey of Masons work by the great p. 6 7 8 9. A bill of Measure with the charges in money according to the articles of agreement p. 10. Estimates Contracts Rates Rules and Proportions observed by Carpenters p. 11. Proportions and dimensions of a Roof p. 12. The Materials Valuations and Proportions in covering of Structures and finishing of them to make them tenentable and commodious by sundry Artificers p. 15 to 30. The five orders of Columnes or Pillars described with the Artificers and Inventors of them p. 31. to 34. FINIS THE FIRST BOOK PROPOSITION I. A Grocer bought 5 ¾ C grosse weight of Wares which lay him in with all charges defraid 163 lb 13 ss 8 d. sterling and it is demanded what one lb cost or how to sell it by the pound without gain or loss The Rule As the quantity of any one Commodity or wares is unto the total price with the cost and charges so will a l or an unite of the first denomination be in proportion unto the rate it may be sold for An Explanation of Whole-sale and Retail Lib. 2. Parag. 8. Observe in all Commodities where a hundred gross is mentioned it is 112 lb usually noted with a C. for Centum as in this Example where five hundred and three quarters is given which 5 C multiplied by 112 lb and ¾ or 84 lb added unto it the product with the addition will make the summe of 644 lb for the subtile weight and the first number the second number in proportion is the price viz. 3273 â…” 8 the third number is 1 lb on which the demand is made these compound fâ—actions you may reduce into the least denomination or the least but one as in the Table where by the Rule of Proportion in either way you will finde thâ—t one lb of those Wares stood the buyer in 5 ss 1 d or as in the Table 5 2 â—2 ss with all châ—rges defraid according to the demand and state of the Question propounded PROPOSITION II. How to sell aâ—y Wares or Commodities by retail the prâ—ce or value of the whole parâ—el being known and to gain a certain suâ—me of money in the whole quantiâ—y requâ—red The RULE As the quantity of the whole Commodity bought is unto the summe of the price and gain required so will 1 C. 1 lb or 1 yard of the first denomination be proportional unto the price it must be sold at An explanation where
answer to this question will be 113 L 15 S and so for any other of these kinds PROPOSITION XXII A man delivers unto a Merchant a certain summe of money to be received of his Factor upon Bills of Exchange in a forreign Countrey and Coyn the rate and proportion of the moneys in both places being known The RULE As a unite or any one piece of a known Coyn Is in proportion unto a Coyn of another value So any summe of money delivered in the first Coyn Unto the quantity to be received of the second An explanation of Exchanges betwixt Forreign Coyns Exchanges of all Coynes Weights and Measures of forreign places with one another are easily performed by the common rule of Three if first reduced unto any certain proportion by which means any one thing may be converted into the species of another in respect of value or quantity as by some few propositions with examples shall be illustrated and first for this suppose that sixty pound received at a place where one pound is 13 ss 4 D sterling or English how much must the man receive in London at 20 s the pound Sterling whereby to make them equall in value The answer to this proposition will be 800 s or 40 l as in the table equall to 60 Marks the value of one being 13 s 4 d. had the question been stated in any other denomination the solution would have proved the same with the second term as 1 l Scotl. to 40 groats so 60 l Scotl. unto 2400 groats or in the fraction of a pound Sterling thus as 1 l Scotl. to â…” l Sterl so 60 l Scotl. to 40 l. Sterl Thus sometimes you may ease your self by changing the denominations all being true depending upon the seventh Paragraph of my second Book PROPOSITION XXIII Any pieces of Coyn if equal unto some one piece of another and that equivalent to a third to be exchanged with the first how much money of the one will discharge a bill of the other This differs not essentially from the last as admit 10 Ryalls were equall to one Ducat and one of them worth 5 s 6 d how much money Sterling will discharge a bill of Exchange for 4500 Ryals the proportion will be As 10 Ryals is to 5 ½ ss what 4500 Ryals the answer 2475 s that is 123 l 15 s sterling the question solved for if A be made equall to B and B = to C then A and C are equall as by the second Axiom Lib. 2 par 7. PROPOSITION XXIV If upon return of money a certain rare per cent shall be required to find in any summe of money how much must be abated at the rate propounded upon such exchange or return of money The RULE As the summe of 100 l with the allowance per cent Shall be in proportion to 100 l where it is to be paid So will any summe of money received of a Merchant Be proportionable to the money that shall be delivered An explanation upon return of money after any rate per cent Lib. 2. Parag. 8. A Merchant of London was to return money to be delivered at Durham as admit 616 l received by a Carrier which to secure and deliver at the place appointed what was to be returned the Merchant did allow 2 l 13 s 4 d per cent upon this abatement how much was the summe paid at Durham first adde unto 100 l the money to be abated per cent the totall in this proposition will be 102 l 13 s 4 d which must be the first number in the rule of Three direct and will be in proportion thus as 102 â…” L or made an improper fraction viz. â—0â— 3 to every 100 L returned so 616 L received will be proportionable unto 600 L the Proposition answered PROPOSITION XXV Upon assurance and return of money at any rate in the pound sterl to find what a greater or lesser summe will be worth assured at the rate propounded Observe in any proposition made the true state of the question and whether it be customary or of that predicament if customary it is something tolerable in small summes although a little erroneous this caveat concerns other propositions only note well the difference of these in the last the Assurancer was to have so much money out of the summe delivered to him as should but discharge the money he returned which the last rule does solve where the Assurancer had 16 L out of the 616 L so answers the question in the rate required which admit imposed upon every pound sterl the proportion will be as 1 L is to the rate given so will the summe to be returned unto the money due upon it for the assurance And for the probat of this suppose as in the last proposition 600 L were to be returned from Durham to London allowing the assurancer 6 â…– D upon every pound sterl the rule is as 1 L to 32 5 D so 600 L shall be in proportion to 3840 D that is 320 ss or 16 L as before due for the securing of 600 L and not 616 as in the last proposition which is erroneous though allowed of by many PROPOSITION XXVI The rate or proportion for the exchange of any money betwixt two places being known to find how much money of the one place will discharge a bill of exchange in the other city or town The RULE As any one pound sterl or other piece of money Is in proportion to the difference of Exchanges So will any summe propounded of the first money Be proportionable to the coyn where it is payable An explanation of two wayes concurring in one production The rate for exchange here in this example is of a forreigne coyne whereof 1 L 3 ss 4 D is equall to 1 L sterling how much of that forreigne money will discharge a bill of exchange for 240 L 13 ss 4 D sterling in this case 1 L or 20 ss is the first number in the rule the difference in exchange is 3 ss 4 D the summe to be exchanged is 240 L 13 ss 4 D. with these 3 numbers you may finde 40 L 2 ss 2 â…” D. which added to the money paid makes 280 L 15 ss 6 â…” D the totall to be received upon exchange but the more usuall way is according to the table and prescribed rule viz. as 20 ss is to 23 â…“ or 20 3 ss so 1â—â—â—â— 3 unto 5615 9 â— ss which reduced is 280 L 1586 â…” D as before PROPOSITION XXVII By knowing the money paid unto a Merchant and likewise the summe received upon bills of exchange in a forreign coyn to find how the exchange went between those places This proposition is but the former reverst and so requires no rule but that of proportion nor example but the last where the first money paid is 240 l 13 s 4 d the forreign money received upon bills of exchange was 280 l 15 s 6 â…” d the middle number here in the rule of Three must
be 1 l sterling or 20 s if you please the former numbers reduced into improper fractions will stand in the rule of Proportion thus viz. As 14440 3 ss is to 20 ss so will 50540 9 ss be to 1 l 3 s 4 d the rate which the Exchange went at according to the former Proposition enucleated in this In all these questions or any others appertaining onely to the exchange of money there is nothing more required from the value or estimate of any known Coins to finde what summe of the one shall be equall or in proportion unto the same quantity of the other as if 1 l sterling were equall in value unto 25 s of some other coyn the proportion of equality would be viz. As 1 l sterling or 20 s is to 25 s so any summe of the first coyn to an equall quantity of the second or which is all one â—ib 2. parag 1. Aziom 13. as 4 to 5 so any quantity of the first to an equal summe of the second and likewise the contrary to these viz. as 5 is to 4 so any known summe received of the first coyn will be equal in quantity to the summe of the second due to be repaid in exchange which is the sole scope of this rule or the mark that is â—imed at in the exchange of money as for the profit experience in trading will discover it PROPOSITION XXVIII A Merchant delivers so much money with this condition to be repayed in a forreign Coyn and Countrey within any limited time as a year and at any rate per cent per an for interest allowed of there The RULES Rule 1 As 1 L English or 20 ss Sterling To a summ of that money So 1 L Sterl in another coyn If 100 L Sterling Rule 2. What 8 L Sterling interest An explanation of Exchanges Lib. 2. Parag. 7. Axiom 13. and Parag. 10. As in this example suppose 350 L of English money was delivered in London to be repaid upon bills of exchange a year after the receit thereof and to allow 8 per cent per an in that countrey where 24 ss was equal unto 1 L sterl from hence the proportion is as 20 ss is to 350 L so 24 ss in the second row of the table it is reduced unto 2. 35. 24. and in the third row to 1. 35. 12. by this or any of them you may finde the fourth proportionall number to be 420 L the summe to be paid in the forreign coyn and in the fourth row of the table you will find 100 L of that money under 1. and beneath 12 stands 8 L for a years interest these will make 3 numbers viz. 100. 35. 96. from whence a fourth proportionall number will be produced as in the fifth table viz. 33 L 12 ss the interest due upon 453 L so the totall to be received is 453 L 12 S according to the condition and state of the question PROPOSITION XXIX To reduce weights that are customary in one or divers Countreys to an equality from one denomination into another or the weight of any ponderous body being known to find the quantity of a greater or lesser weight The RULE As the proportionall parts of 1 ounce 1 pound 1 stone 1 C weight c. Shall be to any quantity propounded in that weight So will the weight of any other place towne or countrey Be proportionable to the weight thereof demanded An explanation in reduction of weights Lib. 1. Parag. 8. The question here propounded is of a commodity whose grosse weight is 2 C or 16 stone at 14 pound to the stone and it is required to find how many stone there are where custome admits but of 8 pound the proportion of a stone weight in these two places is as 14 to 8 or as 7 to 4 in this rule the third term is the least and yet requires a greater number from whence it is evident the rule must be reverst and the fourth proportionall found in the table will be 28 stone equall to 16 stone at 14 pound to the stone the thing required PROPOSITION XXX How many hundred or pounds of Troy weight will there be found in 5 C Aver de pois when as 1 pound 2 ounces 12 penny Troy is equal unto 1 pound or 16 ounces of the Civil or Merchants weight An Explanation This depends upon the last Proposition and so requires no other rule but onely to reduce the gross weight into pounds subtle which are 560 pound and since 1 pound Aver de pois is equall to 14 â…— ounces what 560 pound by the rule of Three direct you will finde 8176 ounces which divided by 12 the quotient will be 681 â…“ pound Troy and so for all other questions of this kind PROPOSITION XXXI The customary measure of any place being known with the quantity of one propounded to find how much it will make by a greater or lesser measure of another place An explanation in reduction of Measures Lib. 2. Parag. 8. An Inne-keeper bought 20 quarters of corn to be delivered where the custome of the place required 8 ¾ gallons to every bushell how much must the Farmer send in according to the Statute measure containing 8 gallons commonly called Winchester where the Act was made for to fulfill the condition as the bargain was agreed upon the state and operation of this question or the like differs not in the form from the 29 as in the margin is evident where 8 ¾ gallons or 35 4 multiplied by 20 quarters the quantity propounded in that measure which divided by the third number viz. 8 gallons the quotient will be 21 â…› that is 21 quarters and 7 bushels of the lesser measure equall to 20 quarters of the greater the thing required PROPOSITION XXXII How many yards or ells of any one place propounded will be equall or make a given number in some other which hath proportion to the measures of a third place c. and that in any known quantity unto the first The RULES Rule 1. As 20 ells or aulnes of Lyons To 25 yards of London So will be 60 ells of Lyons 100 ells Antwerp Rule 2. 47 ells of Antw. A plurall proportion I II III IV V Antwerp Antwerp = Lyons Lyons = London = 47 ells 100 ells = 60 ells 20 ells = 25 yards An explanation in reduction of measures from plurality of proportion Lib. 2. Parag. 10. In this Proposition there is an equality or proportion derived from divers descents and collaterall lines and may be continued like a British pedegree the equality here re-required is betwixt 47 ells of Antwerp and the yards of London that shall be equall to them if their measures were not known in any certain proportion but as derived from some other and that from a third and so continuing a proportion untill you arrive at one that runs directly from the first As for example here is required how much 47 ells of Antwerp will be of London measure if the proportion
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 â— 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
by which it is apparent that he gained 12 lb 10 ss in the 100 l. or after that rate for 100 l. thus imployed will return 112 ½ l. If any question of this kinde should depend upon Losse the Price at which 't was sold must be less then that by which the Commodity was bought at so the fourth proportional number will be discovered by the same Rule the state of the Question not differing in any thing either by Whole-sale or Retail so it requires no Precedent or Rule but this which will bring your stock short home as unfortunately true as prosperously with increase PROPOSITION VII By the Price which any Wares or Merchandizes were sold at with the rate of Gain or Loss in one Peece how to discover what the whole Commodity cost The RULE As 1 Peece 1 Hund. 1 Yard or 1 Pound weight c. shall be in proportion unto the price thereof so will the number of Peeces or quantity sold be proportionable to the price of them all together An Explanation of Gain or Loss in one Parcel to finde the rest Lib. 2. Parag. 8. Admit 15 Clothes or Pieces were sold for 340 l then was the price of one Piece 22 l 13 ss 4 d as by the first Proposition in this there was present gain 19 ss 4 d upon every Peece which subtracted from the Price 't was sold at viz. 22 l. 13 ss 4 d. the difference is 21 l. 14 ss for the price it cost then will the proportion be as 1 whole Cloth is to 21 7 10 l so shall 15 Clothes be unto 325 l 10 ss as in the Table appears If this Commodity had been sold to loss the differences betwixt the prices makes it evident and then what one Piece or any paâ—t had coâ—â— will be discovered as before with all the whole losse sustained and if it should be required after what rate in the 100 l. the last proposition will unfold it according to the Rule of Trade PROPOSITION VIII To finde the Gain or Losse upon Merchandizes bought and sold with time agreed upon betwixt the Debitor and Creditor for payment of the money at any rate per cent per an The RULES Rule 1. As 100 l sterling is to any interest so a summe given If for 12 Moneths Rule 2. What for the time An explanation of Gain or Losse with time at any rate per Cent. Lib. 2. Parag. 10. Admit a Tradesman had bought a Commodity at 5 d the pound and after 6 Moneths time sold it again for 6 d the l. or suppose the Merchandize was bought at 5 ss the yard and sold it presently again for 6 s the yard but with 6 Moneths given for day of payment or to abate so much as the interest should come unto at 8 l per cent per annum by the sixth Proposition the gain of those Wares will be discovered after the rate of 20 l per cent if present pay but here is to be rebate of money or forbearance of the stock and profit for six Moneths suppose 100 l disbursed for these Wares at first which would make 120 l if paid down on the nail but here use is to be considered for that summe and six moneths time with the encrease to be deducted the interest of which summe is thus found in this Proposition 't is six Moneths and 8 l per centum as in the first row or rule in the Table in the second row under 100 l stands the term for a year in the same denomination with the time given viz. 12 moneths and under the third terme the time limited for payment viz. 6 Moneths the products of them according to the double rule of Proportion in the third line is as 1200 to 8 l. so 720. these are again reduc'd in the operation of the fourth Table as 120 to 8. so 72 unto 4 l. 16 s. and might have been reduc'd again to 5.1.24 which will also produce 4 l. 16 s. that subtracted from 120 l. the remainder will be 115 l. 4 s. which shewes 15 l. 4 s. clear gains in relation to the rate by which t was bought and sold at with the interest for the forbearance agreed upon according to custom and contract but not exactly true PROPOSITION IX By the price of any Wares bought and sold with the time limited for payment to finde the gain made or losse sustained and at what rate per cent per Annum THE RULES Rule 1. As the first price shall be unto 100 l. so the gain or losse If for 12 moneths Rule 2. So the time limit An Explanation in Gain or losse with Time Lib. 2. Parag. 10. A Merchant bought Mace at 6 s. 4 d. the l. ready money and he sold the same again unto a Grocer for 7 s. the l. at this rate the Mace was delivered and upon condition to be payd at the end of 4 moneths next ensuing the receipt thereof and it is required what gain the Merchant made of his money and at what rate per cent per Annum In all questions of this kinde make the price at which t was bought and as 't was sold of one denomination the difference shall be the third terme in the first rule 100 l. the second number and the price for which 't was bought the first term in the second rule under the first number I place the magnitude of a year in that denomination in which the time limited is given as in Moneths Weeks or days in this 't is Moneths as the Letter M denotes the space of time given for payment is 4 Moneths subscribe that under the third number then draw a line from thence towards 19 G and that crosse with another as from 12 M t 2 G in this Example these multiplied crosse-wise the second rule being reverst for the lesse time is given for payment the profit will be the greater in the third row stand the products in the Rule of 3 direct and in the fourth Row or Table is plac'd the form of operation wherein the desired product is discovered to be 31 1â— 19 l that is 31 l 11 ss 6 d 1â— 19 the profit required at the rate per cent per annum PROPOSITION X. A Grocer bought Cloves at 4 ss 3 d the l. and after 6 Moneths time sold them again for 4 ss the l what losse did the Grocer sustain and how much per cent per ann by the last proposition you will find his losse to be 11 l. 15 ss 3 9 17 d. PROPOSITION XI By the difference of prices in any one Commodity bought and sold by whole-sale or retail to finde what time must be allow'd for to gain after any rate per Centum per annum that shall be assigned The RULES Rule 1. As 100 l sterling is unto 12 Moneths so the rate propounded Unto the 1 price Rule 2. so the gain or loss An Explanation in Gain or Loss with time unknown Lib. 2. Parag. 10. A Tradesman bought Nutmegs at 8 ss
were known that four ells of Antwerp were but equall to 3 yards of London measure there would be no more in it then to multiply the ells propounded viz. 47 by 3 which product 141 divided by 4 the quotient would have been 35 ¼ yards but suppose this proporrion not known but by derivation to be collected from others as in this plurality of measures you will find that the city of London according to the English standard for measures hath proportion to the ells of Lyons in France and those again to Antwerp in the Low countreys from whence the proportion will arrive according to the first table as 20 to 25 so 60 then in the second table as 100 ells of Antwerp to so many yards of London supposed to be found what will 47 ells of Antwerp require to have an equality in their measures in the third row or table they are both reduced into a single rule and in the fourth table unto their least denominations viz. as 4 is to 1 so 141 in proportion to 35 ¼ yards as it was before the thing required and I hope explained from whence I will proceed to the customary rules used in Factorage PROPOSITION XXXIII In the first place you must consider what the Merchant allowes his Factor in lieu of his pains and the adventure of his person as whether ½ ⅓ ¼ ⅕ c. that proportionall part taken from an integer the remainder is the Merchants the other shews the value of the Factors person The RULE As the proportionall part of the Merchants adventure Shall be to the whole stock adventur'd in his charge So will the proportional part allowed to the Factor Be to the estimate of his person in the employment An explanation of Factorage Lib. 2. Parag. 8. If a Merchant intrusts his Factor with a summe of money upon condition he should have half the gains in this case the Factors person was valued equall to the adventure but admit ⅓ part of the gaines were to be allowed the Factor and 1000 L committed to his charge the Merchants share will be but ⅔ which is in proportion to 1000 L as ⅓ is unto 500 L the estimate of the Factors person as by the rule and table appears and if in this employment 2000 L were gained by the adventure with all charges defrayed the Factors share would be 666 L 13 ss 4 D and the Merchants 1333 L 6 ss 8 D the one but half the other if the Factor had been allowed but ¼ of the gains in this adventure his person had been valued at 333 L 6 ss 8 D and his gains would have amounted to 500 L if ⅕ had been his proportional part then the Merchants had been and his gains 1600 L the Factors 400 L and the estimate of his person in this employment 250 I c. PROPOSITION XXXIV If a Merchant shall deliver unto his Factor any summe of money and does agree for to allow him 2 7 parts of his gain with this proviso that he employes such a stock of his own as shall be mentioned in the contract between them what shall the Factors person be valued at and how much will his gains amount unto find by the last Proposition what the proportionall parts are unto the Merchants adventure and from the Factors part subtract his stock adventured the remainder will be the estimate of the Factors person and the 2 7 parts of the whole gain will produce his profit As for example Suppose a Merchant delivers to his Factors charge 2000 L conditionally that he employs 300 L of his own in the same adventure the proportion wil be viz. as 5 7 is to 200 L so will 2 7 be unto 800 L from whence subtract 200 L the remainder is 600 for the estimate of the Factors person in the employment and admit the gains at his return were 3675 L 8 ss 9 D the 2 7 parts of it will be found 1050 L 2 ss 6 D and the Merchants share will be 2625 L 6 S 3 D. both Propositions answered PROPOSITION XXXV Of Factorage A Merchant did condition with his Factor to allow him for the adventure of his person a part of his stock and according to that proportion of the whole adventure he should share in the gaines from hence to discover what the Factors person was valued at and the proportion of his profit is the thing required To explain this suppose a Merchant intrusts his Factor with 1680 L and with this condition that if he gained so much money he should have 240 L for his pains and so proportionally for a lesse or greater encrease in all questions of this kind reduce the two summes like fractions into their least denominations viz. 240 1680 which will be 1 7 then by the 33 Proposition as 6 7 is to 1680 so 1 7 to 280 L the estimate of the Factors person in this imployment and suppose he gained all charges defray'd 1481 L 7 ss 6 D what must he have for his pains The answer will be 211 L 12 ss 6 D lib. 2. parag 9. quest 6. that is ◠7 according to the Articles of Agreement made PROPOSITION XXXVI A Merchant conditions with his Factor to allow him out of his gains a certain profit in the pound sterling by which it is required to find what the factorage will amount to in any summe propounded The RULE As 1 L sterling or any other summe of money given Shall be in proportion to what is allowed for factorage So the gains of the adventure in the first denomination Will be proportionall to the gaines for the Factors share An explanation of Factorage Lib. 3. sect 1. cap. 7. table 1. A Merchant had a due but doubtfull debt owing him in another Countrey where he was to employ a Factor who had letters of credence to demand his money due and with this condition to have 13 ⅓ D in every pound sterling that he should procure of it the Factor by his industry recovered 1200 L of the debt what does his salary amount unto by the rule of Three you will finde 67 L 10 S and so like wise in the table according to the rule of Decimals 〈◊〉 by this you may state other questions of Factorage and in this form PROPOSITION XXXVII A Merchant takes up money to fraight his ship with condition to allow 26 L per cent and that to be paid where the goods should be landed with this proviso that the Creditor shall stand to such hazards as belongs to sea viz. Ship-wrack or Pirats c. The RULE If the summe of 100 L sterl or any other money Shall require upon adventure 26 L for interest Then any greater or lesser summe of the first money Will be in the same proportion to the required gain An explanation of Sea-hazard or Bottom-ree Lib. 2. Parag. 8. Cambio maritimo some call this rule wherein the Creditor stands to the hazard with the Merchant at Sea that if the ship be lost he loses
per cent per ann and the principall is here the thing demanded An explanation of this Proposition lib. 2. parag 10. quest 4. In the first rule as 8 l interest is to 100 l principle what 8 â…“ the interest received in the second rule stands the terms of time viz. 12 mo and 5 m. which multipliers and the 2 dividers encreased reciprocally by one another they will produce these 3 numbers viz. 40. 100. 100. all questions of this nature are made either direct or reverse accordingly as the products are placed but by either way the quotient will be discovered 250 l the principal lent as in the table the proposition solved according to demand PROPOSITION XLII What shall the simple interest of a mixt principall as 265 l 13 ss 4 d 1 q. amount unto at 6 l per cent per ann An explanation of interest money by the rules of practise Lib 2. Parag. 9. Queâ—t 4 5 6. The encrease 100 L. 6 In. 265 L. 13 ss 4 ¼ D. Products L 15 94. 00. 1 ½ 20 100 L divid 6 L multipl S 18 80  12 D 9 61 4 Q 2 46 26 100 or 23 50 of any mixed summe will be thus discover'd first place your proposition according to the demand made as here viz. if 100 L requires 6 L interest what shall the principall given as 265 L 13 ss 4 ¼ D in this 6 is the multiplier with which encrease the principall as in lib. 1. sect 1. parag 4. exam 9. and the product will prove 1594 L 0 ss 1 ½ D. here draw a line as in the table cutting off two places on the right hand aâ— 94 because 100 is the divisor the quotient 15 L secondly the remainder 94 or 94 100 reduce into shillings by the multiplication of 20 the product will be 1880 and being no shilling left in the last operation sever 2 places with the line the quotient is 18 ss the remainder 80 which by 12 reduce into pence and adde to it 1 D remaining in the first product cut off 2 figures on the right hand viz. 61 so on the left hand there will be 9 D. the 61 reduced into farthings by 4 produceth 244 to which adde the ½ D remaining yet in the first product the summe is 246 that is 2 Q. and 46 100. so the totall interest for a year of 265 L 13 ss 4 ¼ D at 6 L per cent comes unto 15 L 18 ss 9 D 2 2â— 50 Q as by the operation in the table is conspicuous PROPOSITION XLIII To finde the Use-money of any summe whose principal and interest are of severall denominations as 956 L 7 ss 6 D at 5 L 17 ss 6 D per cent per ann An Explanation To solve any question Prin. Inter. L ss D 100 5. 17. 6. 956 7 6     5 The products 4781 17 6 478 3 9 239 1 10 ½ 119 10 11 ¼ The interest money L 56 18 14 0 ¾ ss 3 74 17 6 D 8 88 Q 3 55 â—00 of this kinde state the proposition as in the head of the table then take the greatest denomination of the interest allowed as in this example 5 L. which multiply through all the denominations of the principall here stated according to sect 1. parag 4. examp 9. the product will prove 4781 L 17 ss 6 D. had the interest been 6 L the product would have contained the principal once more but being 17 ss 6 d divide it into proportional parts lib. 2. parag 9. quest 4. as in the table at A viz. 10 ss 5 ss and 2 ss 6 d. for the 10 ss take ½ the principal that is half of 956 l 7 ss 6 d which will be 478 l 3 ss 9 d. next for 5 s take ¼ part of the principal or ½ the last which is 239 l 1 s 10 ½ d and the half of that again is 119 l 10 s 11 ¼ d. the total of all these is 5618 l 14 s 0 ¾ d. this done divide the greatest denomination by 100 l or cut off two places on the right hand and you will find 56 l and 81 remaining with which proceed as before and you will discover as in the table the interest to prove 56 l 3 s 8 d 3 5â— 100 q. the simple use for a year as was required and thus may all other propositions be expeditely solved by this operation and the rules of practise PROPOSITION XLIV What amounts the interest money unto upon a mixt principall for a time lesse or greater then a yeare as 645 l 6 s 8 d lent for 11 moneths at 5 l per cent per ann An Explanation State the question Prin. Inter. L S D 100 L 5 645 6 8 Product 3226 13 4 Products 1613 6 8 806 13 4 537 15 6 â…” The interest L 29 57 15 6 â…”  20   S 11 55 Months 11 D 6 66 6 Q 2 66 A 3   2 as in the head of the table that multiplied by the interest allowed in this 5 l the product is 3226 l 13 s 4 d. now being the money is to be continued but 11 moneths take proportional parts as in the table at A 6 M. 3 M. and 2 M. for the 6 M. take halfe the first product then ¼ and â…™ or thus ½ of 3226 l 13 s 4 d. is 1613 l 6 s 8 d for 3 Months the ½ of that is 806 l 13 s 4 d. lastly 2 moneths â…“ part of the former which is 537 l 15 s 6 â…” d. this done proceed as in the last or by 42 proposition and you will discover the interest money to be 29 l 11 s 6 d 2 66 100 q. the demand performed and if it had been required for any longer forbearance finde the interest for the term of years by the former propositions and the parts of a year by this PROPOSITION XLV What shall the Use-money come unto of any summe whose Principall Interest and Time are all compounded numbers viz. 543 L 13 ss 4 D to be continued for 9 moneths at 5 L 12 ss 6 D per cent per ann An Explanation The proposition Princip Interest L S D 100 5. 12. 6 543 13 4 Products of interests per cent per ann 2718 6 8 271 16 8 67 19 2 The totall is 3058 2 6 Interest in respect of time 1529 1 3 764 10 7 ½ A L 22 93 11 10 ½ 5 l 12 s 6 d  20   5 L S 18 71 months 9 ½ 10 ss D 8 62 B 6 ½ ¼ 2 ss 6 D Q 2 ½ B 3 ½ being stated as in the head of the table multiply the principal by the greatest denomination of interest viz. 5 L as in the table at A according to the prescribed rules of practise lib. 2. paragr 9. quest 4. for the 10 ss take half the principall and for the 2 ss 6 D â…› or ¼ part of the last so you will produce these 3 numbers 2718 L 6 ss 8 D. secondly 271
or 1 L due at the same terme of time Shall be to a Decimal fraction interest deducted RULE 2. As 106 L upon discount for the terme of a year Shall be in proportion to the Decimall last found So will 100 L Sterling or its value present payment Be proportional to a Decimal for the time required An illustration   Prin. Decimal Principal Decim I  106 l is to 100 L so wil 1 l be to .9433962 II as 106 l is to .9433962 so 100 l is to .8899964 III  106 l is to .8899964 so 100 l unto .8396192 The second Table for discount or rebate of money at 6 L per cent per ann is thus composed for the first year and Rule 1. as 106 L due at a years end shall be worth 100 L present pay so will 1 L principal according to the rule of Three in Decimals be in proportion unto 9.433962 which fraction is in money 18 ss 10 d 1 66 100 q. the value of 1 L due at a years end and presently paid upon discount but if not due until 2 years shall be expired say as 10 6 L is in proportion to the first years decimal fraction viz. 9.433962 what shall 100 L produce 8.899964 then for the third year as 106 L is to the last decimal found viz. 8.899964 so will 100 L present pay be in proportion unto 8396192. which fraction of 1 L reduced is 16 sh 9 ½ d. and thus you may continue it to what number of years you please and inscribe what places of decimals you think fit but make them all to one Radius and one place less upon discount being but fractions or parts of 1 L principall viz. 943396 1000000 as in the first year How to find Decimal numbers for parts of a year upon discount or for half years and quarterly payments These are composed after the same manner as the table of money forborn excepting onely in pointing the numbers for the Roots extraction the first Decimals being all mixt numbers and those of discount are every one proper fractions having onely a point prefixt for the Radius or integer therefore in these make the first point under the second figure on the left hand As for example 943396 is the decimal for the years rebate of 1 L put the first point under the figure of 4 and so in order to the right hand the root thus extracted will be .971286 in 6 places for the discount of 1 L 6 moneths as 6 L percent the square root of that again will be .985538 for 3 moneths and thus proceed with mean proportionals until the places are all compleat between the radius and the decimal last found as for half yearly and quarterly payments they are discovered as were those before in the forbearance of money to which I referre you and Lib. 2. Paragr 6. Proposition 1. and 4. observe the 2 Tables for out of these grounds the other 3 are framed and erected as followeth The invention of Decimall Fractions or proportionall numbers for the third Table Here are two tables Forbearance of money at 6 l per cen 1 Forbearance of Rents at 6 l per cen 2 1 1. 060000 1 1.000000 2 1. 123600 2 2.060000 3 1. 191016 3 3.183600 4 1.262477 4 4.374616 5 1.338226 5 5.637093 6 1.418519 6 6.975318 7 1.503630 7 8.393837 inscribed for 7 years whereof the one is the transcription of the first breviat out of which the third table is composed thus an Annuity Rent or Pension of 1 L per ann is but so much mony due at the term of a year therefore on the head of the table I place the Radius against the interest and principal of 1 L forborn a year viz. in the first table 1.060000 in the second 1.000000 the summe of these two numbers is 2.060000 the rent which will be due at the two years end in which time there will be 2 L in arrears and the annual interest of 1 L to which adde the second yeares forbearance viz. 1.123600 the summe will be 3.183600 for the rents 3 years forborn and thus in order the 6 years added together will make the seventh as 8.393837 and the seven years the 8 viz. 9.897467 which reduced is in money 9 L 17 ss 11 d 1 ½ q. and so much 1 L yearly rent or annuity forborn 8 years does amount unto at 6 L per cont per ann annual payments and compound interest in this manner you may proceed according to what number of years the first table comprehends The construction of Decimal Fractions or proportional numbers for the fourth table The first of these 2 Discount of money at 6 l per cen 1 Discount of rents at 6 l â—er cent 2 1 .943396 1 .943396 2 .889996 2 1833392 3 .839619 3 2673012 4 .792093 4 3465105 5 .747258 5 4212363 6 .704960 6 4917323 7 .665057 7 5582380 tables is transcribed out of the second breviat from whence the the 4th is framed after the manner of the last for 1 L Pension Rent or Annuity due at a yeares end is worth but so much upon discount as the interest rebated which at 6 L per cent is included by this Decimal 943396. and the second years number must be encreased by the Annuity Rent or Pension discounted for therefore adde 889996 unto 943396 the summ will be 1833392 the decimal fraction for the second year and so proceed to the seventh year of the first table by adding that number 665057 unto 4917323 the sixth years discount in this second table the summe will be 5582380. the Decimal for 7 years rebate of rent at 6 L per cent and in this manner continue on the tables to what number of years you please Here 1 L Annuity discounted for 7 years is worth in ready money 5 L 11 ss 7 d 3 q. compound interest rebated How to find the Decimal Fractions or proportionall Numbers for the fifth table RULE 1. As the Decimal for 2 years rent rebated Is equal in value to 1 L annuity for 2 years So is 1 L of annuall annuity the same terme of time In proportion to the Decimal purchased by 1 L Or As 1.833392 to 1 L so 1.000000 unto .54544 Or thus As 1 L 16 Purchase sh 8 d is to Annuity 1 L so will 1 Purchase L be to 10 sh Annuity 10 9 10 d. An Illustration The Annuity Rent or Pension which 1 l will purchase for a year lies involved in the decimal of 1.060000 according to the first table there being onely one years forbearance of 1 L then for the second year take the decimal fraction of 1 L rent discounted for the term of 2 years which is 1.833392 in money 1 L 16 sh 8 d. and it is evident how this summe is equal unto 1 L annuity purchased for 2 years and consequently the proportion will be as in the rule before if 1 L 16 sh 8 d or 1.833392 the decimal for two years rent rebated be equal to 1
7. as in this table and first row in the second stands the product viz. 25011336. to which you may annex the cipher in 210 L. it is not material the number being one place greater then is the Radius yet the product one cipher defective therefore strike off but 5 places from the right hand and the fraction reduced the summe would prove at 3 years end 250 L 2 ss 3 d. But to proceed the second row for the term of years multiplied by 10.14674 the Decimal for 3 moneths produceth in the third row of the table 25378356 the number for 3 years and 3 moneths as noted on the right hand of the Table which multiplied by the Decimal 1003358 for 3 weeks the product will be in the fourth row 25463576 the artificial number for 3 years 3 moneths and 3 week and lastly multiplied by 1000479 the decimal for 3 dayes the fifth row will specifie in the product 25475773 the artificial number for the whole time viz. 3 years 3 moneths 3 weeks and 3 dayes from whâ—nce sever the integers and reduce the fraction the total appears as in the table 254 L 15 ss 1 ¾ d. the true compound interest for the summ and time required The second Table of compound Interest illustrated by Examples QUESTION VI. At the term of 6 moneths A is to pay unto B 500 l but do agree in receiving it presently upon discount after the rate of 6 L per cent per ann what summe of money will discharge it In the second table for discount of money I find the decimal for 6 moneths .971286 which fraction of 1 L Sterling multiplied by 500 L or 5 the product will be 4856430 to which annex 2 ciphers the number will be 485,643,000 from the right hand cut off 6 places and reduce the fraction there will appear 485 L 12 sh 10 ¼ d the true summe upon rebate that will discharge 500 L 6 moneths before t is due which according to the best vulgar custom comes near the truth as by Pro. 47 of this book the discount being but for a short time viz. 485 L 8 sh 8 d 3 q. QUESTION VII A had a Lease in reversion which at the expiration of 7 years was valued worth 1200 L. which Lease B would purchase present pay rebating at 6 L per cent per ann what will be the value of iâ— This differs not essentially from the last for it is no more but to find the present value of 1200 L not due until 7 annual revolutions be completed Look in the second Table for discount of money and in the column against 7 years you will discover 665057 which Decimal multiplied by 1200 L produceth 798,068,400 from the right hand sever 6 places and reduce the fraction the summe will appear in money 798 L 1 sh 4 ½ d very near and so much money present pay B must disburse to A for his Lease in reversion commencing at 7 years expiration the thing required QUESTION VIII A is to pay unto B a Legacy of 1800 L which is to be discharged at 3 several and equal payments viz. at the end of 6 moneths 600 L at the term of a year 600 more and the last payment 6 moneths after that B desire it presently and A is willing upon discount at 6 L per cent per ann what summe will discharge it at one present and entire payment The summe here  The decimals  L S d 1 582771600 1 582. 15. 5 2 566037600 2 566. 0. 9 3 549784200 3 549. 15. 8 1698. 593400 1698. 11. 10 propounded is 1800 L at 3 equall payments the Decimal for discount of 6 moneths is 971286. which multiplied by 600 L the first payment to be due at the half yeares end the product is 582771600 which reduced does prove 582 l 15 s 5 d then is there 600 l upon a years rebate the decimal for that term of time is 943396. which multiplied by 600 L will produce 566,037,600 which reduced into money is 566 L o sh 9 d due upon the years rebate as in the second row of the table now the last payment is 600 L upon a year and a halfs discount to find an artificial number for this the Decimal for a years discount is 943396 and for 2 yeares 889996. the product of these will be 83.96.18.66.64.16 the Quadrat extracted as it is pointed will be 916307 a meane proportionall number betwixt the first and second yeare according unto the construction of these tables before delivered and if multiplied by 600 L the last payment due at that time the product will be 549784200 as in the third row of the table and is in money 549 L 15 ss 8 d. the total 1698 L 11 ss 10 d. which summe will discharge all the 3 payments at one time and present upon discount and the 3 several Decimals whose total is 1698593400 and reduced will prove the same total summe the money deducted is 101 L 8 ss 2 d. The third Tables use of compound interest demonstrated by examples QUESTION IX If an Annuity of 60 L per ann be all forborn 7 yeares how much will it amount unto when that terme expires Look in the third table for Annuities forborn the time specified where against 7 years you will finde the Decimals 8.39384 which multiplied by 60 L the annual rent the product proves 503.63040 cut off 5 places whereby to sever the integers from the fractions which reduce into money and you shall find 503 L 12 ss 7 d. the true value of the 60 L annuity forborn 7 years the question solved QUESTION X. A did owe unto B 186 L and upon covenant to pay unto the said B a rent of 20 L 13 ss 4 d per an untill the debt should be discharged yet after this contract they both agreed to respite the payments untill the last were due with this proviso to pay it all in then allowing interest for the forbearance at 6 L per cent per ann Find what number of yeares would have terminated the Annuitie first agreed upon betwixt A and B for the payment of 186 L by 20 L 13 ss 4 d annual rent which will be performed by the example in the Table viz. as 62 3 L is to 1 year so will 186 L be unto 9 years which rent is to be respited during the aforesaid term Look in the Table of Rents forborn where against 9 years you will find this 11.49132 to be multiplied by the decimal of 20 L 13 ss 4. the Decimal of 13 ss 4 d is as in lib. 3. sect 1. chap. 7. 66667 to which prefix the integer 20 L the total is 2066667. this multiplied by 11.49132 the decimal for the term of years the product will be 237-4873183044 according to the rules of Multiplication in Decimals lib. 3. sect 1. cap. 4. sever off 10 places for the fraction the integer will be 237 L reduce 5 or 6 places of the fraction making the Radius one place more you will
find 9 ss 9 d very near so A must be responsable to B or their heirs at 9 years end for 237 L 9 ss 8 d 3 ◠10 q. This exactnesse was not required nor yet so great a number taken for the fraction of 13 sh 4 d. but these if understood the ingenuous will ease themselves by my labours to which end I will proceed QUESTION XI A was to pay unto B 200 L at the full term of 5 years for which debt A was contented to make B a Lease of a Farm to continue in force the same time whose annual rent was 35 L. which of them gained by this contract interest allowed at 6 L per cent per annum In the Table of Rents forborn under years look 5 the decimal number against it is 5.63709 which multiplied by 35 L the Rent respited the term of 5 years the product will be 197.29815 and reduced into money is 197 L 5 sh 11 ½ d. which subtracted from 200 L the remainder is 2 L 14 sh 0 ½ d. and so much A did gain by the bargain or contract made with B. The fourth Table exemplified in discount of Annuities Rents Pensions or Reversions at 6 L per cent per ann compound interest QUESTION XII What is the present worth of 80 L Rent or Annuity to continue 25 years rebating at 6 L per centum per annum Look in the fourth Table for 25 years against which I find 12.78335 This compound Decimal multiplied by 80 L the Annuity propounded the product proves 1022.66800 which reduced into money will be 1022 L 13 sh 4 ¼ d the true value of 80 L per annum yearly payments rebated for 25 years according to demand QUESTION XIII A man hath a Lease of Lands or Tenements worth 15 L per ann more then the rent and hath a Lease yet 4 years in being the Tenant desires to take another in reversion for 21 years at the same rent what must the Lessee pay for a Fine interest allowed at 6 L per centum per annum  for 4 years  for 25 years  346510  1278335 1 1732550 5 6391675 2 51.97650 6 191.75025 3 51 L 19 sh 6 D 7 191 L 15 sh 0 D 4 139.77375 8 139 L 15 sh 6 D First seek the Decimal for the term of four years 346510. which multiplied by 15 L or by 5 as in the first Table in the margent according to lib. 1. sect 1. parag 4. exam 5. the product in the a row will be 51.97650 in money 51 L 19 sh 6 d. and so much the old lease in being is worth when the new for 21 years enters possession now admit the term of the old Lease and the new added together the summe of years is 25 the profit or overplus of Rent is to continue all the time therefore 1278335 the Decimal for 25 years multiplied by 15 L as in the fifth row of this table produceth in the 6.119.75025 equal in value to 191 L 15 ss the difference of the first Lease and the total time in the 8 row is 139 L 15 ss 6 d. and so the difference of decimals in 4 row reduced is very near without a material error being 139 L 15 ss 5 7 10 d. QUESTION XIV A Tenant hath a Lease of 21 years the present thereof is 41 L per ann during the term of 7 years and after that time shall be expired the Lessee is to pay 50 L rent per ann for the residue of the term what is the value of this Lease in ready money interest discounted at 6 L per cent per annum  for 21 years  for 7 years 1 11.76407 5 5.58238  5  9 2 588.20350 6 50.24142 3 588 L 4 ss 0 ¼ d 7 50 L 4 sh 10 d 4 537 L 19 ss 2 ¾ d 8 537.96208 In the fourth table of Rents rebated the Decimal of 21 years is 11.76407 which multiplied by 50 L the rent of 21 yeares the product is 588.20350 as in the second row of this Table which reduced is 588 L 4 ss 0 2 4 d as in the third row which had been the true value of it at L per ann for the whole term of time but the first 7 yeares of this Lease was but 41 L annual rent therefore the first Decimal was too great by the difference of rent which was 9 L per annum then look into the fourth Table for 7 years and against it you will find 5.58238 which multiplied by 9 L as in the first row of this Table the product in the sixth is 50.24142 and reduced is 50 L 4 ss 10 d very near which subtracted from the third row the remainder is 537 L 19 sh 2 ¾ d as in the fourth row or subtract the Decimals found in the sixth from the second row the difference will be 537.96208 which artificiall number reduced would be 537 L 19 sh 2 ¼ d as before the true value of the Lease required QUESTION XV. There is a Lease to be taken for 21 years at 30 L per ann and 100 L Fine the Lessee likes the bargain but not the condition desiring the annual rent to be but 10 L yearly payments and is willing to give such a Fine as shall be proportionable to the rent abated during the aforesaid term of 21 yeares and here the Fine is demanded In all questions of this kind  The Decimal 1 11.76407 2 L 235.28140 3 S 5.628  1256 4 D 7.536 take the rent abated which is here 20 L per ann for 21 years whose decimal in the 4th Table of Rents rebated is 11 76-407 as in the margent which multiplied by 20 produceth 235.2814 that is 235 L. reduce the fraction neglecting the ciphers the value of 20 L per ann the difference of Rent for 21 years is as in the 2 3 and 4 row in all 235 L 5 sh 7 ½ D. this added unto the former Fine 100 L makes in all 335 L 5 sh 7 ½ D the true summe to be paid for a Fine in lieu of 20 L Rent per ann abated during the Lease of 21 years the thing required QUESTION XVI A had a Lease of 130 L per ann to continue 24 years B had another of 210 L per ann and 11 years to come these 2 men mutually exchanged Leases A upon the contract paid unto B 20 L in ready money which of these had the better bargain and how much A  B 12.55036  788687 3765108 1 1577374 1631.54680 2 1656.24270 1631 L 10 sh 11 D. 3 1656 L 4 sh 10 D. 1651 L 10 sh 11 D. 4 4 L 13 sh 11 D. Against the 24 year of the fourth Table look and you will find the Decimal of it 1255036 for A. secondly the lease of B 11 years hath this decimal 7.88687 these 2 numbers multiplied by their respective rents as in the first row of this table according to lib. 1. sect 1. par 4. exam 6 7. or by the vulgar way In the second
row of the margent A does produce 1631.5464 and B 1656.2427 neglect the ciphers and reduce the numbers in the third row you may find the Lease which A exchanged is worth in present money 1631 L 10 ss 11 d. and the lease which B was owner of being 210 L per ann for the term of a 11 years proves in currant coyn the summe of 1656 L 4 sh 10 D. and A mended his in the barter or exchange 20 L which makes the value of his lease as in the fourth row 1651 L 10 sh 11 D. which still is less worth by 4 L 13 sh 11 D as in the fourth row by subtraction is evident and that B lost so much money by the bargain The fifth Table does demonstrate in its use the purchasing of Annuities Rents Pensions or Reversions at 6 L per centum per annum compound Interest QUESTION XVII What Annuity Rent or Pension will 250 L in ready money purchase for a Lease of 7 yeares interest allowed at 6 L per cent per ann Seek the seventh year in the fifth Table which is the terme of yeares that the Lease continues whose Decimal number is .17914 and if multipled by 250 L the product will be 44.78500 and reduced is in money 44 L 15 sh 8 ¼ d. And this Annuity or Rent to continue the full terme of seven yeares which the former summe of money will purchase as a yearely revenue during that time QUESTION XVIII There was a man who purchased a Lease to continue 25 years at 10 L per ann for which the Lessee paid a Fine of 150 L. how much was the annual rent of this Lease valued at when interest was rated at 6 L per cent per annum This differs little from  Decimals 1 07823  39115 2 11.73450 3 11 L 14 ss 8 D the last for here you are to find what Annuity or Rent 150 L in ready money will purchase for the term as in the fifth Table against 25 yeares stands this Decimal 07823. which multiplied by 15 as in the margent in the first row of numbers whose product in the second row with the cipher annexed is 11.73450 that reduced is in money 11 L 14 ss 8 D the farthing neglected as not material and this annual Annuity 150 L will purchase for 25 years therefore adde this unto the Rent paid viz. 10 L per ann the total is 21 L 14 ss 8 D. the question answered QUESTION XIX There is a Lease of 25 years to come set at 10 L rent per ann and the Fine demanded is 150 L. the Tenant is willing to give 100 L and a proportional annual revenue during the whole term what wil be the rent required the loan for money allowed at 6 L per centum per annum This does not vary essentially  Decimals 1 07823  5 2 3.91150 3 3 L 18 ss 2 ¾ D from the former for the Fine being diminished the annual rent must be encreased take the difference betwixt the two Fines viz. 100 L and 150 L as 50 L the Decimal for the term of years 25 is .07823 which multiplied by 50 or by 5 as in the first table of the margent the product in the second is 3. 91150. which reduced in the third row is 3 L 18 sh 2 ¾ D. the rent which 50 L will purchase for 25 year which added to the former Annuity of 10 L per ann makes the whole rent 13 L 18 sh 2 ¾ D according to demand QUESTION XX. A Citizen giveth over his Trade unto a faithfull servant leaving him his shop ready furnished the Wares prized at 1408 L the Lease of his house valued at 250 L so in all 1638 L which the Master was to receive by equall and annuall payments in the space of 7 yeares the interest agreed upon at 6 L per centum per annum what annuity will discharge this debt To discover this annual Rent look in the first Table for the term of years specified and against 7 you wil find .17914 This multiplyed by 1658 L produceth 297.01412 the Decimalâ— reduced will prove in money 297 L o ss 3 ¼ D. Which Annuity or Rent for 7 years annual payments discharges the whole debt with interest at 6 L per centum QUESTION XXI A Tenant took a Lease of a House and Land for a term of 21 years paying 160 L Fine and 16 L Rent per ann at 7 yeares end the Lessee was resolved to put it off What annual Rent or Annuity must he set the Tenement at to withdraw his former Fine or reserving the same Rent impose another proportionall for the years to come Interest at the rate of 6 L per cent per ann  Rent  Fine 1 .08500 5 9 2949â— 51000 13.6 2 13.60000 6 5576988   2788494 3 13 L 12 ss 929498 4 29 L 12 ss 7 126.411728 First to impose a proportional Rent find by the first Table of Annuities to be purchased what 160 L will buy for the full term of 21 years whose Decimal is .08500 which multiplied by 160 L or 16 as in the first row of this marginal table the product in the second is 13.60000 in the third is reduced to 13 L 12 ss this annual Pension 160 L will purchase for 21 years which added to 16 L per ann the Rent of the Tenement does evidently shew the nature of the Lease as in the fourth row 29 L 12 sh and setting of it at that rate the remaining years the Tenant saves himself To discover what Fine must be imposed the old Rent reserved and yet a â—roportional part for the first Fine The term of years remaining are 14 whose Decimal in the fourth table of Discount is 9.29498 which multiplied by the Decimal of 13 L 12 sh last found viz. 13.6 as in the fifth row in the sâ—xth stand their several products and in the seventh row the totall summe as 1â—6 411728 from whence strike off 6 places which are fractions according to the Rules of Multiplication in Decimals and reduce the test the Fine will be discovered 126 L 8 sh 2 ¾ D which saves the Tenant harmless the old Rent still reserved without gain or loss the thing required As for the Decimal of 12 sh find the fraction or see lib. 3. caâ— 7. table 1. Rules I have here delivered equally ballanc'd betwixt the Buyer and Seller Debitor and Creditor whereby neither side might deceive non yet be deceiv'd by falacious or ambiguous contâ—â—cts As for Interest Money here are composed rules both according to Custome prescriptions of Art and the precepts of humane Institutions which tolerates Usury confined to a Loan of 6 L per centum per annum I cordially wish the frugality of the people would lessen the trade of money and sink the Impost to a Land rate yet there would be many Money-cormâ—rants and their proâ—it great because such Estates lye dormant in Banks obscured from the inquisition of a sax and rarely appea oâ— wake but
s. for 1 Cask taken content in part in truck for Sugars 09 03  ⅕ Cash Debit to Dito Edward 3 l 9 s. received in full satisfaction to cleare the said Truck 3 9   Jan. 29. 1658. Moneys borrowed at interest    ⅙ Cash Debitor to John Malthorse 300 l received of him upon interest 300   6 6 Interest reckoning our Profit and Loss Debitor to Dito John 4 l 10 s for 3 moneths allowance for 300 l at 6 per cent 4 10  Anno 1658. 30 Jan. in London   L S D  Moneys borrowed to be paid upon demand or otherwise    ⅙ Cash Debitor to Simeon Peters 50 l borrowed of him and payable on demand 50    Money let out at Interest    5 1 Edward Price Debitor to Cash 100 l. delivered him at Interest 100   ⅚ Dito Edward Debitor to Interest reckoning or profit and losse 1 l 10 s for 3 moneths allowance for a 100 l at 6 per cent per ann 1 10   House-keeping charges entred    6 1 Profit and Losse Debitor to Cash 50 l paid my servant for 3 moneths provision for house-keeping to end 25 March next 50    Febr. 2. 1658. Moneys paid that are due the time of payment being comâ— Â Â Â 4 1 Jane de Clare Debitor to Cash 60 l. paid him in full of all accounts 60   5 1 Jam. Wilson Debitor to Cash 36 l 4 s 11 d. paid in full for his Sugars as by his Acquittance appears 36 4 11  Febr. 9. 1658. Moneys received that are due time of payment bâ—ing come    ¼ Cash Debitor to John Tâ—urrowgood 39 l 10 s. received in full of all demands to this day 39 10   Moneys received for goods sold at time before due upon rebate    ¼ Cash Debitor to John Benning 24 l. Received in full 24   6 4 Profit and Losse debitor to Dito John 1 l 17 s 6 d for payment before due 1 17 6 Anno 1658. 12 Febr. in London   L S D  Moneys gained by Exchange    ⅙ Cash debitor to Profit and Losse 58 s 4 d for advance of 100 Dollers exchanged for English money at 4 s 7 d per Piece which cost me but 4 s. the difference at 7 d per Piece is 2 18 − 4  To discharge a debt by Assignment    4 3 Thomas Spilman debitor to William Lane for my Assignment poid hâ—m in full of his debt 36 11 − 4  Debt sold to another from whom it was not due    ⅓ Cash debitor to Thomas Goodman 50 l Received of William Short for Dito Thomas his Bill of 82 l 3 s 4 d. which I have sold for 50   6 3 Profit and loss debitor to Dito Thomas 32 l 3 s 4 d lost by the sale of his bill 32 − 3 − 4  Febr. 19. 1659. Part of a debt lost by a Bankrupt and the rest received    ⅓ Cash debitor to Abraham Bland 259 l 7 s 4 d being but â…” Received in full of a debt of 387 l 11 s â…” 258 − 7 − 8 6 3 Profit and Losse debitor to Dito Abraham 129 l 3 s 8 d. lost by him when he fail'd − 129 − 3   Merchandizes sent into another Countrey consign'd to a Factor for my Account    7 2 Voyage to Amsterdam consigned to Hans Butter box debitor to Fustians 80 l for 40 pieces at 40 s per piece shipt by James Hope to Dito Hans to be sold for my account 80   7 2 Dito Voyage consigned to Dito Hans debitor to Spanish Tobaco 440 l for so Potâ—en's wâ—d net 880 l at 10 s per pound shipt by Dito James to the said Hans to be sold for my account − 440   Anno 1658. 19 Feb. in London   L S D  Charges for a voyage or otherwise    7 1 Dito voyage debitor to Cash 9 l 16 s for charges upon the Fustians and Tobaco for Fraight Custom and Excise c. 9 16   Goods ensured    7 1 Dito voyage debitor to Cash 7 l 16 s for insurance of Dito Fustians and Tobacco paid John Mazoone at 30 s per cent is 7 16   Feb. 22. 1658. Money received for fraight of a ships part    ⅓ Cash debitor to Ship the Sampson of London for fraight received of John Wright Master thereof for my ½ share 35 3 8  Money or goods given away to any person    7 2 Profit and Losse debitor to Fustians 1 l 2 s 8 d for one piece given to A.B.    6 1 Profit and losse debitor to Cash 12 l given towards the relief of a fire at Enfield in the County of Middlesex 1 2 8  Gratuities received    ⅙ Cash debitor to Profit and Losse for 200 l received for a Legacy given mâ— by A. M. 12    Febr. 28. 1658. Commodities formerly shipt to another Countrey and advice of the sale thereof    7 7 Hans Butterbox at Amsterdam my account currant debitor to voyage to Amsterdam 613 l 15 s 4 d. as appearâ— by his account sent me and dated at Amsterdam Novemb. 25. instant being the neat proceed of my goods solâ— there 613 15 4 Anno 1658. 28 Febr. in London   L S D  Commodities received to sell for another mans account in Commission    7 1 Hans Butterbox at Amsterdam his account of Wheat debitor to Cash 18 l 5 s for several charges paid at the receit of 100 quarters received out of the Elephant of Amsterdam as followeth  L S D For Fraight at 1 s per qu. 05 00 00 For Custom at 1 s 6 d per q. 07 10 00 For Excise at 6 d per qu. 02 10 00 For Porterage Literage and Cartage at 6 d per qu. 02 10 00 For Meaters allowance 00 15 00  18 05 00 18 5   Commission Goods sold    1 7 Cash debitor to Hans Butterbox his account of Wheat for 100 quarters soâ—d to John Sutton Junior at 58 s per qu. is 290    Provision for Commodities sold     7 6 Hans Butterbox his account of Wheat debitor to profit and losse for my provision for the said Wheat at 12 d per l. 14 10   March 3. 1658. The proceed of commodities paid by bill of Exchange    8 â— Hans Butterbox his account currant debitor to Cash 257 l 5 s. remitted him for his account in Bills of Stephen Swabbers payable at sight to dito Hans by Simon Newman of Amsterdam being the neat proceed of his wheat all charges deducted 257 5  Anno 1658. 24. March in London