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 and Ponderates to Equity and Custome, all usuall Rule [...], legall Bargains and Contracts, in Wholesale or 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.


LONDON, Printed by J. G. for Nath: Brook, at the Angel in Cornhill. 1660.

A DEDICATORY EPISTLE TO THE Illustrious and most Ingenuous MERCHANTS, The Patrons of Commerce and Trade, wishing Success may crown their good Endeavours.


ADVENTURERS (the Primum mobile of this Subject) whose Negotiations are dilated be­yond the Suns annuall pro­gresse, as both the Indies and Polar Stars can clearly witness; to your candid censures I address my self, as compe­tent judges of Commerce and Trade; and to avoid obstructions from fond Informers (with license of the Court) I will render [Page] here a breviate of some occurrences, and the motive wherefore I have harboured this so long, not becalm'd, as some suppose. When first I fram'd this Abstract of Commerce and Trade, (and having shipt the chiefest Rules depending upon Arithmetick) I thought good to ballance them with Geo­metricall Problems and Propositions of Magnitude, with sundry Questions mixt and appl [...]ed to both those liberall Sciences. Thus fraught with variety (according to the Vessels capacity) rigg'd and made rea­dy for a voyage to the publick prospect of the worlds inhabitants, indigent of Prote­ctors for a Convoy, untill reflecting upon the Right Honourable Societies, under whose colours I weighed Anchor, and stood to Sea, willing to strike saile to men of Art, in Peace or War, yet scorning to submit unto a Fleet of vapouring Roman­cers, or empty Liters, whose Top-sails are filled with vain glorious words: these ver­ball Rovers (perhaps) will question and charge me of Piracy, or surreptitious Goods from manuall Trades, and ingenious Arti­ficers.

To all rash and Malignant censurers I shall plead Not guilty; animated, that this no­ble [Page] Consistory of Senators wil vindicate my endeavours, and write upon the Plantiffs Bill Ignoramus; since all Humane Know­ledge depends upon Time (the Worlds grave Tutor) ratified by the sage experi­ence of your selves and others: and as for these, they have been lawfully gained, se­lected and recollected by my Industry, un­der the conduct of Art, and registred upon the account of many years revolutions, ap­plied to Practise, seconded by Reason, and inserted in this form, modeliz'd to my Sense, without prejudice, or intrenching my self upon any others Ground, Claime, Title, or Prerogative.

Neither have I set forth one Adventure (as some have done) and never appeared upon this Theatre again, nor heard of, as if exploded, or cast away at Sea by some e­vil steered course, not Regulated by De­monstration, shap'd by Experience, nor re­ctified by Compasse, or lost by spreading too great a Saile, unable to stem a tu­multuous current of the Times without a Pilot, Masters and Mates now termini covertibiles; yet notwithstanding them, the acceptance of my former Labours hath given me faire hopes of an Insurance for [Page] these purchased by Barter, Exchange, or the expence both of Time and Money, transported from severall Regions, under your protection now arrived and delivered out, for the benefit or pleasure of others.

My request is (worthy Patrons in this Metropolis of Trade) that ye will signe these with your Magisteriall Impressions, and condescend to owne my Adventure, although intended as a guide to young be­ginners onely, and to attend your vacant hours, as an Index to your memories, and a Directory to your dilated courses, since Nature hath provided the biggest Whale but a little Pilot, and Art a small Rudder, to steere the greatest Ship. From hence if this may find a reception in your Socie­ty, the Charges are all defrayed, but Cu­stome to the Stationers Office, my inten­tions (to a serene Auditor) will ballance the other Accounts, and the next Voyage or Return, the Tare and Errours shall be deducted, and ye (Noble Merchants) repre­sented with an ampler Cargazone, if I be ad­mitted, and this to your Patronage (which Hope bids me to believe) so I will subscribe myselfe,


A GENERALL PREFACE TO ALL Adventurers & Negotiators, conversant in Commerce & Trade, with a compendious Discourse, which is to be preferred in an happy Re­publick, viz. the Lawyer, Mer­chant, or Souldier; wishing well to all honest Endeavors.

MAn is a sociable Creature (accor­ding to his naturall inclination) and in respect of temporall im­ployments, the noble Merchant transcends all others, as the Superiour to the Corporation of Tradesmen; they being the supporters of Traf­fique, conservers of Amity, friends to Peace, patrons of Plenty, and grand coadjutors to All, by supplying the indigency or defect of one Countrey, with the excesse or superfluity of some others. For what part of the habitable world [Page] is so sterile, but can export Commodities and Necessaries usefull and advantageous, for the Inhabitants resident in pregnant and fertile Soil [...]? And thus Virgil sayes: ‘—Non omnis fert omnia tellus.’

If Adam had not transgressed, his Race had never been expulsed Paradise, nor humane In­dustry urged by Necessity, terrified by Poverty, solicited by Ambition, or prompted by Riot: 'tis probable severall countreys had diversity of endowments out of Natures treasury conferred on them, whereby to attract exiled men (as brothers) either with a coercent or an obligent Fraternity, by a continuall league of Amity, and intercourse of Trade, whether scituated un­de [...] the temperate, frigid, or torrid Zone; all which the honourable Society of Merchants do perform, keeping a correspondency with the habitable world, surveying Neptunes watery Regions, discovering the Bounds, imbarking the Indie and treasury of the Seas, transpor­ting their Magazines over the proud and an­gry Surges, slighting dangers and the fury of impetuous Storms, thereby to support them­selves, please and supply the defects of others.

Poverty renders Man despicable unto those [Page] who honoured him in Prosperity, it makes him a stranger to his intimate acquaintance; per­haps pitied by many, but relieved by few; it divorces the society of friends (like some mor­tiferous infection) especially the Parasites of the Rich, or the Idolaters of Fortune, who are the worlds mercenary Slaves in golden chains; she appears (to the inamour'd of temporall bles­sings) a more formidable disguised Spectrum then Death; the first is Fortunes Preludium to Contempt, the other Catastrophe to a Tra­gedy of Cares, or a Comedy of Errours, where true Hope attends their Transmigrations from this Scene of Miseries, ushering them to his fa­tall attiring-room, with a Plaudite for those whose parts were acted well; yet Penury in the Interludes often provokes noble minds to act ignoble things, and usually expulseth the fear of any enterprise, and exasperates some to the contempt of penall Laws; therefore humane Industry is urgently necessary, whereby to shun those mischiefs entailed on want; for all despe­rate and unjust courses are to be abhorred, as the endeavours of Societies, and the lawfull adventures of Merchants are to be commended. And thus writeth the ingenious Poet Horace:

Impiger extremos Mercator currit ad Indos,
Per mare pauperiem fugiens per saxa, per ignes.

In English thus:

The nimble Merchant runs to th' Indian shore
Through fire and water, fearing to be poor.

The ingenious Syrians, Phoenicians and Chaldaeans restor'd Arithmetick, conducing much to the furtherance of Commerce and Trade, and the Merchants since, have illustra­ted the practick part of Astronomy, applied to the perfecting of Navigation, by which Art new Territories have been happily discovered, and the Colonies since the Generall Deluge trac'd into America, whereby sacred Religion hath made procession thither, imbraced and re­ceived in climates unknown before to Europe, Asia, or Africa, not inferiour to them all three together. Thus God hath graciously pleased to make them instruments of his Mercy, but to keep within their sphere, or in the circumfe­rence of mundane affairs; the mighty Mo­narchs, with the Peers of this British Island, by custome condescended to have been made free of some Trade, Company, or society of their Subjects, in the Metropolitan of England: [Page] the Lucitanian Kings, with their Nobility, have not onely accepted the title of Merchant, but have really imployed adventures at Sea, to encourage their subjects in advancing their publick good, and strengthening themselves both by Sea and Land.

States by Traffique have risen out of a Fisher­boat, dilating their jurisdictions equall to the potent Princes of the Earth; and to descend unto particulars, how many great and eminent Families in all Countreys have been raised out of the dirt, or from despicable degrees, and yet elevated to the most illustrious Titles that sub­jects could be capable of, or Princes could confer on them, sitting at the helm of their Re­publicks? others again with ship-wrackt con­ditions, emerg'd in their estates, through their own extravagant courses (not steered within compasse) the injustice of others, or the injuries of Fortune; yet it hath often pleased God to allot this means whereby they have been buoy'd up again, and prosperous gales have filled their sails, untill they have anchor'd in the w [...]althy harbours of their eminent Predecessors?

The Pen, Sword and Merchandizing, have been generally in all ages the instrumentall means of accumulating worldly blessings, and preferring men to eminency in Honours, and [Page] temporall possessions; as for those who rise by the exposition of politicall or municipal Laws, I do not deny but it is of it self an honourable imployment, especially to all candid breasts, in whom Justice keeps her Courts of Judicatory, her Scales not used to weigh their gold, but the cause; where bribed Rhetorick is not allowed to gild over an unjust Process, to make the richest cause (though the foulest) seem fair, to procra­stinate with Demurs, or Fines and Recoveries without end or recovery; when as the contro­versie is but about Meum & Tuum; and the generall reason wherefore, the sins of the peo­ple, and civil dissentions; yet cases may be doubtfull, though often visibly unjust. Those Ovid seems to check.

Turpe reos empta miseros defendere lingua,
Quod faciat magnas turpe Tribunal opes.
Base is that bribed tongue which guilt defends,
Base that Tribunal which seeks private ends.

Secondly, for the Sword, grave Cicero pre­fers the unjustest Peace before the justest War; besides, it raises but a few by the suppression of many, and the common Souldier, or generall part, are but the back stairs for others to climb [Page] up by to eminency, and all the others have no­thing to glory in, but how Princes and States are indebted to them; or in their badges of grinning Honour, which they bare before them as Cognizanses of their valour, ingrav'd in their bodies with capitall Characters by the fa­tall Steel, where one may read (as in an History at large) the storming of Forts, razing of Towns, or affronting the Canon, disgorging Death's Commissions, wrapt up in Fire and Smoke; some with half faces, or dismembred bodies, repaired with wooden limbs, like wea­ther-beaten Statues, that have stood century many years in the open air, untill defac'd by the hand of Time.

O wretched state or Principality, where crooked justice must be rectified in iron bodies, her scales thrown away, and appeales made to the Sword as Umpire, licensed by incisions to cure Wounds, contentions to decide Controver­sies, injuries to support Right, Injustice Inno­cency, and tumults Peace! These are dire pu­nishments from above, phlebotomising distem­pered Common-wealths, or politick Bodies falling into a Phrensie: as in humane actions we often see, desperate Diseases have desperate Cures, and by Medicines or Corrosives, many times more violent for the present [Page] then the malignancy of the Malady, fearing a relapse, or a totall subversion; whereas the ad­venturous Merchant is beneficiall to all, in Barter or currant Coyn, and by his happy arri­vall inricheth himself and those he trades withall, exchanging his Cargazones, and di­stributing his Treasure for the accommodation of others. Thus raiseth many, ruines few, a free Trade, by compulsion nothing, onely dam­nifying others. Volenti non fit injuria.

Here I have toucht at the three chief Em­ployments, tending to Riches and Honor, as the sole scope aimed at by worldly men, one of them no friend to Peace, nor necessary at all times, of Necessity rarely; litigious men are the Lawyers Stewards; and which of these three Vocations ought to be preferred in a glorious Common-wealth, most candid Reader, judge, I will not be one of the Inquest to give my verdict, because most will censure according to their educations, or as their naturall dispositions incline them, which renders man partiall, by being prone to what he loves or follows: yet that I may not be censur'd for what is past, I will thus far ex­pose an account of my self. Before the uncivil Scots commenc'd a civil War, I had serv'd both by Sea and Land in a just defensive quar­rel, which the Law of God and Nature does al­low; [Page] the Maritine Employment pleased me best, by reason my former studies had initiated me in the grounds of Mathematicall Sciences, whereby Navigation seem'd facile and delight­full: as for the Common Law, I never lov'd contention, nor put on the Gown, but onely have observed the practice of men, and found all these courses good and laudable, if not abused by sinister ends, and the lawfull endeavours of every man (in honest vocations) highly to be commended: so I will make no farther a pro­gress herein, but retreat to my subject and in­tended course.

Many will start Objections (as Huntsmen Hares) and pursue them over others unwarran­table grounds, which incited me to make my former books of Arithmetick better for use, and more perspicuous to the understanding by this Treatise, 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, [Page] 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 [Page] 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.


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. [Page] 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.


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 ƲNCLE, 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 'tis 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 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.
  • 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 [Page] 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.
  • 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.

  • 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.
  • [Page]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.
  • 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.
  • 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 di [...]meter of the [Page] 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.
  • 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.



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 ⅔ 8: the third number is 1 lb, on which the demand is made: these compound f [...]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 th [...]t one lb of those Wares stood the buyer in 5 ss: 1 d: or as in the Table 5 2/ [...]2 ss: with all ch [...]rges defraid, according to the demand and state of the Question pro­pounded.


How to sell a [...]y Wares or Commodities by retail, the pr [...]ce or value of the whole par [...]el being known, and to gain a certain su [...]me of money in the whole quanti [...]y requ [...]red.


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 gain is imposed up­on the parcel: Lib. 2. Parag. 8.

Admit a Draper bought [...] 58 yards of Cloth, which stood him in (with all charges) 13 lb: 1 ss: at what rate by the yard must he sell it for, whereby to gain 1 lb 9 ss: adde the required profit unto the price, the summe will be 14 lb: 10 ss: that is 58 Crowns, or in shil­lings 290: to avoid fractions, the least denomina­tion is usually best: here the fourth proportional found will be 5 ss, the price of one yard according to the gains required, as by the operation in the Table is made evident.


A Tradesman bought a whole piece of Cloth con­taining 28 ¾ yards, which did stand him in (with all charges defraid) 19 lb: 3 ss: 4 d. sterling, how [Page 4] should he sell it, whereby to gain 1/10 part in every yard, or forc'd unto so much loss in retail.


RULE 1. As the Denominator is to the price known, so the fractions summ.

As the quantity given,

RULE 2. so an Unite of the same.

An explanation, where gain or loss is impo­sed upon a part, Lib. 2. Parag. 10.

This Questi­on [...] is stated ac­cording to the Double Rule of Proportion, ei­ther for gain or loss, by change­ing the ex­tremes in the first Rule, viz. in this 10 for 11, the fraction in all such cases making two terms; the Denominator in the first place being Divider, the price of the Wares or Merchandizes the se­cond term, and the summe both of Numerator and Denominator must possess the third place, if for gain; but must be made Divider, if the Propositi­on be for loss: the first number in the second Rule ought to be the quantity propounded, either in Number, Weight, or Measure; and the last Number an Unite on which the querie is made, of [Page 5] gain or loss: or, which is all one, if an improper fraction as in the Table 4/4, the Denominators be­ing made equal, viz. 135/4 and 4/4 and consequently may be omitted, one being a Multiplier, the other a Divider; their Products are these 1150/4 · 115/6 · 44/4 · the first and third Numerators may be reduced by 2, and their Denominators cancelled; they will stand thus, as in the third Table, viz. As 575 to 115/6 so 22 unto 253/345 which is in money 14 ss. 8 d, the price of one yard with the profit required.

The reason is evident; for if 20 ss were the In­teger, the Numerator would have been 2 ss and consequently the proportion as 20 to the middle term, so 228 the summe of Numerator and De­nominator to the gains required. This question may be easily solv'd without a Double Rule, as thus: by the first Proposition you may finde that one yard cost 13 ss. 4 d. 1/10 part of it is 1 ss. 4 d, the summe 14 ss. 8 d. as before: but this may be of good use in other questions, and therefore con­veniently inserted.


How a Commodity must be sold by retail, upon a­ny certain loss of money in the whole parcel or quan­tity.


As the quantity of any Commodity or Parcel is to the difference betwixt the Price and Losse, so shall 1 C, 1 lb, or one yard of the Commo­dity it self be proportionable unto the rate it must be sold at.

An Explanation upon Loss sustained in any Commodity. Lib. 2. Parag. 8.

A Grocer bought 340 lb sub­tile [...] of a Commodity which cost him in ready money with his char­ges 13 lb. 16 ss. 3 d. and by this parcel he lost 1 lb. 1 ss. 3 d. what was it sold for a pound? the loss in the whole subtracted from the price it cost, the remainder or difference is 12 lb. 15 ss. which in pence is 3060 d. so the proportion will be as 340 lb, is to 3060 d, so shall 1 lb be to the price of it; which is 9 d, as in the Table appears: and as for the trial of it, the pro­portion will be as 1 lb is unto 9 d, so will 340 lb be unto 3060 d, or 12 lb. 15 ss. as by the first Proposition.


Ʋpon the price of any Commodity known, how to sell 't by whole-s [...]le or retail, with gain or loss, [Page 7] at any rate in the 100 lb that shall be requi [...]ed.


As the summe of 100 lb sterling is in propor­tion unto the price of the Wares, so shall the rate in money for gain or losse be in proportion to a fourth number, which added to the price of the Commodity, gives the gain, and subtracted from it, shews the losse sustained at the rate required.

An Explanation of gain or loss as any [...]ate per Cent. Lib. 2. Parag. 8.

Suppose 1 Gro [...]e bought 4 C [...] weight of Prunes, at 16 ss. 8 d. the hundred, how must he sell them by whole-sale again, and to make of his money 20 lb in the 100 lb. or after that rate? The answer will be 3 ss. 4 d. which if taken from the price at which they were bought, the remain­der or difference is 13 ss. 4 d. and if sold at that price, there will be after the rate of 20 lb in the 100 lb lost: and if 3 ⅓ ss. be added to the price, at which 'twas bought, the summe is 20 ss, and if vended at that rate, it will bring the desired pro­fit.

If this had been Cloth, and the whole Piece had contained yards 28 ½, which co [...]t in money 23 lb. 15 ss: by the first Proposition find the price of one yard (if it must be sold by retail) the answer will be 16 ⅔ ss. now the question at 20 lb per cen­tum will be the same by retail, as was the former [Page 8] in whole-sale. Many of these Questions may be performed without calculation, as in this Example, where 20 lb per cent. is required. The profit in money here is ⅕, and so the gain or losse in the Commodity must also be ⅕: the price in this was 16 ss. 8 d. that is 50 groats, and ⅕ part of it is 10 groats to be added or subtracted accordingly as it is gain or losse.


The price of any Wares or Merchandize by which the said Commodity was bought and sold: what gain was made, or loss sustained in the 100 lb: or after what rate or proportion.


As the price (by which any Merchandize was bought) shall be in value or proportion unto 100 lb sterling, so will the price of the Wares by which they were sold, be in proportion to the true gain or losse sustained.

An Explanation of Gain or Loss sustained, at any rate per Cent. Lib. 2. Parag. 8.

A Draper bought Kerseys [...] at 6 lb. 13 ss. 4 d. the Peece, and sold them all a­gain for 7 lb. 10 ss. how much he gained, and after what rate in the 100 lb [Page 9] is the thing required: the price by which 'twas bought, and likewise the rate at which 'twas sold must be reduced into one denomination, or by the Rule of Fractions, viz. As 20/3 lb the price is to 100 lb, so 15/2 unto 112 ½: 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 'twas 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.


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.


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 'twas 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 pa [...]t had co [...], 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.


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.

  • 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 'tis 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 [Page 12] 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 twas bought and sold at, with the interest for the forbearance, agreed upon according to custom and contract, but not exactly true.


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.

  • 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 twas bought, and as 'twas 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 'twas 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 'tis 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, [Page 14] wherein the desired product is discovered to be 31 1 [...]/19 l that is, 31 l: 11 ss: 6 d 1 [...]/19: the profit re­quired at the rate per cent. per annum.


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.


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.

  • 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 the l, and sold them all again at 9 ss the l, what day of payment must he allow, whereby to gain af­ter the rate of 20 l per cent. per ann. in all such like Cases, as 100 l to 12 Moneths, so 20 l. secondly, as 8 ss the price, unto 1 ss the gain made: the first rule is reverst, the other direct: in the third row of the Table stand the products, and under that again (in the fourth Table) is plac't the opera­tion in a reverst proportion, but may be made direct if you please: the answer to the question here in this, is 7 Moneths and 15 dayes, the time of payment; which makes the gains proportionable unto 20 l per cent. per annum, the thing required: had the Proposition been of losse, the operation is the same, so it needs no example but this.


If 124 l of Cynamon cost 20 l sterling, and that sold again for 23 l what day of payment was there given, when the Merchant made after the rate of 16 l per cent. per ann. of his money so laid out? this question will be solved by the last Proposition, and [Page 16] found that the day of payment was at the term of 11 Moneths and ¼ of a Moneth.


With the price and quantity of any Wares on Merchandize, to finde how they must be sold, upon several days of payment, either in Gain or Losse, at any rate given per cent. per ann.

  • Rule 1
    • As 100 l sterling shall be to the gain so the price of wares
    • so shall 12 Moneths
  • Rule 2.
    • to the prod. of times
An Explanation of Gain or Loss in several pay­ments, Lib. 2. Parag. 10.

A Merchant had certain [...] Wares which stood him in 60 l: these goods he sold unto another, who paid him so much money for earnest, as that the Mer­chant made of his money laid out 12 l per cent. per an. yet was to receive it at two several payments, viz. 40 l or ⅔ of his money 2 Moneths after the Wares were delivered; and the other 20 l, or ⅔ at the term of 3 Moneths after the contract: now to [Page 17] find what money the buyer paid down, observe this table, where in the first row stands this propor­tion, as 100 L is to 12 L gains, so 60 L the price of the wares; in the first place of the second rule the term of a year (in moneths) is inserted; lastly ⅓ or 2 [...]/3 moneths, which number is composed by the summe produced of the terms for payment and the money, viz. as 2 moneths, by [...]/3 of the money to be paid, and [...]/3 of the money by 3 moneths, whose summe is [...]/3. these terms multiplied according to the double rule direct, will produce, as in the third table; these three numbers, viz. 1200. 12. 140. which in the fourth table are reduced to 120.12. 14. and maybe made (retaining the same propor­tion) 10. 1. 14. or 5. 1. 7. the quotient will be found by any of these, or reduced unto 1 ⅖ L. that is 1 L. 8 ss. the earnest given, and the rate at 12 L. per cent. per ann. as was required; if there had been more times of payment given, the proportionall summes to be paid, multiplied by their peculiar terms or respite of time given, and those summes collected into one totall, the operation will be as in this last example.


By the gain made, or losse sustained per cent. per ann. to finde what any other s [...]me must gain or [...]se in any part of a year.

  • Rule 1.
    • As 100 L in money
    • Is to the gains or loss,
    • So any other summe;
    • If for 12 Months
  • Rule 2.
    • What for 3 Mo.
An explanation of gainer loss proportionable to a stock and time. Lib. 2. Parag. 10.

Admit a man employes [...] his money in the way of trade, by which he gains 16 L per cent. how much does he gain with 80 L in the same employment for 3 moneths time? The state of the question, or a­ny of this kind by the first rule, is thus: As 100 L to 16 L the gain or loss, what 80 L in the second rule there is 12 moneths and 3 moneths: their products (according to this double rule of Three) are 1200 and 240, as in the third table, and in the fourth table as 120 to 16 L gains, so 24; or reduced, it will be as 5 to 16, so 1 unto 3 ⅕ L, or 3 L 4 ss, the proportionall gaines made by 80 L in 3 moneths time: if it had been em [...]loyed to loss, then 3 L 4 ss must have been subtracted from the stock, which in this propositi­on was 80 L, the remainder will be 76 L 16 ss; the question solved.


By the profit of a small stock in money, and a short time to find what gain is made in the hundred per ann. or the contrary in loss.

To solve this, and prove the last, I will reverse the former proposition; and suppose a Tradesman employed 80 L for the space of 3 months, in which time he gained 3 L 4 ss. and here it is required to find after what rate it was per cent, per ann. the state of the question will be as 80 L to 3 ⅓ L the gains, so 100 L, and if in 3 moneths, what in 12 moneths, or a year? The answer to this will be as in the last Prop. 16 L per cent. per an.


Divers tradesmen joyn their stocks together, with which they buy a Commodity, whose price and quanti­ty is known, from whence they take unequall shares, what part then must every one pay?


As the whole quantity of any Merchandize:

Is in proportion unto the whole price thereof,

So shall each particular mans part or share

be proportionable to the money he must pay.

An explanation in equation of payments in gain or losse. Lib. 2. Parag. 11.

Four Grocers did

 A 2403000
lb LB 3003710
1656 207.C 5166410
 D 6007500
The totalls1656207 [...]0

joyn their stocks to­gether, and bought with it 1656 lb of Pepper, which cost them [...]07 L, whree­of A did take for his part 240 lb B 300 lb, C 516 lb, and D 600 lb; the totall summe of the wares must be the first number, the whole price the second, and each par­ticular the third number, and then A must pay 30 L. secondly, B 37 L 10 ss. thirdly, C must dis­burse 64 L 10 ss. and lastly, D must pay 75 L. and in the same manner it will be proportioned with gain or loss, to each respective part as in the table,


In whole-sale, or by retail, if the price of any two com­modities be known with the price and quantity of the one to finde what quantity of the other shall be equiva­lent to it.


As the price of any Wares (the quantity un­known)

Shall be in proportion unto 1, or a unity of it,

So the price of that whose quantity is known,

Will be to a parcel of the first, and equall to the other.

An explanation of Barter, or vending one commodity for another. Lib. 2. Parag. 8.

A Tradesman exchanged [...] Salt at 20 d. the bushel for Su­gar at 15 d the lb, of which commodity he desired 1 C weight gross; how many bu­shels of salt will there be re­quired to be equall in value unto 1 C weight of sugar: by the first table here you will find that 112 lb of sugar at 15 d the pound comes unto 1680 d. then acccording to this rule and in the second table, you may see the pro­portion, viz. if 20 d bought 1 bushell of salt, then 1680 d will buy 84 bushels of salt, being equall to 112 lb of sugar. This trading with one merchan­dize for another is called Barter, derived from Ba­rato, implying an exchange of commodities, the most ancient way of commerce.


The worth of any wares in ready money, if valued at a greater price in barter, how to set a rate upon the price of any other commodity to be bartered for it, that shall be proportionable to the first.


As the price of any Merchandize in ready money

Is unto the value of the same Wares in barter,

So the second Wares (in the first denomination)

Shall be proportionable to the price of it in barter.

An explanation upon the rate Wares made pro­portionable in barter. Lib. 2. Parag. 8.

If 8 Bolts of Hol­land [...] cost 37 L 10 ss, and valued in barter at 40 L, and this to be exchanged for Wooll at 6 L 5 ss the hundred, what must it be ra­ted at in the barter? according to the rule and state of the question, a fourth number will be found (as [...]n the table) 6 L 13 ss 4 D, the rite put upon the Wooll in barter proportionably answering the enc [...]ease, as the Holland is prized, which is the thing required.


In any grosse weight, as Sugar, Currens, &c. up­on the allowance of Tare, to find the Neat weight, and the price of it; and if there be Cloffe allowed to find also the Neat and the price, by knowing what the grosse [...]o [...]ind was valued or bought at.


As 100 grosse weight of any Wares or Merchan­dizes

Shall be in proportion to the pounds allowed for Tares,

So will any gross wares that are known or weighed

Be unto the allowance given for the Tare there­of.

An explanation of Tare, Neat and Cloffe in gross weights. Lib. 2. Parag. 8.

Tare is an al­lowance [...] be­twixt the Mer­chant and the Grocer, for all such commo­dities as are weighed in boxes, chests, casks, &c. for which the allowance is agreed upon when they bargain, as from 6 lb to 18 lb in the C, and is called the Tare; which subtracted from the grosse weight (that is, the chest, or cask and wares together) the remain­der is the Neat; as suppose here are weighed four chests of Sugar, the one in gross weight 6 C and 14 pound, the second 7 ¾ C and 10 pound, the third 8 ½ C and 4 pound, the greatest 9 ¼ C, the summe or totall of them in all 31 ¾ C grosse: then the proportion is as 1 C is to the Tare given (which admit 14 lb) so 31 ¾ C unto 444 ½ lb. or by the rule of [Page 24] Three without fractions (as in the table) and then to the fourth number found, viz. 434 lb. adde in the Tare for the parts, as ¾: which is for the ½ 7 lb & for ¼ adde 3 ½, the summe is 10 ½, the totall 444 ½ lb. as before, which divided by 112 l is 3 ¾ C. 24 ½ lb, the true Tare of the grosse weight 31 ¾ C: from whence subtract 3 ¾ C 24 ½ lb, the remainder will be 27 ¾ C 3 3/2 lb, the Neat weight, as in the table appears, and so for all questions of this kind.

As for Cloffe, it is onely an allowance for the re­fuse of the commodity, which hangs upon the chest or cask, for which is usually allowed but 3 or 4 pound in every parcel, with the parts of pounds, if there be any; but yet in this I strike off ⅛ C 3 ½ lb, and there will remain 27 ½ C 14 lb Near: now to find what it is a pound by the whole weight, or the contrary, see Prop. 1.


Upon any Indian Spices sold by whole-sale, with the allowance for Trett, to find the subtle weight Neat, and how much it is a pound; or by the pound subtle of one sort, to find what any other quantity did cost.

The first RULE.

As 26 pound weight of any Indian Spices

Is in proportion unto 1 pound for the Trett,

So shall any quantity of the same Wares

Be proportionable unto the Trett thereof.

The second RULE.

If 50 lb weight subtle of any Spice propounded

Did cost a certain and known summe of money,

What is the price of another quantity of the same,

When 4 pound per cent. shall be allowed for Trett.

An explanation of Trett, with reduction of the pound subtle. Lib. 2. Parag. 8.

Here first you are to [...] know, that the custome betwixt the Merchant and Grocer is to weigh all sorts of his wares by the C grosse, which containes 112 pound, for which in some he allowes Tare, as was said before; but in Tobacco and sundry other com­modities, with all Indian and Arabian Spices, their grosse weight is reduced into simple pounds, usu­ally called the pound subtle, and in every such hundred there is commonly four pound allowed, which is called the Trett; that subtracted, is by many called the Neat weight: this is readily found by dividing the whole quantity by 26, accor­ding to the first rule (which produceth the Trett) and that quotient subtracted from the totall of the pounds subtle giveth the Neat of the refined weight. As for example: A Grocer bought 50 [Page 26] pound of Mace subtle, which cost him 18 L 15 ss, what shall the subtle weight of 4 ¾ C 1 lb gross of the same commodity stand him in, with abating 4 lb per cent. for Tret? first the grosse weight of it reduced will be 533 lb subtle, which divided by 26, giveth 20 ½ lb for Trett, and subtracted from 533 lb, the remainder is 512 ½ lb subtle Neat, as in the first and second table; and in the third table the question is stated, if 50 pound of Mace cost 18 ¾ L, then 512 ½ lb will stand him in 192 3/16 L, that is 192 L 3 ss 9 D, as by the operation in the table will appear; and to finde what it is a pound, the first Proposition will resolve the querie.


If 1 pound of Cloves cost 3 ss 6 D, what is the price of 676 pound, deducting 4 pound in every hundred for Trett?

The subtle weight here propounded is 676 lb, and abating 4 lb per cent. for Trett, which comes unto, by the last Proposition, 26 lb, which deduct­ed from 676 pound, there will remain 650 pound, then by the first Proposition, if 1 pound cost 3 ½ ss, what shall buy 650 pound? the answer to this question will be 113 L 15 S, and so for any other of these kinds.


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.


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, [Page 28] 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 ⅔ 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.


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.


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.


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 [Page 30] direct, and will be in proportion thus, as 102 ⅔ L, or made an improper fraction, viz. [...]0 [...]/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 ⅖ 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.


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 ⅔ D. which added to the money paid makes 280 L 15 ss 6 ⅔ 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 ⅓ or 20/3 ss. so 1 [...]/3 unto 5615 9/ [...] ss. which reduced is 280 L 1586 ⅔ D, as before.


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 ⅔ 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 ( [...]ib. 2. parag. 1. Aziom 13.) as 4 to 5, so any quantity of the first to an equal summe of the [Page 33] 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 [...]imed at in the exchange of money, as for the profit, ex­perience in trading will discover it.


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.

  • 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.


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.


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 [Page 36] found in the table, will be 28 stone, equall to 16 stone at 14 pound to the stone, the thing required.


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 ⅗ ounces, what 560 pound: by the rule of Three direct you will finde 8176 ounces, which divided by 12, the quotient will be 681 ⅓ pound Troy; and so for all other questions of this kind.


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 ⅛, that is, 21 quar­ters and 7 bushels of the lesser measure, equall to 20 quarters of the greater, the thing required.


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.

  • 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.
AntwerpAntwerp= 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 re­required 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. [Page 39] As for example: here is required how much 47 ells of Antwerp will be of London measure; if the proportion 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.


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 [Page 40] is the Merchants, the other shews the value of the Factors person.


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 [Page 41] 1600 L, the Factors 400 L, and the estimate of his person in this employment 250 I, &c.


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.


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.


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.


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 [Page 44] 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.


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.


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 the money adventured: the operation of this rule is facile, the interest just, and [Page 45] the explanation short: the money here contracted for (according to the conditions of 26 L for interest per cent.) is 640 L, and the fourth proportionall found will be 166 ⅖ L, or 166 L 8 S, as in the table of the margent does appear, which with the principle makes 806 L 8 S, to be received where the money was payable, or should be due, the ship being arrived with the adventure at the appointed Port of the Countrey or Kingdom, as the voyage was intended.


Definitions and Etymologies of Usury and Interest Money, with the several operation compendiously displayed.

USury is derived particularly from Usu­ra, ab usu aeris, or generally from the use and occupation of any thing, as Money, the worth or estimate of it, upon some mutuall contract, where­in the Debtor allows the Creditor a Loan in lieu of the money or goods borrowed; which in times past hath been at liberty as men could agree; but when the unsatiable avariciousness of rich misers attracted extortion from the indigency of borrow­ers, the corroding use of money was by provident Lawes confined to a certain rate, as to 10 L per cent. per ann. afterwards to 8 L, and now of late to 6 L, that is, if a Creditor lends 100 L for a year, he may legally exact 6 L profit for the use of the mo­ney lent.

These are divided into 3 parts, viz. Principall, Time, and Interest: the first signifies the summe, or value of the money or goods so lent: Time is the forbearance of it, as Dayes, Weeks, Moneths, or Years. Thirdly, Interest is the profit that arises from the other two, and is derived from two com­pound Latin words, viz. inter and est, ab edo, to eat or devour, as it is the property of Use to do; they have these proportions, as the Principall to the Time, the Rate contracted for, and Interest to it self, and generally as commixt with one ano­ther.

Interest resembles Janus with two faces, one looking upon the time past, the other on that to come: i [...] this tract the Principall runs, like a snow-ball rising upon an even superficies, equally moving, but the encrease unequall, although pro­portionall to the body, as it is magnified in the motion; and if continued, in time it will gather up all: this is called Forbearance. And Rebate or Discount of money is like the tract in which a snow-ball moved, and in its descent takes up all untill it is staid, leaving the ground bare from whence it takes a seeming originall, where Time hath not arrived, but beholds it, as sea-men an ob­ject, which seems little at a great distance, and en­creases to the Optick sense by unsensible approa­ches.

Use or Interest hath in either Predicament two Species, viz. Simple or Compounded, the first is computed from the Principall and Time onely, up­on a certain rate given or allowed, whether ascend­ing or descending, as in Forbearance, or upon [Page 49] discount, which are thus explained; if 100 L be continued for 2 years, at 6 L per cent. per ann. the creditor at that term of time is to receive but 112 l, that is 12 L for simple interest in lone of the mo­ney forborn; here 100 L is the principal lent, the term 2 years, the use 6 L per ann. whereas in com­pound interest, the first payment attracts a propor­tional use: as admit in annual disbursements, in the second year there is an use required, or imposed on the 6 L due, if continued, and therefore it is called interest upon interest.

Discount or rebate of money is upon a legacy, or summe due to be paid at a time to come, yet satis­fied or discharged with so much present money, as immediately put forth at an interest or rate allowed forborn untill the legacy should have been due, re­turns again to its first principal or summe, the mo­ney paid being computed at the same rate of inte­rest for the forbearance, as was the discount made, as by following examples shall be illustrated, ob­serving these proportions, viz.


As the principal and time for which a lone is al­lowed,

Shall be in proportion unto the interest thereof,

So will any other summ of money to be borrowed

Be proportional to the interest for the same time.


What comes the interest of 145 L unto, forborn a year at 6 L per cent, per ann?

An explanation of simple interest. Lib. 2. Parag. 8.

Any question of this nature [...] is with facility performed by the common rule of Three, as if 100 L principall forborn a year requires 6 L interest, the 145 L for the same term of time will exact 8 7/10 L, as in the table, that is, 8 L 14 ss. the question answered.


A Money-Merchant employed at Use 250 L sterling for 5 moneths, at the rate of 8 L per cent. per ann. and the simple interest of it is here requi­red.

An explanation of simple interest, lib. 2. par. 10.

All questions of this

 Prin. In. Prin.
1 Rule100-8-250
2 Rule12-5
Product1200. 8. 1500
Or as3 to 1 so 25
Facit8 L.. 6 ss 8 D

kind doe consist of 5 termes, viz. 100 L Principall, secondly, the rate for Use, as in this, 8 L. thirdly, the Principall lent, as in the first rule; in the second rule under 100 l is placed the time for which 8 L was due, as at a yeare, or 12 moneths: the fifth number is the term for the principall bor­rowed, viz. 5 moneths, the products of those are 1200. 8 and 1250, and may be reduced (as in the 13 and 14 Axiom, lib. 1. parag. 7.) to 3.1. 25. the quotient here answers the question, viz. 8 L 6 ss 8 D, the proportionall interest, for the summe and time required.


A Banker did lend 650 L. which principall was repayed at the term of 6 moneths 3 weeks and 3 days; what came the interest of it to at 6 L per cent. per ann.

An explanation of simple Interest. lib. 2. parag. 10.

In this double

 Princi. Inter. Princ.
1 Rule100... 6... 650
 D — D
2 Rule365 192
Prod. 36500. 6. 124800
Or as- 365 to 6. so 1248
facit 20 l 10 ss 3 d. 2 34/73 Q

rule the first term is 100 l. the second its interest for a yeare, the third is the prin­ci [...]al lent: the first term of the second rule 365, the num­ber of dayes in a vulgar year; the last term is 192, the number of dayes terminating the time, accoun­ting 4 weeks to the moneth; the products of these are 36500, and 124800, and reduced will be 365 and 1248. which multi [...]lied by 6 l the interest is 7488, and divided by 365 the quotient will be (in a direct proportion) 20 l 10 ss 3 d 2 34/73, as in the table, the simple interest of 650 l. the time requi­red.


A man received 8 l 6 s 8 d for 5 moneths interest of a summe unknown, but at the rate of 8 l 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 ⅓ 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.


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. Que [...]t. 4, 5, & 6.

The encrease

100 L. 6 In. 265 L. 13 ss. 4 ¼ D.
Products L 1594. 00. 1 ½ 20
100 L divid. 6 L multipl.S 1880
D 961/4
Q 246
26/100or 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, a [...] 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 [Page 55] 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 2 [...]/50 Q, as by the operation in the table is conspicu­ous.


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

1005. 17. 6.95676
The products4781176
239110 ½
1191011 ¼
The in­terest moneyL 5618140 ¾
ss 374176
D 888 [...]
Q 355/ [...]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 [Page 56] 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 5 [...]/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.


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.LSD
100 L 564568
537156 ⅔
The interestL 2957156 ⅔
S 1155Months 11
D 6666
Q 266A 3

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 ⅙. 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 ⅓ part of the former, which is 537 l 15 s 6 ⅔ 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.


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

1005. 12. 6543134
Products of in­terests per cent. per ann.271868
The totall is305826
Interest in respect of time152913
764107 ½
(A)L 22931110 ½
5 l 12 s 6 d 20  
5 LS 1871months 9
½10 ssD 862B 6½
¼2 ss 6 DQ 2½B 3½

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 ⅛ or ¼ part of the last, so you will produce these 3 numbers 2718 L 6 ss 8 D. secondly, 271 L 16 ss 8 D. and thirdly, 67 L 19 ss 2 D. the totall is 3058 L 2 ss 6 D to be divided by 100 L, if forborn a year; but the term of time here is but 9 moneths, as in the table at B, which I divide into two parts, viz. 6 M. [Page 59] and 3 M. then take half the totall, that is, 1529 L 1 ss 3 D, and for 3 moneths the half of that 764 L 10 ss 7 ½ D. the totall is 2293 L 11 S 10 ½ D, to be divided by 100 L. now proceed according to the former examples, and you will find the interest de­manded 22 L 18 S 8 D 2 ½ Q. the proposition solved.

If this question had depended on moneths, weeks, and dayes, you must have taken proportio­nall parts, and proceed, as before is specified; so there needs no more examples for the ingenious, to whom all other questions (in the rules of pra­ctise) will be direct, and indirect for others, to in­cumber their understandings with multiplicity of wayes in this kind, therefore I will onely shew you the discount of money, and proceed to Decimall Tables of compounded Interest.


Upon any interest per cent. and the summe of mo­ney that shall be due at the term of a year, to find the worth of it in ready money, or present pay, the inte­rest deducted from the summe.


If 102 L and the annual interest due at a years end

Be worth a 100 L at one entire and present pay­ment,

What shall any other summe due at that term

Be worth in ready money, the interest deducted?

An explanation of this rule in discount, or rebate of money, lib 2. parag. 8.

Admit the interest were [...] 6 l per cent. per ann. which added to 100 l makes the summe 106 l to be rebated: for if this principal were due at the term of 12 mo­neths, it were worth 100 l present pay, because at 6 l per cent. it would encrease in a years space unto 106 l again: from hence this rule of antepayment is framed, and all questions of this condition (if terminated by a year) are solved, as in this example; suppose 546 l shall be due at the term of a year, and desired presently, rebating at 6 l per cent. per ann. the proportion is evident, viz. as 106 is unto 100, so shall 546 be to 515 09 [...]/1000 l, which decimal fra­ction is 1 s 10 ½ d. so 546 l, which should have been due at a yeares end, is worth upon discount present pay 515 l 1 s 10 ½ d, as in the table is de­monstrated by a decimal, and in a natural fraction, it will be 515 5/53 l.


A Legacy, or any summe of money not presently due, and to be discharged at two severall payments, as the first at 6 moneths end. the other at the term of a year, how much money will discharge it at one pay­ment, discounting 10 l interest per cent. per ann.


As 12 moneths, or the true term of a year

Is in proportion to the annual interest allowed,

So the moneths, or term for day of payment

Shall be proportional to the interest for the time.

An explanation of discount or rebate of money, for dayes, weeks, moneths, &c.

In all questions upon re­bate [...] of mony at simple inter­est for the space of a year, ob­serve the last proposition: but if for a greater or shorter term of time, viz. moneths, weeks, dayes, &c. or dayes, weeks and moneths; in all such cases you ought to find a proportional interest for those annual parts, because the money due at several payments is terminated therein, [Page 62] as the other in a year. As for example: there is a Le­gacy of 1000 l bequeathed to T. W. at equall pay­ments, viz. 500 l to be paid at the end of 6 months, and the other 500 l at the period of a year: what is it worth present pay, rebating at 10 L interest per cent. per ann. as for the last payment, form the rule of Three according to the last proposition, viz. as 110 L is to 100 L, so 500 L will be in proportion to 454 L 6/11 L. now for that due at 6 moneths end, find a proportionall intere t for the time (ac­cording to the rate allowed) as by the first of these tables in the margent, which is 5 L. and by the se­cond tables operation you will find for the fourth proportionall number 476 4/21 L, the value of the first 500 L present pay: the summe of both pay­ments 930 170/231 L, 930 L 14 sh 8 48/77 D. the Legacy as valued present pay upon rebate at 10 L per cent. per ann. simple interest, which in the first table re­quired no rule to discover it, but many other pro­positions may, therefore it was inserted by me, and made plain as it is generall; if the respite of time had been for more or fewer moneths, with weeks and dayes, the manner of operation is the same in effect, therefore to write ane more of this would prove superfluous unto the ingenious Arith­metition; so of simple interest I will here con­clude.

Many rules do seem originally derived from Truth, or extracted from Art, but if well observed, they are easily detected, being erroneously reered upon falacious grounds, and their derivations from imaginary principles, viz. as in interest, dis­count of money, Equation in payments relating to [Page 63] Time and Interest, &c. These I have inserted to please some, but not to delude any, the wayes be­ing common in generall received customes, plain, easie, and of good use, the errours not being great or considerable in small summes, or in a short for­bearance, as in Bonds, they rarely pleading pre­scription of years, or exeeding an annual revoluti­on, upon forfeiture in transgressing a penal Law; whereas rebate or discount of Mony often depends upon long terms, involv'd with multiplicity of ante­dated years, as in purchasing of Leases, Pensions, An­nuities, Reversions, &c. therefore these were com­posed so compendious as I could, since there be better rules extracted from Artificial numbers, and Decimal Arithmetick in compound Interest, as those following.

A Decimal Table of Interest money forborn any num­ber of dayes, weeks, moneths, or years, to 25 inclu­sive, accurately calculated at 6 l per cent. per ann.
DayesDecimall numbersYearesDecimall numbers
Weeks VIII1.593848
Moneths XIII2.132928
The second Table of compound Interest money dis­counted for dayes, weeks, moneths, or yeares, unto 25 inclusive, exactly calculated at 6 l per cent. per ann.
DayesDecimall numbersYearesDecimall numbers
Weeks VIII.627412
Table 3. Forbearance of annuities, rents, or pensions from 1 year to 25, at 6 l per cent. per ann.Table 4. Discount of an­nuities, rents, or pensions, from 1 year unto 25, a [...] 6 l per cent. per ann.Table 5. Purchase of an­nuities, rents, or pensions from 1 year unto 25, at 6 l per cent. per ann.
YearsDeci. N.YearsDeci. N.YearsDeci. N.
IX11.4913 [...]IX6.80169IX.1470 [...]
XVII28.21 [...]88XVII10.477 [...]6XVII.09544
The construction of Decimal Tables for Use money, made proportional for any interest, time, or terme of years required, with the applications of these il­lustrated with usefull and compendious examples.

All questions of compound interest money may be comprehended and solved by one of the 5 pre­cedent Tables, calculated (without sensible errour) and extracted from the former prescribed rules, as in the 38 and following Propositions of simple in­terest: And first, here observe that these Tables are composed upon the worth or interest of 1 L princi­pal per ann. after the rate of 6 L per cent. yearly payments, as the Law now commands, with a pro­hibition of any greater interest, upon the penalty of a forfeiture, excepting such cases wherein there depends some apparent hazard, as in Exchanges, Cambio Maritimo, or in Bonds and Obligations not satisfied, that antedate the Act, &c. and upon this foundation are erected these tables, whose cal­culations I will first exhibit to your view, both for farther satisfaction, & the composing of any others upon other rates or proportions; and then proceed unto the use and explication of these.

The proportions of compound Interest Money, in Decimall numbers, due upon the lone of 1 L Principall.

As 100 L sterling lent for term of a year

To the summe of the Principal and interest allowed,

So shall 1 or an unite of the first denomination

Be unto the principal and interest in a Decimal.


As 100 L sterling forborn the term of a year

Shall be in proportion to the last years Decimal,

So will the summe of the principal and interest

Be unto a Decimal for the succeeding year.

An illustration.
I 100 lis to 106so wil 1 l be to1.060000
II 100 lis to 1060000so 106 l is to1.123600
IIIas100 lis to 1123600so 106 l unto1.191016
IV 100 lis to 1191016so 106 l unto1.262477
V 100 lis to 1262477so 106 l unto1.338226

In the construction of these tables, take an unite with what number of ciphers you please for the Radius, one place more then you intend to in­scribe, [Page 69] but of no necessity, as here 1,000,000, the seventh place being an integer, all the other to­wards the right hand are fractions, or representing their places according to my third book of Artifici­all Arithmetick: now for framing the first table (wherein the principal is forborn) adde the princi­pal and interest together; the summe is here 106, annex 4 ciphers or points to it, equal to the Radi­us, and it is a decimal fraction for the 1 L forborn a year; or by the first rule, as 100 L is to 106, the principal and interest allowed, so shall 1 L princi­pal be in proportion to 1.060000, which is a mixt decimal fraction, and comprehends the 1 L princi­pal, with the interest 06/100, and reduced is 1 ss 2 d 1 ⅗ q. but leaving it involved, as the encrease of the first year, all the rest will be discovered by the second rule successively, viz. as 100 L to 1.060000, so 106 the principal and interest to 1.123600, the decimal for the second year; then for the third year, as 100 L is to 1123600, so 106 in proportion to 1.191016 in the same manner of operation, you will find 1,262477 for the fourth year, and 1,338226, a proportional decimal fra­ction comprehending 1 l principal forborn 5 years, with the compound interest of it, which is 6 ss 9 d, and not one farthing more: thus you may proceed to what number of years occasion shall require.

To finde Decimal Numbers for any parts of a year, as moneths, weeks, dayes, or for half years and quarterly payments.

Take the Decimall for a yeares interest, viz. 1.060000, whose Quadrat Root extracted as in lib. 2. parag. 1. examp. 5. you will find 102956, a proportional decimal, for the interest of 1 l forborn 6 moneths, in money 7 0 [...]44/10000 d. the mean proporti­onal betwixt 1.02956 and 1.06000 will be the de­cimal for 9 moneths, viz. 1.04467, and be­tween an unite or 1, and 102956 will be .1.01467, a decimal mixt number (according to compound interest for 3 moneths) equal in value to 1 L 0 ss 3 ½ d. and thus you may with facility discover all the other numbers: if the annual table had been for half yearly or quarterly payments, you must find 1 or 3 mediums between every continued and suc­ceeding year; which to effect, I refer the Reader to lib. 2. parag. 6. prop. 1. and 4. and observe to an­nex ciphers to the Decimal (whose Root is requi­red) in such a number as to equal the places in the table, and point them from the left hand to the right, so that the first prick of your pen may be o­ver the radius or integer. In other things observe lib. 2. parag. 1. exam. 5.

The framing of the second Table for discount or rebate of money.

As 100 L with the interest due at a yeares end

Is unto the principall 100 L present pay­ment,

So an unite or 1 L due at the same terme of time

Shall be to a Decimal fraction interest dedu­cted.


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.
I 106 lis to 100 Lso wil 1 l be to.9433962
IIas106 lis to .9433962so 100 l is to.8899964
III 106 lis to .8899964so 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 [Page 73] 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)
11. 06000011.000000
21. 12360022.060000
31. 19101633.183600

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 [...]er cent. (2)

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.

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:


As 1.833392- to 1 L- so 1.000000 unto .54544.

Or thus,

As 1 L 16Purchase sh 8 d- is toAnnuity 1 L, so will 1Purchase L be to 10 shAnnuity 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 L annuity to continue 2 years; what annuall [Page 77] rent or pension will 1 L purchase for the same term of 2 years? which fourth proportional num­ber discovered, will prove .54544, as in the second year of the fifth table, and reduced, is in money 10 sh 10 9/10 d. the annuity or annual pension pur­chased by 1 L for 2 years, which at 6 L per cent. in the term of 2 years returns to its first principal, the interest considered: now for the third years deci­mal, as 2.673012 is unto an unite with ciphers, so will 1 L for a purchase be in proportion to 37411, in money 7 sh 5 d 3 q. an annuity to continue 3 years; and thus proceed to what number of years you please, since by the third, fourth and fifth &c. are framed out of the 3, 4, 5 years, &c. respective­ly answering the years of discount or rebate of rent, as in the fourth table; the fifth being thus finish­ed, if the half years and quarterly payments be re­quired, they may be extracted by finding mean proportional numbers, as hath been declared in the calculation of the former table of Decimals; and as for parts of a pound sterling, I refer you to lib. 3. sect. 1. cap. 7. but here note that the precedent tables be continued to one or two places more, otherwise er­rours will creep in at the root or end of these num­bers by annexing of ciphers; for which cause (as it is the common custome) these 3 last tables were framed on a lesser Radius (as by one place or de­gree of figures and ciphers) then are the two first.

The description, use and explantion of these Decimal Tables, accommodated to the compound interest al­lowed, at 6 L per cent. per ann. calculated with­out sensible errour in the forbearance or discount of Money, Annuities, Rents, Pensions, and Reversi­ons, with the purchase of them due upon yearly pay­ments.

The first Table is divided into 4 columns, and begins with one comprehending the parts of a year, ascending by dayes, weeks and moneths; the third row contains the years from 1 to 25 inclu­sive, both noted with numeral letters; upon the right hand of these are placed (in Arithmetical cha­racters) the Decimal numbers made proportional for 1 L forborn, respectively answering the times included, calculated u [...]on the Radius of a million 1000000. the second table is for discount of 1 L principal, after the rate of 6 L per cent. per ann. made by the former Radius, viz. 1000000, for the same parts and term of time as was the last. This discount or rebate of money is by some termed In­terest damageable, by reason it is ever lesse then the Principal, although upon a dayes discount, or any shorter time, as you may see in the head of the table, with a title to each column; the first hath the Radius prefixt to the Decimals, the second of Discount have onely points to denote their places, as Primes, they being all proper fractions, and parts of 1 L. the third, fourth and fifth Tables have each 2 columns onely, the first numbring the years from 1 to 25 in numeral letters, and against [Page 79] those annual computations are placed the Decimal numbers depending on those years, as by their titles do appear: the third and fourth encreases, the fifth declines the Radius; which prolix numbers in these the three last Tables, extends to 100000, and so much for the model and form of them.

The first Tables use illustrated.
QUESTION I. If 1000 L be forborn 1 day, what shall be the inte­rest of it, after the rate of 6 L per centum per an­num?

Look in the first Table for 1 day; against which (under the title of Decimal numbers I find 1000160, which multiplied by the principal 1000 l, or annex 3 ciphers to it, the product is 1000, 160000, from whence sever the Radius by cutting off 6 places from the right hand, you will find 1000 L for integers struck off, and the remain­ing fraction .160000, which reduce, as in lib. 1. sect. 2. parag. 1. paradig. 10. or multiply it by 20, and from the product cut off 6 places, and so pro­ceed; you will find the loan of 1000 L to be 3 ss 2 d 1 ⅗ q.

QUESTION II. What will the interest of 300 L amount unto, if for­born 3 weeks, after the rate of 6 L per centum per annum?

The decimal for 3 weeks is 1.003358. which multiplied by the principal 300 L produceth 301, 007, 400. from whence cut off 6 places and reduce them, you will find 301 L 0 ss 1 D 3 q. the encrease of 300 L for the time required, viz. 1 L 0 ss 1 d 3 q.

QUEST. III. What will the interest of 200 L rise unto, if for­born 6 moneths, after the rate of 6 L per centum per annum?

The Decimal for 6 moneths forbearance of 1 L is 1.029563, so the rule is in this and all the rest; as 1 L, or the decimal 1,000,000 is in proportion unto 200 L, the principal propounded; so the de­cimal of 1 L forborn the same term of time shall be proportional to 205.912.600. from which com­pound fraction sever 6 places numbred from the right hand, the integers are 205 L, the fraction 912600 reduced, will be in money 18 ss 3 d, so here the interest of 200 L for 6 moneths proves [Page 81] but 5 L 18 sh 3 D, whereas, according to cu­stome, you may discover amongst the vulgar errors the loan of this principal forbo [...]n half a year comes to 6 L, that is, 1 sh 9 D too much.

QUESTION IV. How much comes the interest of 150 L unto, if for­born 7 years, at the rate of 6 L per centum per an­num?

The Decimal against 7 years is 1503630. which multiplied by 150 L produceth 225, 544, 500, and reduced, is in money 225 L 10 sh 10 68/100 D, so the encrease of 150 L, all interest forborn 7 years, swel [...] to the summe in clear profit 75 L 10 sh 10 68/100 D, which by the common current of simple interest does multiply in the seven years apprenti­ship (when the Principal shall be discharged the Indenture) but 63 L, which is less (I conceive) then the intention of the English Laws allow by 12 L 10 sh 10 d. for if any loan upon a principal can be legally exacted in equity, use upon the interest (so often as due) may be as justly claimed by the same prerogative, according to Humane institutions, not warrantable by the Divine Law.

QUESTION V. If 210 L be forborn the term of 3 years, 3 mo­neths, 3 weeks, and 3 dayes, what will be the encrease at 6 L per centum per annum?
The ProductsIDecimals 1191016 2382032 
The totall is— 254 L 15 ss 1 ¼ d.

In all questions of this kind, seek the Decimal for the longest term of time allowed, as here 3 years, whose artificial number is 1191016, which multi [...]lied by 210 L (the principal lent) or by 21, lib. 1. sect. 1. parag, 4. exam. 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 [Page 83] 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 wh [...]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 [Page 84] 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 tis 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 i [...]?

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
15827716001582. 15. 5
25660376002566. 0. 9
35497842003549. 15. 8
1698. 5934001698. 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 the Quadrat ex­tracted as it is pointed will be 916307, a meane proportionall number betwixt the first and second yeare, according unto the construction [Page 86] 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. [Page 88] 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 [Page 89] 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
351 L 19 sh 6 D7191 L 15 sh 0 D
4139.773758139 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. [Page 90] 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
 5 9
3588 L 4 ss 0 ¼ d750 L 4 sh 10 d
4537 L 19 ss 2 ¾ d8537.96208

In the fourth table (of Rents rebated) the Deci­mal [Page 91] 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
2L 235.28140
4D— 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?
12.55036 788687
1631 L 10 sh 11 D.31656 L 4 sh 10 D.
1651 L 10 sh 11 D.44 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, [Page 94] 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

311 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

33 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 Decimal [...] 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
1.0850059.2949 [...]
313 L 12 ss929498
429 L 12 ss7126.411728

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 [Page 99] 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 [...]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 s [...]xth stand their several products, and in the seventh row the totall summe, as 1 [...]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. ca [...]. 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 cont [...]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-corm [...]rants, and their pro [...]it great, because such Estates lye dormant in Banks, [Page 100] obscured from the inquisition of a sax; and rare­ly appea o [...] wake but with the noyse of a Forfei­ture o [...] the Owners Land, or the liberty of his per­son. The Interest, like a Monster, by an unlawfull conception, and a prodigious birth (grown greater then the Principal) makes appeal to the rigor of the Laws, against those who bore too prodigal a Saile, and now like to suffer wr [...]ck betwixt Scylla and Charybdis, or swallowed by those yawning waves.

Usury is like a Cancer, which by an unperce­ptible Consumption ingratefully wasts that body where by Corruption it took a being; I wish none to adore the Golden Calf, nor yet slight the ma­terials, their use being good and laudable, where Vertue is Treasurer, Discretion Controller, and Charity Purse-bea [...]er: but if abused by being cast in another mould, or the three adverse parties in office, it will as e [...] ly catch those (who make worldly wealth their Mammon) as lime does Birds; so the danger is great, and the more, when usually the love of Money multi [...]lies, as their Stocks and Magazines encrease; and those who have most are often most miserable in want, ignorant in the use of temporall blessings, and glutted with ex­cesse, become immedicable by those surfeits; like men in Dropsies, the more waterish they grow, the more they desire drink, with an unsatiable thirst, so feeds the humours, and that the di­sease. And thus I will conclude with the ingenu­ous Poet, Ovid.

[Page 101]
Sic quibus in [...]umui suff [...]sa venter ab unda,
Quò plus s [...]n potae, plus sitiuntur aquae.

In English thus,

Men s [...]ell'd with Dropsies grow excessive dry,
And drinking, covet more untill they die.


Generall Rules of Practise, by the Art of Memory.

MErchandizes and all Commodities are sold either by number, weight, or measure, and those by gross o [...] retail, viz, as in Tunnes o [...] siz'd Loads, by the Thousand, by the Weigh, Tod, Clove, by the Hun­dred, whereof there are accounted 4 sorts, as 6 Score, 5 Score and 12 lb, 5 Score, and also 60 Warp, and sundry sorts by measure, as the Tunne, Chaldron, Quarter, Barrel; the Gross, Dozen, &c. as by the following Tables are delineated, whereby their values in the least species or denomination may be computed in the greater, without obstruse rules or incumbring the memory with [...]eserv [...]tions, but by vulgar notions and natures common dictates onely, having imprinted in your memory the gross summs, and what those amount unto in coyn of the least denominations, as in shil. g [...]oats, pence & farth. [Page 104] but for those, to whom these accounts are un­known, or where for want of practise they have been obliterated, or the recollection trouble­some, I shall present you here with a Table ready calculated, for the Numbers, Weights, and Mea­sures, most frequently used in England, and gene­rally received either from former Statutes, or custo­mary Laws, ratified by the undeniable prescription of Time, and intermixt, are these:

A TABLE of Numbers, Weights, Measures, and what their several gross summes amount unto, in Shillings, Groats, Pence, and Farthings, registred in Arithmetical Characters, and by Numeral Let­ters.
2240or XX. C g. [...]1203768968268
2016or XVIII Cg.1001633120880220
1680or XV. C g.84028007001150
1500M D75025006501113
1344or XII. C g.6742 [...]805120180
1120X C g.560181344134134
896VIII. C g.44161418831480188
800VIII C40013683680168
672VI C g.3312114021600140
600VI C3001000  [...]000126
560V C g.2809682680118
500V C250868 180105
448IV C g.2287941174094
400IV C20061341134084
365CCC LXV185618 10 [...]077 ¼
336III C g.16165120 80070
224II C g.1143148 [...]188048
200CC100 680168042
144CXLIV74 [...]800120030
112I. C. g.512 [...]174094024
70LXX3101340510015 ½
63LXIII33 [...]10053013 ¾
56LVI. ½ C g.2160188048012
50L2100168042010 ½
42XLII2201400360010 ½
30XXX1100100026007 ½
28XXVIII. ¼ C18094024007
25XXV15084021006 ¼
21XXI11070019005 ¼
18XVIII018060016004 ½
14XIV014048012003 ½
10X0100340010002 ½
6VI06020006001 ½
2II0200800200 ½
1I01004001000 ¼

A description of this Table.

Be pleased to observe here are 13 Columns, where­of the first contains (in Arithmetical Characters) the principall Numbers, Weights and Measure, noted in the head of the table with lb for pound weights, or Num. for numbers, beginning with 2240, a siz'd load, tun, or 20 hundred gross; from hence continued down to an unite, in such an order or series of numbers most frequently used in the Com­merce and Trade of this our British Island: in the next stands their subtile and gross weights, noted with numeral letters, distinguished in the post-script by the letter g, denoting gross: the third and fourth Column shews what summe of money they do make in Shillings: in the fifth, sixth and seventh Column, what so many groats amount unto: the three next Columns what those gross or subtile summes do make in pence: the three last (in the least denomination of money) & what the value ri­seth to Pounds Sterling, Shillings and Pence, as by their titles in the head of these tables do evidently appear.

The benefit of this Table, by sundry Examples illustrated to ease the Art of Memory.


It is required (without calculation) what 2240, or 20 C gross amounts unto in shillings, look under its title and you will find 112 L 0 ss. in groats 37 L 6 ss 8 D. so many pence comes to 9 L 6 ss 8 d. and in farthings 2 L 6 ss 8 d.


In things sold by Retail. Admit a Commodity vended for 3 half pence the pound, and it is requi­red at that rate how much it comes unto by the Tun; I take it in the least denomination of Coyn, (that is 6 farthings) and at one farthing the pound under that title I find 2 L 6 ss 8 D. for which you must impose so much on every farthing contained in the price, which was 6. then consequently the summe must be 6 times 2 L. secondly, 6 times 6 ss. and also 6 times 8 D. or for brevity, 6 times 2 L is 12 L, and 6 Nobles is 2 L. in all 14 L, at 1 ½ D the lb, as was required.


At 3 D the pound, what comes a tunne unto? under the title of Pence I find 9 L 6 sh 8 D, at a penny the lb. then 3 times that is 28 L. admit a [Page 108] commodity at 8 D the lb. you may work this as be­fore, but being the price is 2 groats, under that title you will discover 37 L 6 sh 8 D. and since 2 groats is the price of one lb, that doubled is 74 L 13 sh 4 D. if the price had been 3 sh the lb, the tunne would have come unto 336 L, as by the ta­ble is evident.


How much comes 10 D a day unto by the year? I look down in the table for 365 (the number of dayes in a uulgar year) and under the title of pence I find 1 L 10 sh 5 D. now 10 times that is 15 L 4 sh 2 D, or summe it up in your memory thus, viz. 10 L then 10 Angels, 10 groats and 10 D. or take, it in groats and pence, as 6 L 1 sh 8 D, and 1 L 10 sh 5 D makes 7 L 12 sh 1 D. this dou­bled (the question depending on 2 groats and 2 pence) the summe will be as before, 15 L 4 sh 2 d.


If one pound of Cheese cost 3 ¾ D, what comes the Weigh unto? This properly belongs to a cer­tain quantity of Wooll and Cheese, cons [...]sting of 32 Cloves, whereof one contains 8 lb, so the Weigh is 256 lb. which having found in the table, I seek it in the colume of pence, and find 1 L 1 sh 4 D. and in the row of farthings 5 sh 4 D. the summe 1 L 6 sh 8 D. and being that there was 3 times so much to be imposed in either denomina­ation, the summe is 4 L for the Weigh at the rate propounded.


Wine sold at 2 sh 5 D the gallon, how much is that a tun, containing 252 gallons? Having found the number, look against it (the column of shil­lings) and you will discover 12 L 12 sh (at 12 D the gallon) which doubled is 25 L 4 sh. to which adde 5 L 5 sh (for the 5 D) the summe is 30 L 9 S. the column of pence answering that number being but 1 L 1 sh, so it is easily multiplied by 5. Or take it as mixt in their severall columns of groats, and pence, 'twill be all one in the total.


Currants sold at 3 ¾ D the pound, how much comes 1 C weight gross unto? The farthings con­tained in the price are 15, and against 112 in the last column I find 2 sh 4 D to be imposed on every farthing, that is 15 groats & twice 15. in all 1 L 15 S. or take it in both columns of pence and farthings, as 3 times 2 sh 4 D. and thrice 9 sh 4 D. if this que­stion had been propounded on 100 lb subtile, the answer wil be 15 pence and twice 15 shillings, that is 1 L 11 sh 3 D.


Fish sold by the warp or couple, at 2 sh 10 ½ D the warp, what co [...]es 4 C unto? 60 in this com­modity is 120 Fi hes to the C. look 60 in the table, against which I find (in the column of shillings) [Page 113] 3 L, then for the 2 sh I set down 6 L, or keep it in my memory; in the next column I observe 1 L, and for the 2 groats in the price 2 L, then for 2 D (in the column of pence) I impose 2 Crowns, and for the 2 farthings in the price 2 sh 6 D, in all 8 L 12 sh 6 D, the price of 60 couple: now 4 times that is 34 L 10 sh. according to the demand.


If 1 pound of Indico cost 8 sh 7 D 3 q. what comes a quarter of 100 unto subtile? The answer will be 10 L 16 sh 1 D 3 q. look 25, and for the 8 sh in that column impose 10 L. for the 7 D, 14 sh 7 D. and lastly, for ¾ D take 1 sh 6 ¼ D, the summe will be as it was before, and according to my rules of Practise, lib. 2. parag. 9.

By these 9 Examples all obscurities in this kind are cleared, difficulties made easie, and burdens to the memory removed, made facile even to com­mon capacities, without tedious rules of Art, the Numbers, Weights and Measures of Commerce and Trade-being known to those who are conver­sant, or Masters in their own occupations; and if otherwise, this will be a guide to conduct them, without deviation, to the end of each gross summ, and may be accommodated unto the Numbers, Weights and Measures of any forreign or trans­marine place; if occasion requires, or necessity ur­ges, which I refer to the ingenious.

Any day of the year assign'd for the receipt or payment of money, or other business, to finde what day of the week 'twill fall upon for any time to come.

The Julian KALENDER.
BisNew-years day MonethsDayes
 1659Saturd.IJanuary1, 8, 15, 22, 29
1660SundayIIFebruary5, 12, 19, 26
 1661Tuesd.IIIMarch5, 12, 19, 26
 1662Wednesd.IVApril2, 9, 16, 23, 30
 1663Thursd.VMay7, 14. 21, 28
1664FridayVIJune4, 11, 18, 25
 1665SundayVIIJuly2, 9, 16, 23, 30
 1666MondayVIIIAugust6, 13, 20, 27
 1667TuesdayIXSeptemb.3, 10, 17, 24
1668Wednesd.XOctober1, 8, 15, 22, 29
 1669FridayXINovem.5, 12, 19, 26
 1670SaturdayXIIDecemb.3, 10, 17, 24, 31

The Tables use explained.

This Table contains 6 Columes; the first hath onely 3 Crosses, to signifie those years against them to be greater then the rest, being Bissextiles, or Leap-years: in the next are the years that shall be elapsed since the birth of Ch [...]ist, from 1659 unto the year 1670. In the third Colume are placed the week dayes, which begins each year respectively, or the [Page 113] first day of January: in the fourth and fifth stands the 13 moneths: the last column shews the week­daye, in every moneth, on which New-years day did fall upon in any of these years.


It is required to know what day of the week shall be the fourth of December in the year 1659. against which I find Saturd. for the first day of the year, and likewise the third of Decemb. the next is Sunday the thing desired. The Saturdayes in this moneth 1659 are upon 3, 10, 17, 24, 31. Saturday concluding both moneth and year, and Sunday beginning the year 1660, as in the Table.


Admit it were required in a Leap-year, to know what dayes of any moneth shall be Sunday: here you are to observe that in Bisextiles, or Intercalary years, there is one day added to February, which then hath 29. so after that moneth take one from the day found, as in the year 1660. the first Sunday in March, in October, and the last day of December is required. New-years day I find to be upon a Sunday, and in the Columns of Moneths against March stands 5, which should have been the same day of the week; but being February had 29 dayes this year, the 4, 11, 18, 25, are the Sundayes in March this year. Secondly, against October I finde 1, which should have been the same with New-years day in a common year, but now the last of Sep­tember, [Page 114] so the 7 day of October shall be the [...]rst Sunday, likewise 14, 21 28, and from any other number subtract 1. and then for December, the last Lords day shall be 30, and the 31 to conclude the year shall be Monday.

A Gregorian KALENDER.
BisNew-years day MonethsDayes
 1659feria 4 ☿IJanuary1, 8, 15, 22, 29
1660feria 5 ♃IIFebruary5, 12, 19, 26
 1661feria 7 ♄IIIMarch5, 12, 19, 26
 1662feria 1 ☉IVApril2, 9, 16, 23, 30
 1663feria 2 ☽VMay7, 14, 21, 28
1664feria 3 ♂VIJune4, 11, 18, 25
 1665feria 5 ♃VIIJuly2, 9, 16, 23, 30
 1666feria 6 ♀VIIIAugust6, 13, [...]0, 27
 1667feria 7 ♄IXSeptemb.3, 10, 17, 24
1668feria 1 ☉XOctober1, 8, 15, 22, 29
 1669feria 3 ♂XINovem.5, 12, 19, 26
 1670 [...]eria 4 ♀XIIDecemb.3, 10, 17, 24, 31

This Kalendar of 12 years is made for the pay­ment or receit of Money, or Merchandizes assign'd upon a prefixt day of the month in Forreign parts, to find on what day it will fall upon: observe this Table does not essentially differ from the former in construction, but in the dayes of the moneths, the Reformed Account being 10 dayes before ours, so that the 22 day of December, according to the [Page 115] Old Style or computation, is the first day of Janua­ry in the New, and so all the other moneth; pre­cedes our 10 dayes, their Septimana, or Week­dayes are diversly reckoned, but most usually thus, viz. Sunday, Feria prima, Dies Dominica, or Dies Solis, ☉. Monday, Feria secunda, or Dies Lunae, ☽. Tuesday, Feria tertia, or Dies Ma tis, ♂ Wed­nesday, Feria quarta, or Dies Mercurii, ☿. Thurs­day, Feria quinta, o [...] Dies Jovis, ♃. Friday, Feria sexta, or Dies Veneris, ♀. Saturday, Feria septima, Sabbath, or, D [...]e [...] Saturni, ♄. The f [...]r [...]t computati­on is an Arithmeticall progression from 1 to 7. the other ac [...]ording to the Planets, denoted by their Characters, as they are appro [...]riatod unto those pe­culiar dayes: in other things this Table differs not from the former, so I refer the Reader to those 2 Examples.

THE SECOND BOOK. Demonstrating a Sympatheti­cal affection between Arith­metick and Geometry, by solution of several Problemes or Propositions of Mag­nitude with exactness by the assistance of Art and Numbers.


In any right-lin'd Triangle propounded with the Perpendicular and Basis, to find the Area or content of it in square Inches, Feet, Yards, Perches, &c, in whole numbers or fractions.

The Theoreme.

The superficiall content of any right-lin'd Triangle is half the Square produced, in multiplying of the Ba­sis by the Perpendicular. Lib. 1. Prop. 16. Trigon.


IN the Triangle A.C.D. from the Angle at A. let fall a Perpendicular, as A. B. upon the Basis or ground-line, C.D. This Perpendicular suppose to be measured in inches or feet, &c. but here in this admit 4 feet, and the basis C. D. 5 feet, the pro­duct of these is 20 square feet, the half of this 10 feet superficial content of the Triangle A.C.D. the thing required. All right-lin'd multiangular and irregular figures may be reduced into Triangles, and thus measur'd, a Probleme of great use to the Surveyer.


In all plain right-angled Triangles, with either of the two sides known, to find the third side; from whence with any line how to describe or set out a per­fect square for any Plat or Building, &c.

The Theoreme.

In any lain right angled Triangle given, the square made of the Hypothenusal (or Subtendant side) is e­qual to the square made of both the containing sides. Lib. 1. Prop. 23. Trigon.

In the last Triangle A.C.D. having let fall a Perpendicular from the Angle at A, as the line A. B. making 2 right angled triangles, viz. A.B.C. and A. B. D. whereof A.B. is 4. and b.C. is 3. their squares 9 and 16, the summe of them 25. whose quadrat root is 5, as by the demonstration may be explained in the second book, pag. 122. the true length of A.C. the Hypothenusal required, and the squares of A. B. 16. and B.D. 4. will be 20. wh [...]e root will be A.D. as 4 4/9 or 4 47/100. but nei­ther of them exactly true, as lib. 2. par. 1. examp. 5. but to return, if the Subtendant side A. C. were known, and one of the other two containing sides, the third side will be discovered; as admit A.C. 5, and A.B. 4. their squares 25. and 16. the difference 9. whose quadrat root is 3. for the side B.C. or if the square of 3 (that is 9.) were taken from 25. the [Page 120] remainder will be 16. the root 4. for the Perpendi­cular A.B.

In all plain right angled triangles, these numbers are onely rational, to be found without fractions, or their products and quotients 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.


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 'twill 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.


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 [Page 123] 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 [Page 124] 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 by seasoning and joynting them, and in their lengths to fit them on a joyce; some will prove faulty, as shaken or maim, and sundry other casualties, for which you must allow, especially in good work, and rebated 1/10, in square joynts 1/15 or 1/16 lost in well shooting of the boards, although seasoned.


To measure Hangings, Wainscot, Pavements, Land, &c.

The last Theorem is an undoubted speculation to all these, so I will shew the practise of it com­pendiously with examples; and first, there is a Room to be hang'd, containg of Flemish yards, in height 4 of those measures, and in compasse 25, the product of them is 100. the superficial content; in this room there is a chimney-piece containing 9 ½ square yards, and the Window 10 ½ yards, the summe 20, which deducted from 100 yards, the remainder will be 80 Flemish yards to furnish that room. And as for Wainscot, the operation's the same, but differing in yards, and sometimes by cu­stome, in takin those measures, as in the height and compasse of the room wainscoted, some using a small line extended straight upon each pannell, and then rising over each stile and quarter. Thus Joyners will make their work both of a greater height and compasse then a line extended over all can do, the reason the workman gives, they must be paid where their Plane goes; but their measures admitted of, finde the su­perficiall content in the same manner as it was before, yet the Wainscot of that roome, by the same measure, may exceed the other 5 or 6 yards, yet more or lesse according to the Joyners work.

Pavements are usually measured by the foot, or yard square, as Board and Hangings are: the longest lineall measure used in England is the Rod, Pole, or Pearch, whose lengths are various for Land, as custome hath introdu­ced and continued them in particular Coun­treys, and those from 15 to 25 feet in length: the most equall and generally received Pearch is 16 ½ feet long commanded by Statute, yet 160 square Pole is one Acre of ground, according to the Rod by which it was measured, and in that Pro­vince where it is allowed. But as for our pre­sent purpose, the Survey being taken (though the field be never so irregular) it may be reduced into Triangles, and then measured, as was said before in the first Probleme.


The Area here surveyed is represented by the fi­gure A. B. C. D. E. whose superficiall content by naturall Arithmetick will be thus discovered: Draw a straight line from E to C. now A C in this proves a subtendant side to the right angled triangle A.B.C. whereof A.B. was measured by the chain, and found equal to C. D. 45 ½ Perches: from E let fall a Perpendicular on C. D. as E.F. measured with the scale (by which the Plat was ta­ken) 39 Poles: the work thus prepared, by the first Prob. B. C. 60 2 [...]/33 or 60 2/11 P. multiplied by 45 ½ P. according to the rules of fractions (as in lib. 1. sect. 2. Parag. 4. Parad. 4.) will produce 60692/22 take ½ of it, 'twill be 60697/44 which is 1379 21/44 square Perches. Again, by the first Probleme, in the Tri­angle E.C.D. the line C.D. 45 ½, or 91/2 Poles, mul­tiplied by the Perpendicular E.F. 39 P. produceth 3549/2 square Perches, ½ of it is [...]549/4 that is 887 ¼ P. the true content of the Triangle C.E.D. the summe of these two Triangles is 2266 [...]/11 P. which divided by 160, the square Perches contain­ed in an Acre, the quotient will be 14 Acres, 0 Rood, and 26 square Pole, the superficial quan­tity of the Field, as was desired. And thus the Triangle A.E.D. proves 3 A. 12 Pole.

Any Parallelogram or long square propounded, whose dimension is required, multiply the length by the breadth, the product answers your desire: As for example in Decimals, the figure to be mea­sured is A.B.C.D. in length B.C. or A.D. 60 P. [Page 129] 10 ½ F. in breadth 45 perches 8 feet and 3 inches, what is the Area or superficial content of this ground? 160 square perches makes one Acre, which contains 4 Roods, and one of them 40 Pole; now from the dimension of this field, in the se­venth table of Decimals look 10 ½ feet, that is 21 half feet, whose Decimal is 6364, to this prefix the integers given as 60 Pole, which number will stand thus, 60.6364. and 45 perches 8 feet and 3 inches, that is ½ a rod, will be 5 for the half pole, so the multiplier is 45.5, the product of these is 2758.95620, which decimal fraction being very near an unite, the integer I make 2759 square per­ches, which divided by 160 pole, the quotient will be 17 acres and 39 square perches, the Area or su­perficial measure of the Field required. This Proposition in Decimals is usefull for Survey­ers.


Reduction of any squared Superficies from a grea­ter unto a less, and the contrary, where the custome of severall Countreys allowes of various measures.

The Thorem.

The Area or superficial content of any figure is in proportion unto a greater or lesser quantity, as are the squares made of those measures by which the figure was measured.

In the last Probleme there was 80 square yards [Page 130] of Arras hangings according to the Flemish mea­sure, which hath proportion to the English Stan­dard, as 3 is to 4, whose squares are 9 and 16, and being they were in the lesser measure, multiply 80 by 9, the product is 720, which divided by 16, the quotient will be 45, the true number of yards ac­cording to London measure, as was required.

In the Land measure there was last found 17 acres 39 pole, which admit according to the Sta­tute, the length of a perch was to be 16 ½ feet, and it is required to know the content of that field where the pole is but 15 feet long: these mea­sures in half feet will be as 33 is to 30, which re­duced is as 11 to 10, the squares of these are 121 100, the Area found was 17 A. 39 P. and is in the least denomination 2759 perches, which multiplied by 121 produceth 333839, and divi­ded by 100 is 3338, rejecting the fraction, being less then halfe a pole, and divide 3338 by 160, the quotient will prove 20, the remainder 138 P. di­vided by 40 will be 3 R. and 18 P. remaining; so the field of 17 A. 39 P. will prove in the lesser measure 20 acres, 3 rood and 18 pole, the proposi­tion solved in the Parallelogram A B C D, inclu­ding the woody and marish ground.


The making and dividing of Rules in proportional parts, whereby the superficies of any right angled figure may be conveniently measured with more brevity by instrument, yet with less exactness then by Arithme­tick.

The Theorem.

With the breadth of any rectangled figure given, di­vide the square inches contained in a foot, the quoti­ent and fraction will shew the inches and parts of the figures length which shall be equall to a square foot.

The Carpenters Rule for measuring of board and timber is commonly in length 2 feet, a thing neces­sary, but of no necessity whether longer or short­er, for this length will contain a foot of board, al­though but 6 in. b [...]oad, and what the length of the Ruler cannot comprehend, is usually termed under measure, with which I will begin. The side of a foot square is divided into 12 equal parts, called inches, the quadrat of 12 is 144, the number of square inches contained in a foot, and if it were demanded what length shall be required at 1 inch broad to be equal unto it (being an unite is divider) the answer will be 144 inches, that is in length 12 feet; if the breadth were 1 ½ inch, with which (according to the last Theorem) divide 144 the quotient will be 96 inches, that is in length 8 foot, at 2 inches broad 72 inches or 6 feet in length, at 2 ½ broad 4 F. 9 [...]/ [...] inches, at 3 inches in breadth 4 feet in length, and so proceed in the under mea­sure by half inches if you please, untill you come at 6 inches, with which divide 144, the quotient will be 24 inches, or 2 f. in length: the board measure being now upon the two foot Rule, containing 24 inches, and each inch usually divided into 4 equal parts, the board measure commonly proceeds [Page 132] also by quarters of an inch, so 144 divided by 6 ¼, in the quotient will be 23 1/25 inches in length; then for 6 ½ inches take in length upon the Ru­ler 22 2/13 inches; at 6 ¾ take 21 ⅓ inches, at 7 you will find 30 4/7 inches, and thus proceeding in quar­ters to 8 inches, which will require 1 ½ foot or 18 inches in length, and 9 broad 16 inches, at 10 broad 14 ⅖ inches, at 11 inches broad 13 1/11 inches, and 12 inches is the side of a foot square; from hence ascending, the square exceeding 12 inches the length will lessen, but thus proceed by quar­ters to 24 inches, from thence to 3 feet broad by half inches, and after that by whole inches onely, the difference growing scarcely sensible, and how­soever not considerable in things of this nature, for if they should be continued to 4 feet, the differ­ence betwixt 47 and 48 inches in this square mea­sure will be but 3/47 parts of an inch; these propor­tionals found, you may inscribe them upon a Ru­ler, with figures to them, and so made ready and apt for common use, if exactnesse be requi­red, make use of the Problemes delivered you be­fore.

Yards are divided after the same manner, in their proportional squares to any breadth assign'd, but usually such measures are taken in feet, one F. being the least in breadth that is commonly measured, 9 feet making a yard square, 3 being the side, & fre­quently without any under measure, beginning at 3 feet for the breadth for any such superficies to be measured, from thence proceeding by inches with their quarters to 10 feet in breadth, and more if need require: the side of this square contains 3 [Page 133] feet, that is 36 inches, whose quadrat is 1296 square inches, that divided by 48 (which is 4 feet) the quotient will be 27 inches, that is 2 feet 3 in­ches in length equal to a yard square; 5 feet broad requires 21 ⅗ inches; 6 feet or 72 inches must have 18 inches in length, 7 feet broad 15 [...]/7 8 feet broad 13 [...]/2 inches in length, 9 feet will have 12 inches in length and a long square 10 feet in breadth, every 10 ⅘ in length will be equal unto a yard square; and according to these dimensions, having found the parts in length answering to the feet in breadth from 3 unto 10 F. by the parts found you may inscribe them upon a Rule 36 in. in length, then find the quarters in the same manner to place between the feet and inches. The pole for Land-measures is onely divided into equal parts, is quar­ters, &c. and so likewise the chains, distinguished usually with brass rings, and those again by tenns, both ready, exact, and of excellent use, especially in Decimal Arithmetick.



To find the Area of the least Quadrangle, or square figure that can comprehend the circumference of any Circle propounded.

The Theorem.

The Diameter of any Circle squared makes each side a Tangent to the Peripheria, or circumference thereof.

A Demonstration.
Definitions and terms.

A Circle is a Geometrical Figure comprehended [Page 135] with one line, as E F G H E, termed the Periphe­ria or Circumference, the part contained (as in other figures) is usually called the Area, in the middle of which there is a point, denominated the center, as at 14; from whence all right lines drawn to the Circumference are equal, and infi­nite, and if any one be terminated at both ends with the Circumference, it is called the Diame­ter, as the line E G, 14; whose square is 196, for the content of the Quadrangle A B C D, each side being a Tangent, so named from touching, and not intersecting the circle, as in E F G H, being the least square that can be made containing the circle: which in this Probleme is the thing required.


The diameter or circumference of any Circle be­ing known, to find the greatest circumscribed Qua­drangle, or square made within that Circle propounded.

The Theoreme.

The quadrat root extracted from half the square made of the Diameter shall be the side unto the grea­test Quadrangle that can be circumscribed by that circle.

An exact proportion betwixt the Diameter and the Circle was never yet discovered unto man, his knowledge therein confined within a small cir­cumference of his own imagination; but as for [Page 136] circles within our capacities accommodated to hu­mane use, the proportions are usually these, viz. as 7 is to 22, or as 71 unto 223, so will the Dia­meter of any circle be in proportion to the cicum­ference of it, the last is most exact, but the first most in use, as in this, the Diameter E G being 14, the circumference of the circle will contain 44 of those equal parts, so the one being known the o­ther mey be found wonderful near the truth; now as for this Probleme draw a line, or suppose one drawn from E and G to F, these sides are equal by construction, and by the 11 and 28 Proposit. Trigon. lib. 1. will inclose a triangle, right angled at F. and by this second Probleme, the subtendant side E G squared will in quantity contain the squares of the two equal sides, and consequently half the square of E G 196, that is 98, must be e­qual to the square of F G, whose quadrat root ex­tracted in tenths, lib. 2. parag. 1. examp. 5. Arith. there will appear 9 399/1000, for the side of the greatest inscribed Quadrangle, the content of the whole square is 98 as before.


To find the nearest quadrature of a Circle, that is such a square, whose superficial content shall without sensible errour represent the Area of the Circles Peri­pheria.

Three Theoremes.

A squared Diameter multiplied by 11, and the product divided by 14, the quotient is the vulgar A­rea: or thus, the semidiameter multiplied by half the circumference is the supposed quadrature, or the cir­cumference squar'd and divided by 12 4/7 will be equal unto the superficial content of the given circle: these 3 do erre, and yet agree in one.

1. In the last demonstration E F G H is a circle propounded, whose superficies is required, or the nearest square in content unto it; the Diameter E G 14 squared is 196, which multiplied by 11 produceth 2156, and divided by 14 the quotient will be 154, the superficial content required of the Quadrangle I K L M, the side of which square is the root of 154, that is 12 ⅖ I K.

II. For the second Theorem I take again the same circle, the half of which circumference is 22 of such equal parts in which the semidiameter was found 7, which if multiplied by 22 wil produce 154 for the superficial square of that circle, not exactly true but wonderfully near, as by the former rule, and the root extracted in centesms is 12 41/100 very near.

III. According to the third Theorem of this Pro­blem, in the former figure admit the circumference onely known in this 44, w [...]ich squared is 1936, [Page 138] and if divided by 12 4/7 that is [...]8/7, the quotient will be 13552/88 or 154, as before; thus diversity of wayes confirms your work upon a good foundation, al­though an exact proportion betwixt the Diameter and Circumference is inextricable to Art, but real in Nature, and conspicuous to Man, although he cannot find it out, but leaving those that seek it, while I shew you the use of these last Problemes; and that you may find the Diameter or Circumfe­rence mutually by the other proportion, if requi­red, observe as 71 is unto 223, then if 14 were the Diameter multiplied by 223 and that product di­vided by 71, the quotient will be 43 69/71 for the Circumference; which if it had been 44, the Dia­meter would be 14 2/223.

A Treatise of Solids.

All solid bodies usually measured, are divided into 5 Species, viz. Cylinders, Squares, Pyramids, Cones, and Segments of the two last, the forms of which fi­gures I here present unto your view, as an ocular de­demonstration.

Definition of these figures, which in their several species are here propounded, and their dimensions required.

Solid bodies to be measured are considered in ge­neral, whether they be Circular, Right or Oblique angled; and these particularly in respect of each superficies one to another, or in, relation to their sides and bases, and most of them comprehended by some one of these 5 species.

I. Cylinders are bodies long and round, equal at either end, right angled at their bases with their sides, whose length and circumference is contained under one superficies, as is the figure A B C D.

II. Squared or rectangled Solids are all such bo­dies, whose sides are parallels one to another, and right angled with the basis at either end, as the fi­gure E F. G H. I K L.

III. A Pyramid hath but one basis, which is usu­ally right angled in the 4 sides, the foot alwayes acute-angled with each superficies, and terminated at the other end in puncto, as the figure M R S T.

IV. A Cone hath but one base, and that round, the other end is terminated in a point, as was the former, and the length is contained under one su­perficies, as is the figure V W X Y Z.

V. Segments are parts of either of the two last, the lesser end being cut off, so making 2 square or 2 round unequal bases, one acute angled with the side, the other obtuse, as the figures N O R S T, or P R, or W X Y Z, &c.


To finde the solid content of bodies that have two bases, and those equal at either end, the distance be­twixt them or the length of which body is measured in a right line.

The Theorem.

All bodies whose length is a straight line, right angled with either basis, the superficial content multi­plied by the length (in the same denomination) will produce the solid content in inches, feet, yards, &c. as it shall be required.

First for the Cylinder A B C, whose length A C is supposed 30 feet, the Diameter A B or C D 3 ½ feet, that is 7 half feet; by the last Probleme you will find 38 ½ which divided by 4 (as in lib. 1. pa­rag. 5.) the quotient will be 9 ⅝ or 77/8 square feet for the basis, which multiplied into the length 30 feet, the product will be 288 ¾ feet, the solid con­tent of that Cylinder, as in the figure does ap­pear.

If this round and long body were a tree with the bark taken off, and intended for board, slit work or building timber; in all such cases (according to common custome) a fourth part of the cir­cumference is taken for the square of all such timber, called Girt Measure, which square multiplied by it self, and that product in the [Page 142] length (of the same denomination) will shew the totall content: As for example, admit the Cylin­der were the trunk or body of a tree thus to be measured be the former Probleme, the circumfe­rence will be found 22 half feet, that is 132 in­ches, the fourth part of which girt is 33 inches, whose square 1089 multiplied into the length, viz. 30 feet, that is in inches 360, the product will be then 392040, which divided by the cube of 12, the number of inches in a solid foot, viz. 1728, the quotient will be 226 1512/1728, or reduced to 226 ⅞ feet, the true content required according unto cu­stomary measure for timber to be squared.

If the bark be on, as in Ash, Elm, or any timber fell'd in the winter season, it is as the buyer and sel­ler can agree, or referr'd to custome, which in some places abating one inch in the square found, and for old Elms 1 ½ inch, in other places abating a tenth part of the solid content so measured, that is, allowing 1 foot in 10. of these two wayes both are indifferent in timber, that is 17, 18, 19, or 20 inches square, but in small timber an inch abated in the girt is too great an allowance, and too little when the timber is very great; but here I will not prescribe you either way, for a foot allowance in 10 hath as great an errour as the other, but contrary to the former, when one is too little, the other is too much; so I will write no more of this but caveat emptor.

The measuring of square Timber.

Timber or stone cut four square, the sides are pa­rallels one to another, as the figure E F and I K, which here suppose 3 feet, the other two sides as H I or G K 2 feet, their square or basis is 6 feet, as H I G K, which multiplied into E H the length that product will be 180, and so many cubical feet this squared piece contains; but here observe, that according to girt measure the 4 sides make 10 feet ¼ of that is 2 ½ feet for the common square, which is apparently false, custome herein exceeding the truth, and will prove 187 ½ feet, which is too much 7 ½ F in this squared piece of timber.


The dimension of Pyramids and Cones, either in Timber or Stone, and to finde the solid contents of ei­ther species in inches, feet, or yards, &c.

The Theorem.

The magnitude or solid content of these figures is found by multiplying the superficial basis of either, in a third part of the length.

The Pyramid (whose dimension is here required) admit represented by the figure M R S T, the side of the basis 3, whose square is 9, the Pyramid in length 30 of the same measure, the third part of it [Page 144] is 10, which multiplied by 9 (the superficiall basis) the product will be 90, for the solid content re­quired.

If the solid content of M P Q were desired, the square at P or Q the basis is 4, the side being 2, which multiplied by 6 ⅔ being a third part of the length M P or M Q 20, the product of 4 and 20/3 is 26 ⅔ the solid content required: if these dimensi­ons were in yards, it would contain 26 such cubes and 18 feet; or if found in feet, then 26 F. and 1152 inches, as in lib. 2. pag. 154. Arithmetick may be proved.

The little Pyramid M N or M O is but 1 yard or 1 foot at base, 10 times that is the length, one third part of it, or 10/3, the product shews the con­tent to be 3 ⅓, that is in cubicall yards 3 and 9 feet; if the dimensions were in feet, the solid content would have been 3 feet and 576 cubical inches, the thing required.

All Cones are measured as the Pyramids are: as for example, in the figure V Y or V Z the Dia­meter at the base Y Z is 3, the superficial content of that circle, by the 11 Probleme will be found 7 1/14 or 99/14 which multiplied by 10 (one third part of the length) the product proves 990/14 or 70 5/7 the solid content of the Cone in cubical inches, feet, or yards, according to the parts, by which it was mea­sured.

If the solid content of the lesser Cone V X had been required, whose length is 20, the diam. at X the base is 2, and by the 11 Probleme the superficies of it is 3 1/7 or 22/7 which multiply by 20 the height, produceth 440/7 or 62 6/7 the content in cubical parts [Page 145] of 3 times the Cone; the third part of 62 6/7 is 20 20/21 the true dimension of the figure V X.

To find the lesser Cone V W, the diameter at the base is 1, the square 11/14, which multiplied by 10/3 the length, the product will be 110/42 or 55/21, that is 2 13/21 the content of the Cone in cubical pars required.


The dimension of all Segments in tapering Timber or Stone, &c. as they are the parts of solid Pyramids and Cones.

The Theorem.

Unto the squares of the two extreames or bases, adde the Geometrical mean square, which summe multiply bypart of the height, orof the totall by the height, the product will be the Segments solid content requi­red.

Admit the solid content of the Segment P Q R S T were required (which is part of the Pyramid M T as in the figure) the squares at the 2 ends are 4 and 9, their products 36, the square root of it is 6, for the Geometrical mean square, the summe of these 3 squares (viz. 4, 6, 9,) is 19. which multiplied by ⅓ part of the length, that is by 1 [...]/3, the product will be 290/3 or 63 ⅓, the solid content of that Seg­ment.

To find the Segment N O P Q, the superficial squares of the 2 bases are 4 and 1, their products 4, the square root 2, which 3 number, viz. 4, 1, and 2, [Page 146] added together makes 7, and multiplied by 10/3 (viz. N O P Q by construction) the product will be [...]0/3 or 23 ⅓, the true content of that Segment, and the summe of these two, viz. 63 ⅓ and 23 ½ is 86 [...]/ [...], to which if you adde the little Pyramid found by the last Probleme 3 ⅓ the totall of this with the 2 Segments compleats the solid content of the whole Pyramid M R S T 90, as before, which demonstrates all the several dimensions to be true, in the same manner the Segments of Cones are measured, having first found the squares at either end as in Prob. 11. so to the ingenious Artist no more examples will be required, yet being a thing in con­troversie, and not well understood by mechanicall men, for ampler satisfaction I will explain it with one demonstration more, Segments being the most frequent form of all, and so more diligently to be observed.

An ocular Demonstration in measuring of all tapering timber, whether round or square.

The Pyramidal Segment here proposed for to be measured is A. whose length is 15 feet, the square at the greater basis is 9, and the lesser end 1 foot, as at A, and according to the last Probleme the mean square 3, the summe is 13, which multiply by [...]/ [...] part of the length in this by 5, there will be produced 65 feet, the true solid content required; [Page 148] which to prove, take the Segment A into pieces as B C and D, there would be 9 of them, and all of one length, but severall forms, viz. B a foot square taken from the middle of the Segment, then will there be 4 pieces like wedges a foot square at the base, and ending in a line at A, having no thick­ness, as the four corner pieces are perfect Pyra­mids, containing one foot square at the base, the other ending in a point, as D, each of whose di­mensions, according to the last Probleme, must be 5 cubicall feet, being the length is 15, and con­sequently 4 of these will contain 20 feet, and as for C, 2 such pieces turned end for end, will be equall to the figure B, containing 15 feet; then one of them is 7 ½ feet, and 4 of those will make 30, the totall of the 9 pieces in content is 65 cubical feet, equall as they are all together in the figure A, which is evidently proved, as was re­quired.

But this Segment (according to common practise) is measur'd in the middle) by taking the Arithmeticall mean, that is by adding the sides of the two squares together, and taking the half of that for the common square, as in this, 1 and 3 makes 4, the half 2, whose square 4 multiplied into the length, 15, the product will be 60 feet, for the content, according to custome, which is apparently erroneous, and 5 feet too little in this piece, as before was demonstrated; divers other errours (in measuring of solid bodies) are crept in for want of Art, and having got possession of igno­rant people, they plead prescription and custome [Page 149] of the place, whereas Custome cannot establish a Law upon a bad Title, and a false ground nor Er­rour prevail against Truth, nor Ignorance convince Reason, supported by Art upon Demonstration; but leaving the rough-hewn and cross-grain'd people to their own imaginations, although them­selves confess a profit by some trees, and a disad­vantage by others, but know not from whence, as in flat timber, which some call ill weighed; as for Cants, and multiangled figures, their bases may be measured by triangles according to the first Pro­bleme of this Section: which found, their con­tents will be discovered by some one species in the dimension of the 5 former figures, according to the precepts of Art. Yet I would not have any man for to exact upon the buyer, but wish him some advantage or allowance in every load of green timber, as in every 40 or 50 cubicall feet; and my reason is, because no green timber will hold measure when the bark is taken off, and some trees will shrink more then others, as I have found by experience, in a moneths time 2 feet in a load and more.

Here I have briefly delivered you the man­ner and custome in measuring most kindes of solid bodies, whereby to understand what you doe, yet such exactnesse is not alwayes requi­site in rough timber, especially where there is much to be measured, and therein to avoid confusion, mark the trees as you measure them with 1, 2, 3, &c. and enter them in a book with the year and day of the moneth, the owners [Page 150] name, and the field or wood wherein they grow: this done, make 4 columns, one for the number of trees, secondly for their lengths, in the third co­lumn their squares, and in the last their contents; by this means any tree will be quickly found, and if any mistake be you may correct it at your leisure; observing this course many abuses will be avoyded betwixt the buyer and seller, as in cutting any tree shorter, or altering their marks, &c. and will be ready for your own justification: and besides, it is necessary in some place of your book to enter the buyers name, with the conditions agreed upon for the price by the foot or load, with articles for mea­suring, as in girting any tree more then once, and whether in the buyers or the sellers choice so to do, also what allowance to be abated for bark, as in Elmes, Ashes, &c. and sometimes in Oaks the bark will not run; besides a limited time should be agreed upon how long after the fell the trees must be measured, and the ground cleared; such things as these do often make cavils, when not a­greed upon before; below the middle of any tree the buyer may girt it where he pleases, and this is general, divers other particular things there are for which I refer you to practise, and how the common Ruler is made for measuring of timber, observe this following Proposition.


The framing and dividing of the Carpen­ters Rule, whereby the content of squared solid Bodies (as Timber or Stone) may be disco­vered in cubicall feet.

The Theorem.

Divide the number of Inches contained in a Cubicall Foot, viz. 1728, by the square inches of any common Basis given, the Quo­tient shewes what length must be required in in­ches of that body to be equal unto a Cubicall Foot.

All Timber to be measured by this common Ruler, is supposed to have four equall and pa­rallel sides, or reduced unto it by girting the tree with a small line, and taking ¼ part or that for a common square. This done, and the Ru­ler divided into inches, and every inch into eight or tenne equall parts, begin first with the un­der measure, as one inch square will require 1728 in length, that is 144 feet, to make one [Page 152] cubicall foot; 2 inches hath 4 for the square with which divide 1728, the quotient will be 432 inches, or 36 feet in length to make one foot; 3 inches square will require 16 feet in length; 4 inches 9 feet, 5 inches squar'd is 25, with which divide 1728, the quotient will be 69 3/25 inches, that is 5 feet 9 3/25 inches for the length, at 6 inches the side of the square, that is 36, will have 4 feet in length: 7 inches must have 2 feet 11 13/49 inches in length to make one foot, at 8 inches square 2 feet 3 inches in length will be equall to one cubicall foot. Thus you may finde the under measure to each quarter of an inch, with Decimall fractions, if you please, as at 8 ¼ inches, by my former rules of fractions, the square will be 1089/16 with which divide 17280, the quotient will be 2 feet 1 inche and 4/10 or ⅖ very neare: and a tree 8 ½ inches square will require in length to make a foot 23 9/10 inches almost. Now having past the under measure, you may proceed in the same manner to 36 inches, or more if you please, but it is unnecessary, the encrease be­ing so little, as halfe inches not well to be distinguished; so in case a tree shall prove above three feet for the side of the square, I have prescribed rules in number how to measure it, or by the Ruler thus, Take half the square and so measure the tree according to the length, the quantity so found will be ¼ of the whole content, as in the Demon­stration, page 109 of my Naturall Arthme­tick. [Page 153] Thus having found all the parts from an inch unto 36 or 40 inches, you may make a table of them, or inscribe them on a Ruler, as you think good.




The dimension of round, concave and dry measures, as Pecks, Bushels, Strikes, Corn­hoops, &c.


THe Measures used in England of this kind are more various and uncertain then are the Weights; few Market Towns, Villages, or Farm [Page 156] Houses, but have bushels of severall capacities, whereas the Statute made at Winchester commands them a size of just 8 gallons: the modern Writers of this subject do affirm, that a Wine gallon (ac­cording to the Standard) filled with water, and then poured into a square or regular vessel, placed Ho­rizontily, hath been often measured, and found to conteine 231 cubical inches very near, yet perhaps intended for 230 ⅖, by reason that ancient Writers do affirm the proportion between the Wine & Beer gallon to be as 5 is unto 4, and so consequently a Beer gallon to hold 288 cubicall inches, which is ⅙ part of a solid foot; and it is very probable that the measures instituted by the wise and just prece­dent race of this Age, extracted their weights and measures as from a grain of Wheat, and thence proportionally derived from one another, as a pint of good Wheat, equall in weight to 1 lb Troy, and a bushell to weigh half a hundred gross, & something more, but leaving this discourse and not measuring their actions by imaginations onely, but find the content of this bushell in Wine measure, the depth of it being found 8 ⅛ inches, the diameter 17, whose superficiall square by the 11 Probleme will be dis­covered 227 1/14 inches, neglecting the fraction multiply this superficies by 8 ⅛ or 65/8, the product will be 14755/8, that is 1844 cubicall inches, which divided by 230 ⅖ or 1152/5, the quotient will be 8 gallons, for the capacity of this vessel in Wine mea­sure, as was required; and with the former fracti­on 1/14 more, it will prove 8 7/1000 gall. but when a bro­ken number proves considerable it must not be o­mitted, but in such a case as this reject it if you please.

This former Figure represents a Bushell, which was well approved of in the Countrey, although I cannot; for having measured it (as before) I filled it with a Wine quart, and found it to contain but 8 gallons Wine measure, whereas (according to Winchest. Stat.) it should be 8 Ale gallons, and one of them to contain 288 inches, as Mr. Windgate af­firms, M. Outhred, & that excellent Artist M. Briggs allows the content of an Ale gallon but 272 cubi­call inches, which is generally esteemed on, being sealed by the approbation of these 2 famous Geo­metricians, and equal to the Standard; yet I will not confine you to their authority, nor perswade you to let another measure your corn by their bushel, since measures are so various every where: the scope I here do aim at is to find the capacity in cubical inches in concave vessels; which found, ap­ply them as you please, or as the place admits.


Gauging of Vessels, by finding the capacities or quantities of liquid measures, or cubicall inches contained in them, from the least Rundlet to a Tunn, either of Wine or Beer.


Any Vessel of Wine or Beer may be thus mea­sured; if the Diameter at the Head and Bung be equall, it makes a perfect Cylinder; for the di­mension of which figure I refer you to the 12 Prob. and the last: but vessels of this kind are com­monly biggest in the middle; and from the bung to the head, or either end, they have circular sides, which if continued would end in a point, as the Cone does, and hath 2 bases, yet is no segment of those which are bounded with right lines, but ra­ther [Page 159] a Sphaerocide or Sphaeroides, which Sphaerall Segment may be thus measured. The length of this Butt or Pipe is 50 inches, the diameter at the bung 30, and at the head or either end 21 inches. This known, by the 11 Probleme find the superfi­ciall content at the head and bung, which in this will prove 346 ½ and 707 1/7 square inches, take ⅓ part of 364 ⅓, that is 693/6, and ⅔ of 707 1/7 will be 9900/21, both which reduced are 231/2 and 3300/7, adde these together, their summe is 3217/14, which multi­plied by 50 inches, the length of the vessel, that product wil be 410850/14, and reduced to 205435/7, which is 29346 3/7 inches. In this case you may reject the fraction, and divide 29346 by 231, the quotient will be 127 gall. and 9 cubical inches; or make the divisor or dividend a unite more as you see cause; or if more exactness and less trouble be desired, see 22 Axiom lib. 2. parag. 7. as for example, 205425 to be divided by 7 and that quotient by 230 ⅖ or 1152/5 the dividers multiplied will produce 8064/5, that is 1612 or 1613, with which divide 205425, the quotient will be 127 gallons, 1 quart and 1 pint ferè, the content of this pipe in Wine measure, which multiplied by 4 produceth 509 G. 2 Qu. and divided by 5 the quotient will be 101 G. 3 Q. 1 P. and ⅕, the content of this Butt in beer mea­sure. Such Propositions are exquisitely performed by the Decimall Tables.


With the Diameter of any Circle known to find the Circumference of it in proportional parts unto 100, 1000, or 10000, &c.

In all questions of [...] this kind, make choice of some proportion be­twixt the Diameter & Circumference, as in the 10 Probleme and first, as 7 to 22, unto 22 annex 3 or 4 ciphers, which divi­ded by 7, the quotient will be 31428, or unto 223 annex ciphers at pleasure, 71 must be then divisor, the quotient will be 31408, which proportionals may be made more numerous, if occasion requires; but first suppose 17 were a Diameter propounded, whose circumference is required in a Decimal fra­ction, the proportion will be as 10000 the suppo­sed Diameter is unto 17 the true Diameter, so will 31428, a supposed circumference, be proportio­nable to 53.4·276. which differs but little from the 10 or 11 Prob.


With the diameters of two circles known, and cir­cumference of the one to finde the circumference of the other, or a diameter with 2 circles given, to finde the other diameter.

The Theoreme.

Circumferences of all circles are in proportion one to another, as be their respective diameters.

Admit the diameters of two [...] given circles were 17 and 21, the circumference of the first (in a de­cimal fraction) is in proportion, as 7 to 22.53.43. the second number multiplied by the third will be 1122·03, which divided by 17, the quotient proves 66, the circumference of the second circle, which was required. If the circumferences of any two circles with one given to find the other, the manner of operation is the same, so it requires no example.


With the diameter and superficial content of one circle, to finde the superficies of another, whose diame­ter is known.

The Theorem.

All circles have proportion one another, as the su­perficial squares made of their diameters have.

As for example, Suppose the [...] Diameters propounded were 7 and 14, whose squares are 49 and 196 (their proportions as 1 to 4) the superficial content of the first circle is 38 ½, but as a decimal in the table it is 38.5, which multiplied by 196, the product is 7546.0, and di­vided by 49, the quotient will be 154, the superfici­es of that circle, whose Diameter was onely known, as by the 11 Probleme may be also proved.


The superficiall content of any two circles propoun­ded, with one of their diameters given to find the o­ther.

The former squares are here a­gain [...] propounded with one diame­ter known, whereby to find the other: in this example I take 14 for the diame­ter, the superficial square of whole circle is 154. the diameter squared is 196 for the second num­ber, and the superficial square of the other circle is 38 ½ or 77/2, which multiplied by 196 produceth 15092/ [...] or 7546, and divided by 154, the quotient [Page 163] will be 49, whose square root is 7 for the diame­ter required, as in the last Probleme.


To find the content or convex superficies of any Sphere or Globe, whose diameter or cicumference is found or propounded by 4 several wayes, according to Art.

1. By the Diameter or Circumference, find the Area or superficial Content of that Circle, accor­ding to the former Problemes; which multiplied by 4 produceth the convex superficies required: As for example, admit 7 were the Diameter of a Sphere, the nearest Quadrature of that circle is 38 ½, which suppose 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.

[Page 164]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.


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 [Page 165] 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.


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 [Page 167] 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.


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, [Page 170] 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.


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 [Page 171] 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 the thunder and lightning, from which good Lord deli­ver us. This tract I will leave, and return to such Propositions as may be exactly peformed by Arith­metick, and founded upon Demonstration.

Compendious Rules for marshalling of Souldi­ers in any rectangular form of battel, either in one body, or in several Squadrons or Re­giments.

Battels are considered in two several respects, one depending upon the number of men to be put into a Military array, the other reflects upon the ground, on which the Battalios are to be orde­red.

A square battel of men hath an equal number both in rank and file, yet the ground in such cases lon­ger on the file then upon the rank.

A square battel in respect of the ground hath the rank and file equal in length, yet the number of men in rank exceeding those in file.

In respect of the men to be drawn forth in bat­talio, it is either termed a square battel, or in pro­portion, as the men in rank to the number of those in file.


If a square battel of men be required of any number whatsoever, the Quadrat root extracted from the list, or number of Souldiers delivered in, shews the number to be marshalled either in rank or file: As for example, a Serjeant Major delivers [Page 173] in a list of 22500 souldiers to be ordered in a square battel of men, the quadrat root of that number is 150, and so many must there be placed in rank, and so many likewise in file, lib. 2. parag 1. examp. 2. Arith.


If the difference of the men in rank to those in file should be in any proportion required, observe these Rules.


As the term which is given for men in file

Shall be to the term propounded for the rank,

So will the number marshalled in this Array

Be in proportion to the root, or men in rank.


As the term propounded for men in rank

Shall be unto the term which is for the file,

So will the whole number of souldiers marshalled

Be in proportion to the square root for those in file.

As for example, [...] 20184 souldiers are to be ordered in battel of array, & in such propor­tion between the rank and file, as 8 to 3, that is as 8 men in rank for 3 in file therefore 20184 (the number of souldiers) [Page 174] multiplied by 8 and divided by 3, the quotient will be 53824, the quadrat root of it will be 232, as in the first table, for the number of men to be placed in rank, the number for the file is found, if you di­vide 20184; by 232 the quotient will be 87, or by the second rule to find the men in file; as 8 the term for the rank unto 20184, the number of soul­diers, so will 3 the term for the file be in a direct proportion unto 7569, the quadrat root will be 87 for the number of men in file, according to the se­cond table in the margent.


To marshal in battalio any number of Souldiers, when there is a double proportion stated, as in respect of the men and ground both for the rank and file.


As the product of the two terms for the Rank

Shall be in proportion to the number of Souldiers,

So will the product of the two for the File

Be to a fourth number, whose square root is the File.

For the illustration of [...] this Proposition, sup­pose the number of sol­diers to be marshalled near 41160 in this or­der and proportion, viz. as for 3 in rank, 7 in file, and in respect of the ground as 2 is in propor­tion to 5; the products of these terms are 6 and 35. then say as 6 is to 35, so will 41160 be unto 240100, whose square root will be 490, as in the first table, with which divide the list of souldiers given, viz, 41160, the quotient will be 84, the true number of men both in rank and file, or by the second table, as 35 is to 6, so will 41160 be in proportion to 7056, the root 84; or with this di­vide the list of souldiers, the quotient will be 490, as before, and so in all questions of this kind, by the rank found you may find the file and the con­trary.


If an Army were drawn out in their particular Re­giments, and those again divided into several squa­drons with their depth and proportion both in rank and file.

This Proposition (although of most use) depends upon the former; for having the number of Regi­ments, or lift of the army, they may be reduced into little squadrons, as the Maj. Gen. shall think fit, and then marshal those according to order in what proportion shall be required, betwixt the rank [Page 176] and file, by one of the 3 last Propositions, of which I have given you examples, not according to custom, or the Military Discipline practised in any place, but whereby you may solve any question of this kind, and not as precedents, but rules onely; for the Foot squadrons 10 deep is the most that I have heard of, the usuall custom in Europe is 6 deep for the Foot and 3 for the Horse, when they charge the Enemy.


For the incamping of Souldiers in their severall quarters.

For a quartering of Souldiers in the field, it is performed by the common rule of Three; as for example, suppose a Regiment of 1000 men may be quartered in a square of ground containing 20 per­ches, what shall the side of a square be to lodge a greater or lesser number; the proportion will be, as 1000 to 400 perches, so shall any number of soul­diers be to a proportional square of ground, whose quadrat root is the side required: and for example, admit the number of souldiers were 24000, then say as 1000 men is to 400 the square of 20 pole, so 24000 men wil be in proportion to 9600, the quad. root of it in a decimal fraction is 97 [...]/10 perches, the side of a square that will incamp those men accor­ding to the proportion given: but here are sundry occurrences to be consulted on, which must be re­ferred to the experienced Master de Campo to mar­shal up together, as in respect of the enemy, the [Page 177] Campanio, the advantage of ground, the securing of passages; and multitudes of other things to be considered, in preserving the Army so well as when ingaged in fight, by reserves, or how to draw off and make retreats, &c. depending more upon the practise then any Theory, or prescription of Rules.


The perpendicular height of any Tower or other place being given, to find at any distance (appointed from the basis thereof) how long any scaling ladder or rope extended must be to reach the top or summity of it.

According to the state of this question, the rope or ladder will include a right-angled triangle, and by the second Probleme of this book, the quadrat root extracted from the summe of the squares made of the two containing sides will be equal to the Hypothenusal, which is the ladder or length of the rope: as for example, admit there were a Turret in height 45 feet, there was a Moat before it in breadth 22 feet, the square of 45 is 2025, and the square of 22 is 484, the summe of these squares is 2509, the quadrat root of it is 50 feet for the length of the ladder or rope that will reach unto the summity or top of it, if the remainder had been considerable, you might have extracted the root with a fraction, as in lib. 2. parag. 1. examp. 4 or 5. Arith. but some (where ignorance hath got the up­per [Page 178] hand of their reason) will say (peradventure) what care they for this; give them rope enough; and so say I with all my heart.


To find the height of an accessible Fort, Turret, or any other place, by a common square, or with two sticks of equal length artificial joyn'd together at right angles.


Admit the height required were the Tower C D, I move my station from F towards D, holding the triangle or square parallel with the ground-line and perpendicular by help of a plummet, as at K, where by both ends of the little square I behold the Towers summity, as at C. Now by the 19 Proposi­tion of my Geometry, A B must be equal to B C, and A B or L D is found by measure 48 feet, the t [...]ue height of B C, to which adde B D or A L (the [Page 179] height of the square above ground) viz. 3 feet, the summe 51 feet, for the altitude of C above the Ho­rizontal plain F D, the proposition answered.


To finde the distance unto any Fort or place, al­though not accessible, yet discovered by this square or triangle.

Erect a staff perpendicular, whose height is exactly known, as in the last Scheme E G, which admit 6 feet, or 72 inches; upon the top of it cut a notch, so that the square may fall down in it something straight, yet so as to turn at E. suppose the distance required were G D, place your eye at E, then turn the square upwards or downwards, un­till by the edge of it you see the basis of the Tow­er, or place at D. the square being fixt, look down from E to F. at which place a mark upon the ground, and measure the distance F G, which is he [...]e 8 inches: here you have 2 equiangled trian­gles, viz. G E F, and G E D, and by the 19 pr [...] ­position of my Geometry the sides are proportio­nal: now admit this little triangle were delinea­ted in the greater, as G H L, then is G L equal to G E, and G H to G F. thus are they in the rule of proportion, as G H 8 inches is to G L 72 inches, so will E G 72 be in proportion unto G D 648 inches or 54 feet, the true distance required.


To finde the height of any place approachable by the shadow which it makes, with the help of a Pike erected perpendicular to the horizontall plane, or by any Tur­ret, whose height is directly known, or by the height of any Tower, to finde the distance, though not approa­chable.


The height of the Tower A B is required, to be found by the shadow which it makes upon the Ho­rizontal place, as in this figure; suppose B D by measure found to be 12 per 6 3/10 in. upon the same horizontall plane, I measure the shadow of some other body, or erect a Pike perpendicular, as C D, whose height above ground is 7 feet, and the length of the shadow which it makes extends it self from [Page 181] D to E, by measure 12 feet 3 ⅓ inches: this known, the proportion is, as E D 12 feet 3 ⅗ inches is to C D 7 feet, so the shadow B D 198 feet 6 [...]/10 inches unto 112. 98 for the height of the Tower A B, which caused the shadow, that is 113 feet 3 in­ches and more, much exactness is required (in que­stions of this nature) or else little truth to be expe­cted, and shadows commonly falling in broken parts, which made me herein use the Decimals, yet with more exactness performed by Natural Arith­metick, and vulgar fractions, and so found 112 F. 11 inches 28/100, if the height A B had been known 113 feet, and the distance or extent of the shadow B D required, the proportion would have been, viz. as C D 7 feet to E D 12.3, so will A B 113 feet be unto 198 feet 5 4/7, that is 198 feet 6 inches and [...]/7 for B D, the distance required, which is very near the truth.


To discover the altitude of an accessible place by a mirrour or looking-glass, or by a Towers height known to find the distance unto it.

Let the position of your Glass or Mirrour be ho­rizontally plac'd at some convenient distance; from thence go backward into a direct line, untill you can descry in the glass the top of the Tower, or object whose height is required; then will the di­stance from your body to that part of the glass (where the summity of the Turret was represented) be in proportion to the distance from the glass to the [...]er [...]endicula [...] basis of the Tower or Sconce, as [Page 182] the height of your eye is to the perpendicular height required; for by the Optick Science it is an apparent Maxime, that the angles of Incedence and Reflection are equal, as A D B, and F D E, and your body being parallel with the Tower, the Ra­dius of your sight incloseth a triangle, equiangled with that of the Turrets shadow, as by the 8, 9, or 10 Proposition of my Geometry, and consequently by the 19 proposition of the same book those tri­angles are proportional in all their sides; this is so visible that it needs no explanation, if they can see themselves from their shadows, or shall ever be­hold my Trigonometry, to which I refer them for 2 more ample satisfaction; and this to their im­partiall and judicious censures, yet wishing a legal trial to answer unto my charge (if there shall be any fomented) in the mean time, hopes of a can­did construction from a serene verdict free from all obstructions of malice to obtenebrate my intenti­ons, bids me with comfort to proceed.


A Captain of a Castle expecting to be beleagured, makes good his out-works, and having fortified those best where he conceived most danger of be­ing stormed; he over-looks the inventory of his Magazine, and takes a list of his Souldiers, with the supernumerary persons, in all 800. by which he findes his provision of victuals good but for 3 moneths & 3 weeks, that is 105 dayes: having more [Page 183] men then were necessary, and expecting no relief under 6 moneths, or 168 dayes, the question is' how many men must be dismiss'd this fort (before the enemies approach) whereby the same victuals might last the just time required?

The Solution.

The rule thus stated, accor­ding [...] to lib. 2. parag. 8. Can. 9. Arith. in a reverss'd proporti­on, viz. as the provision of victuals for 105 dayes allowed for 800 men, what number will 168 dayes require, allowed in the same proportion, which according to the rule, will prove 500 men, as in the operation of the margent is made evident, and consequently there must be 300 ment dismiss'd of the supernumeraries, [...]nd Souldiers not able to perform their duties, or of those least serviceable to defend the works.


The Castellain commanded the Master of the great Artillary (or chief Gunner) to render a strict account of all the guns (mounted upon this Fort-royal) whether offensive or defensive, with the dia­meters of each bullet belonging to every piece of Ordnance, with the weight of the said bullet, and quantity of powder; also the distances in Geome­tricall paces, that each piece will convey the shot, so laden, both at point-blank, and at the utmost randome; which accordingly was thus delive­red in.

The Table or Inventory.
The number of GunsThe names of this Ar­tillaryEach bullets diame­terEvery bullets weightThe due charge of pow­der.The distan­ces in paces at pointblank and random
10Canon748 15/6426 lb340 & 1600
10Dem. can.630 ⅜18 lb350 & 1700
8Culvering517 37/6415 lb420 & 2100
8Dem. culv.4 inch.9 lb8 lb320 & 1600
6Sakers3 ½6 15/5125 lb300 & 1500
6Minions33 51/643 ½ lb280 & 1400
4Faulcons2 ½2 101/5122 ¼ lb260 & 1200
4Faulconets21 ⅛1 ½ lb220 & 1000


There are in this Fort 56 pieces of great Artilla­ry, as are specified in the Table, viz, the whole Canon hath a bullet of 7 inches diameter, in weight 48 lb and 4 ounces almost; to which there is al­lowed for every shot 26 lb of powder: this Gun discharg'd will carry on the level-range 340 paces, and shot at random 1600. and note that all pieces for battery ought to be planted within ½ or ⅔ parts at most of the paces they carry point-blank; but as for our present purpose, the magazine of powder was found here 10 T. 11 C. 4 st. and 12 lb weight, and the question propounded is, whether this quan­tity of corn-powder will discharge the 10 whole Canons 20 times round, the 10 Demi-canons 30 times, the 8 Culverins 40 times, the 8 Demi-culv. 50 times, the 6 Sakers 60 times, the 6 Minions 70 times, the 4 Faulcons 80 times, and the 4 Faulco­nets 100 times.

The Solution.

Reduce first the gross weight of powder deliver­ed into pounds subtil, and you will find 21100 gross to be 23632, to which adde 4 st. and 12 lb, that is 68 lb, the total is 23700 lb.

3010Dem. Can.181805400
508Dem. culv.8643200
706Minions3 ½211470
804Faulcons2 ¼9720
1004Faulconets1 ½6600
45056Totals79 ¼69023190

In the first column stands the number of charges impos'd upon every Gun, in the second the num­ber of each piece, in the third are inscrib'd the Ord­nance, in the fourth each particular charge, in the fifth is placed the whole quantity of powder that charges all the guns of each sort, the sixth and last column contains the whole quantity of powder ac­cording to the number of their several charges, whose totall is 23190 lb.


The last Proposition was not judg'd convenient, being but 510 lb of powder remaining: upon which, by order there was deducted from the Ma­gazine 3000 lb, viz. for small shot, for Grana­does, for murdering shot (in case there should be any breaches made) for wast and priming powder, the query next stated was how many shot about [Page 187] the 20700 lb will make, which according to lib. 2. parag. 11. Arith. may be thus stated: The fifth column (in the last table) contains the quantity of powder that charges all this great Artillary once round about, whose total at the bottom of the same column is 690 lb for the first number, the magazine or whole stock of powder is the second number, viz. 20700, which in this may be total­ly divided by the first, that is by 690. so the first and second numbers are now 1 and 30. each par­ticular for every species is comprehended in the fifth column, to a proportional allowance, that each piece shall spend, being once discharged, and then the fourth proportional number found shall be the quantity that every kind shall spend at an equal number of shot to be made, whose total (if the operation be true) shall be equal to the second number in the rule, or the Ammunition delivered in for this purpose, as by the following rule is made conspicuous.

 260 7800
 180 5400
As 690 lb is to 20700, so120 3600
or reduced30 900
 21 630
As 1 in proportion to 30, so9 270
 6 180

By this it is made aparent the Canon must be allow'd 7800 weight of powder, whereof there are 10 in number, so each whole Canon must have 780 lb, which divided by its proper charge, viz. 26 lb, as in the fourth column and former table, the quotient will be 30 shot, again, for the 4 Faulcons there is allowed 270 lb, so for one of those guns 67 ½ lb, which divided by its allowance of powder the quo­tient will shew 30 charges; and so many shot eve­ry piece of Ordnance will make round with the al­lowance according to the last table. A Castle that is fortified both by is Nature and Art, provided with Ammunition, Mann'd, and victualled well, and all things necessary for a defensive War closely be­leaguered; if the men stand sound, and yet sur­render it to the enemy before 6 moneths being ex­pired, it will be conceived the souldiers are better fed then taught.

Ladles for guns are proportioned according to the bullets, the plate made plain at first, and in breadth ⅗ parts of the bullets circumference, the ⅖ abated, whereby to empty the Ladle in the Guns chamber.

Generall Rules and Observation, or a Contexture of various questions.

Iron bullets are proportioned to Lead, made in equal moulds, as 5 to 7, and iron to equall bullets of marble, 7 to 3, the proportioning of their weights is uncertain, when bullets of iron will dif­fer, though cast in the same mould, one metall be­ing more pory then another.

The Demi-culvering bullet 4 inches diameter, is generally received as a gage for the rest, whereby to find their weights or magnitudes: this bullet made of some iron, will be just 9 lb weight, and it is a medium almost betwixt the least and greatest sort of Guns upon carriages usually made, yet I have seen and measured one, the diameter of whose concave Cylinder was above 20 ¼ inches, the cube of the bullet 20 inches is 8000; then say as 64 is to 9 lb, so will 8000 be unto 1125 lb for the weight of such a bullet.

Gun-founders of brass pieces use an allay of cop­per and tinne, proportioned to every 100 lb weight of brass, but the mixture various; which you may find in any piece of Ordnance, having the true weight of the gun and the allay, as thus; sup­pose a Cannon to weigh 7000 lb subtile, and the allay for every 100 lb of brass 40 lb copper, and 10 lb tinne, then state your question in form, according to the rules of society, as in lib. 2. parag. 11. Arith. as thus:

 lb  lb
As 150 is to 7000, so100Brass 4666 ⅔
or reduced by 5040Copperunto1866 ⅔
As 3 shall be to 140, so10Tinne 466 ⅔
 150totals 7000

All Guns more fortified with metall on the one side then on the other, if discharged at a mark, the bullet will fall wide from the object, inclining to that side which is most fortified or thickest in me­tal: the reason (I conceive) is, that the thinnest part is soonest hot (by the agility of the fire) and so from thence dismisses the bullet with the greater force, or else in imitation of sulphurious Meteors fir'd in the wombs of clouds, break forth in their deliverance with amazement to mortals, and strikes most at that which is strongest, or most fortified to resist.

Two pieces equal in all things, but their length, and if charged and levelled alike, the longest will convey its bullet farthest; yet if discharged toge­ther at a mark within distance of either gun, the bullet from the shortest piece will be at the place first, or the object aimed at.

Three Cannons discharged

2 30
Facit 7800

twice spent 156 lb of powder, how much will 10 equal guns to them spend? if 30 times dis­charged with the same allow­ance, which stated, as in the margent, according to lib. 2. pa­rag. 10. quest. 3. Arith. or may be reduced to 1. 26. 300, or thus, 1. 156. 50. the fourth proportionall found will be 7800 lb.

Most guns will shoot at random 4 times so far and more then their level-range, and some of the great Artillary 5 times; the best random of a piece is held when elevated 22 or 23 degrees of the qua­drant above the horizontal plain.

Alwayes observe to keep your link, stock, match or fire, to lee-ward of the gun or powder.

An iron bullet will flie farther then one of lead, but the greatest batters most at 80 or 90 paces; and either of them with most force from a gunne a little elevated, then on the level range, although within distance, and the heavier bullet will raze a work the soonest.

No bullet from a gun, that is levelled and dis­charged, does move in a direct straight line, but cir­cular, ascending first with the violence of there, and over-shoots the mark within the level-range; and as the heat lessens it tends towards the seat of gravity, and at point-blank crosses the line of level, protracted from the center of its concave cylindar, which arch is greater accordingly as the gun is ele­vated from 1 to 45 degrees of the quadrant, and lesser if discharged below the level-range.

All guns, if over heated with often shooting, are apt to break; those perpetrated with cold and fro­sty weather are most subject to an eruption at the first shot; the reason is, that in all metal there is a radical humor, which connexes and keeps the parts together, and is made weak by being dilated with over-much heat, or contracted with too much cold, leaves the parts enervated, and each mem­ber of that body dissoluble, or easily discorporated, and the sooner by opposition of its contrary, the agile and penetrating fire invading the condensed cold.

Any bullet discharged from a gun does strike most violently against that which is hard, firm and strong to resist, and soonest deaded where it wants opposition, as being shot against wooll, sand, any soft earth or moveable object, and hath more vio­lence at reasonable distance then near the Cannons mouth which delivered it unto a convoy of the subtile Air; the greatest force of any bullet for battery, is generally conceived from ¼ to ½ of the level-range of that Piece which made the shot, and from [...]/2, the force of the bullet lessens in its raptile or violent motion.

The weight and content of Caskes for Powder.

A Barrel or empty Firken ought to weigh 12 lb, and should contain 100 lb of powder neat; so the weight of a Firken thus filled is 112 lb, that is 100 grosse, and 24 of such Firkens makes one last containing 2400 lb neat.

The common ingredients and quantities in making of Powder.

The ordinary Powder is composed of these 3 Simples, viz. to every lb of Salt-peter adde ¼ of Charcoal & ⅙ part of Sulphur: To these take any 3 proportional numbers at pleasure, according to the 15 Axiom, lib. 2. parag. 7. or 14 Arith. As for ex­ample, 60, 15, 10, or 12, 3, 2, the least without fractions is usually best, as the least trouble, and ad­mit one Last of Powder were the quantity to be made, as 2400 lb, the proportion will be thus:

lb12Peter1614 3/17
As 17 is to 2400—so3Coale423 [...]/17
 2Sul [...]hur282 6/17

As for the quality and goodnesse of Powder, ex­perience is the best tutor; yet as a common and general observation, good powder will be bright in colour, tart upon the tongue, and very salt in tast, apt to burn, and quick in being fired: the Brim­stone makes it apt to kindle, the cole continues the inflammation, by which the Salt-peter is resolv'd into a windy exhalation, and strives to dilate it self restrained in the concave of the gun, vents it self at the mouth of the Piece, being the easiest passage; but if the bullet be rusted in, or over charged, and cannot get out, it will force a passage through the weakest part, as subterranean Meteors do when [Page 194] much rarified, and restrained in the concaves of the solid earth.


If a barrel of powder will charge a Demiculve­rin 12 times, burning 8 lb at a discharge, how ma­ny shot wil a Last of powder make for a Canon that spends 26 lb at every charge?

This question is sol­ved, [...] as in lib. 2. parag. 10. quest 4. Arith. in the first rule; stand the quantities of Powder propounded, and the Shot made in the Demi­culverin in a proportion direct; the second is each charge of powder reverst, and by their products made direct, as against III. in the last it is reduced to 13. 6. and 192. these by the common rule of 3 will produce 88 8/13. so in a Last of powder there will be 88 shot good for discharging the Cannon, and the 8/13 is 16 lb of powder over, for pri [...]ing and waste, &c. the question answered, the thing r [...]qui­red.


There is a Rope 3 inches in compasse, and one 4 [...]imes so big is required: the greatnesse of these is [...]ccording to the squares made of their diame­ters, as in the Problemes of this book, their cir­cumferences [Page 195] being also in the same proportion; so the square of 3 is 9, which multiplied by 4 produ­ceth 36, the quadrat root of it is 6 inches, the cir­cumference of the Rope required.

PROPOSITION XIX. By knowing the weight of a fathom of any Rope, to finde the weight of another either greater or lesser.

A Rope in compasse 4 inches, and every fathom of it admit does weigh 3 lb, how much shall a Coy­ler Rope weigh that is 6 inches in circumference; which two circumferences, if multiplied by 7, they would retain the same proportion: and so likewise if those products were divided by 22, as in lib. 2. parag. 7. axiom 13. Arith. then institute the rule of Three, with the circumferences given and squared, viz. as 16 shall be to 3 lb weight for a fathom of that Rope, so will the greater square 36 be in pro­portion unto 6 ¾ lb, that is 6 lb and 12 ounces for the weight of each fathom of that Coyler rope, whose circumference was 6 inches, the thing requi­red. Many such propositions the Gunners do us [...], which for brevity I here omit, supposing these m [...]y suffice young practitioners, so with strong hopes, and a slight fortification, I will conclude this work.


A Mount or Plat-form is to be raised for battery, on which the great guns are to be mounted; the General commands the Captain of the Pyoners to draw a trench about it, as he and the Engineers should conceive convenient; which according to order was thus design'd: the Plat-form set out 4 square, 70 [...]aces on every side: at the line or verge of this Trench (where the labourers first break ground) 16 feet over, to be 10 feet broad at the bottom, and 8 feet deep; the turf to be orderly laid at the brim, and the earth digg'd out of the Trench disposed of within that, for a wall to raise the Ordnance, and defend the men within the Wo [...]ks; which wall is ordered to be made 21 feet at bottom, and 18 feet broad at the top. The query is, how high the wall will be made of the earth digg'd out? and how many cubical yards is in the said Trench? and what the labourers work may be worth if paid by the great, or task-work.

The breadth of this Trench at the brim is 16 feet, at the bottom 10, the summe 26 feet, the half 13, which multi [...]lied by 8 feet (the depth of the said Trench) the product will be 104 superficial square feet; the wall to be made is to be in thickness 18 and 21 feet, the Arithmetical medium 19 ½ or [...]/2, a [...] in lib. 2. parag. 5. theo [...]em 1. Arith. with which divide 104, the quotient will be 5 feet 4 inches, the true height of the wall required.

The square of this Platform is 72 Geometrical [...]aces, that is, 350 feet, and the 4 sides contains [Page 197] in extent 1400 feet, which multiplied by the square made of the Trenches breadth and depth, as before found 104 feet, the product will be 145600 cubical feet; at each corner of these Trenches there will be a Pyramidal Segment reverst with the greater end upwards, whose mean square is 13 feet, as is the Trench, the quadrat of it 169, which multiplied by 8 the depth, produceth 1352 cubical feet, 4 times that (for the 4 cor­ners) will be 5408. this added to the former summe 145600, the total will be 151008 cubi­cal feet, which divided by 27, the quotient proves 5592 cubical yards contained in the whole trench; which at 6 D the yard to dig and carry on to the works comes unto in money 139 L 16 ss, the true manner of measuring a Segment, and likewise the fraction in the last division was neglected, as unnecessary in these gross works. Each of these Segments contains 50 cubical yards of earth, which may raise a Rampire, Sconce, or Bulwark at each angle of the Platform 6 feet higher, 16 feet square at the bottom, an [...] 14 f [...]e [...] a [...] the top.


As for the marshalling and quartering of Souldi­ers, with sundry other Military Propositions, I have here instated proposals, and delivered Examples for speculation onely, and transferred the forme to the judgement of experienced Commanders; since most Propositions (depending on this Subject) are undeterminable, but according to the custome of the Country, the advantage of the Place, the num­ber of Horse or Foot, the Enemies condition, with multitudes of occurences intervening every day, & those circumspectly to be cons [...]derd by the field-Officers, or Council of war sitting upon this Tragick Scene, as Germany hath learned by sad experience under the Swords tuition this later age, whose Di­sci [...]les have been generally Separates, oppugnant in opinion, yet united and armed with factions have commenced War under specious colours to [Page 199] procure Peace, oppress'd the Truth to support Reli­gion, supprest Kings to establsh Monarchy, and by rude Anarchy, pretending to introduce Civility, with divers such zealous Paradoxes by an Hyperbo­lical Faith. But leaving all to God, whose De­crees are inscrutable, his Wisdome infallible, his Justice certain, his Mer [...]y without limit; Infinite and Omni [...]otent in all his works. To whom be all Honour, Praise and Glory world without end.


THE DEBITOR AND CREDITOR: OR A Perfect Method of keeping Merchants Accounts, after the Italian manner.

By Thomas Wilsford.

LONDON, Printed for Nath: Brook, at the Angel in Cornhill. 1659.

PRECEDENTS OF MERCHANTS ACCOUNTS, In form of DEBITOR & CREDITOR, According to the Italian manner, and the most Modern method Epitomiz'd.

THe efficient and final cause of keep­ing Merchants Accounts after this manner, is for sundry respects in Commerce and Trade, by experi­ence prov'd urgently necessary in steering an ample course of Traffique, yet waving all doubtful reckonings, and avoyding confusion in multiplicity of business, and diversity of affairs, of various natures, which a good form will pro­cure, and produce these effects, viz. The Owner or Cash-keeper may at any time, and upon all oc­casions, [Page 204] readily find out any contract, either by way of Barter or Money, present pay, time limited, or mixt; also any summe of money, Goods im­barqued, shipt off, returned, or remaining in their Ware-houses, with the quantities, qualities, and value of them; also all Receipts and Disbursments, whether charg'd or drawn upon their Friends, Fa­ctors, Correspondents Accounts, their own, or any Company trading by Sea or Land, with the ballan­cing of their Estates betwixt Debitor and Creditor, as what he owes, or is owing him, with all Bills, Bonds, Obligations, Debts or demands contracted on either side.

Any man that begins to drive a Trade or adven­ture a Stock into forreign parts by way of Traffique, or Commerce in multifacious Negotiation, ought to take an Inventory of his present and personall estate, whether it be in ready Money, Goods, Debts, Wares, or Remainers, attracted by any state, Bonds, Bills, Leases, or Reversions transferred unto him, or by transportation of a trade, from some other Merchant or deceased Friend; which In­ventory must be entred in form of Debitor and Creditor, according to the engagements of the Factors, Correspondents, Administrators or As­signs, inscribing the Creditors names, the summe, time, 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 [Page 206] 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 [Page 207] 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-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 [Page 208] 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, &c. as quotations to the Leagers, page and folio. Besides all this, 'tis 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 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 [Page 209] 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 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 com [...]rised by some Ac­countants [Page 210] 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, w [...]ite them, o [...] the Wares Debitors.

[Page 211]III. If a man delivers Wares, or payes money, Bills or Exchanges upon the account of another, that party (upon whose account tis 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 'twas 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.

[Page 212]X. A Factor that drawes an Echange upon the Merchant, Company, himself, or others; to the party or parties (u [...]on who [...]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 subsc [...]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, b [...]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, [Page 213] that party or parties (upon whose account 'tis re­ceived) mu [...]t be subscribed C [...]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, shi [...]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 Me [...]chant from his Factor or Resident receives Returns in money or merchan [...]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 [Page 214] 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
  • [Page 215]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 thing
  • 3 Those of whom we buy
  • 4 The Goods which are sold
  • 5 The parties which sell
  • 6 Goods wherewith we pay
  • 7 Those who are to re­ceive
  • 8 The party who insureth
  • 9 The insurance reckon­ing
  • 10 Goods sent or shipt off
  • 11 Goods on which is lost
  • 12 Profit and Losse.

The Title of the Journall.

Anno first January 1658. In LONDON. The forme of regulating a Journall page, with the marginall quotations specified, as thus.

The pages prepared according to th [...] Diaries former description, yet in multiplicity of affairs many do make two columns in the left margent, the first for to insert Debitor or Cre­ditor, the other with figures in refe­rence unto the Leagers page to shew where each party or parties, parcel or parcels stand charged or discharged.

And where any party or parcel is discharged, draw a line between the terms in form of a fraction, placing Debitor [...]bove the said line, and Cre­dito [...] beneath it, with the figures or numbers of the Leagers page; one shewing they are discharged, and the other where.

But as for this, the figures onely in most Jou [...]nals are conceived to b [...] sufficient directions, as in the follow­ing Diary our Journall shall be made conspicuous.

Here insert the year of our Lord. [...]he journall page.The Title of the Leager, Anno 1658. in LON­DON. The form of ruling the Leager. Cash Debitor.Where Creditor in the L [...]ager.LSD
16581First Jan. Creditor to stock for several Coyns of money.18000000
  Which signifies no more but the figure 1 in the second columne on the left hand points to you that Cash in the first page of the Journall is made Debitor, and the figure 1 in the first column on the right hand tells you that Cash has his Credi­tor entred in folio 1, viz. Stock is Creditor as may appear by the said questi­on in the said page of the Journall and page of the Leager the like, mutatis mutandis is to be obser­ved in the Creditors side of the Leager, will be conspicuous in the Lea­ger hereunto annexed.    

THE JOURNALL; Number A in LONDON. 1658.

Anno 1658. first Jan. in London.
  The form of inscribing Debitors and Cre­ditors in the Inventory.   
Gr [...]/ [...]CAsh Debitor to Stock 800 l for se­veral coyns of gold and silver re­maining, as by conclude of my former books appear, which amount to in Sterling mony to800  
  Goods or Merchandizes in the ware­house, or otherwise in my possession, and, are unsold.   
  [...]/1Fustians Debitor to Stock 226 l 13 s 4 d. for 200 Pieces resting unsold, which cost 22 s. 8 d. per piece226134
  [...]/1Spanish Tobacco Dr. to Stock 293 l 6 s 4 d. for ten Potacoo's remaining unso [...]d, weighing neat 880 poundat 6 s 8 d per pound, is293064
  [...]/1Colchester Sayes Debitor to stock 34 l 6 s 8 d. for 20 Pieces unsold, which cost 34 s per Piece3468
 2/1Couchaneal Debitor to Stock 230 l 11 s 3 d. for 14 C 3 qu. 14 po. neat at 15 l 10 s per C.230113
  Ships, Parts, Houses, Land, &c. Inventored.   
  [...]/1Ship the Sampson of London Debitor to stock 200 l for my [...]/8 part thereof, which cost me200  
  [...]/1House the Nags head at Rumford Dr. to stock 350 l for the principal, it cost me350  
  Money due upon Bond, Bill, or other agreement, insert thus.   
 3/1Abraham Bland debitor to stock 387 l 11 s. payable the last of this moneth, as appears by his Obligation dated the 5. of December last38711 
  [...]/1Thomas Goodman debitor to stock 82 l 3 s 4 d, as by his bill under his hand appears payable on demand8234
 3/1William Lane of Ipswich debito to stock 36 l 11 s 4 d being the rest of an old account due on demand36114
  Money due to others from us by bond, bill, or agreement.   
 ¼Stock debitor to Barnaby Clemens 300 l being so much due by my Obli­gation dated the 3. of November last, and payable the 5. of March next300  
 ¼Stock debitor to Thomas Spilman 36 l 11 s 4 d. by my bill payable on de­mand, for certaine houshold-stuff bought of him, the particulars appears by his bill36114
 ¼Stock debitor to John Maz'oon 305 l payable on demand305  
Anno 1658. 3 Jan. in London.
  The form of inserting Debitors and Gre­ditors in Traffiques continuace, and first of goods sold for ready mo­ney, secondly for time.   
 ½Cash debitor to Fustians 24 l 14 s. for 13 pieces sold to John Deport at 38 [...] per Piece2414 
 4/2John Thurrowgood of Chester debitor to Fustians 39 l 10 s for 20 Pieces sold 39 s per Piece, payable within 30 dayes3910 
  Jan. 15. 1658. Goods sold part for time, part for ready mony.   
 4/2John Benning debitor to Couchaneal 51 l 15 s for 3 C neat, at 17 l 5 s per cent. ½ at 6 moneths rest instant5115 
 ¼Cash debitor to Dito John 25 l 17 s 6 d. received in part this day25176
  Goods bought, paying present money.   
 5/1Lead debitor to Cash 204 l 11 s 3 d for 95 Pigs, weighing 13 tunne 12 C 3 qu. at 15 s per C.204113
  Wares bought not paying present money.   
 ¾Claret Wines debitor to Jane de Clare for 5 tunne at 12 l per tunne60  
Anno 1658. 15 Jan. in London.
 Commodities bought part for time, part to be paid ready money.   
5/5Sugars Debitor to James Wilson 54 l 7 s 4 d ½ for 10 hh. wai. gro. 42 C 3 qu. 11 pound tare, of each hh. 22 po. neat, 30 C 0 qu. 23 po. at 30 s per cent. all duties cleared, ⅓ to pay money ⅔ at a moneth547
5/1Dito James Debitor to Cash 18 l 2 s 5 d ½ for ⅓ paid in part182
 Jan. 19. 1658. Wares sold and delivered in Barter.   
5/5Edward Price Debitor to Sugars 12 l 12 s fot 2 hh. wad. net. 6 C at 42 s per hh. to receive for the same Pro­vince oyles in barter.1212 
6/5Province Oyles Debitor to Dito Ed­ward 9 l 3 s. for 1 Cask taken, con­tent in part in truck for Sugars0903 
Cash Debit. to Dito Edward 3 l 9 s. received in full satisfaction to cleare the said Truck39 
 Jan. 29. 1658. Moneys borrowed at interest.   
Cash Debitor to John Malthorse 300 l received of him upon interest300  
6/6Interest reckoning our Profit and Loss Debitor to Dito John 4 l 10 s, for 3 moneths allowance for 300 l at 6 per cent.410 
Anno 1658. 30 Jan. in London.
 Moneys borrowed to be paid upon de­mand, or otherwise.   
Cash Debitor to Simeon Peters 50 l borrowed of him and payable on de­mand50  
 Money let out at Interest.   
5/1Edward Price Debitor to Cash 100 l. delivered him at Interest100  
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.110 
 House-keeping charges entred.   
6/1Profit and Losse Debitor to Cash 50 l paid my servant for 3 moneths provision for house-keeping to end 25 March next50  
 Febr. 2. 1658. Moneys paid that are due, the time of payment being com [...].   
4/1Jane de Clare Debitor to Cash 60 l. paid him in full of all accounts60  
5/1Jam. Wilson Debitor to Cash 36 l 4 s 11 d. paid in full for his Sugars as by his Acquittance appears36411
 Febr. 9. 1658. Moneys received that are due, time of payment b [...]ing come.   
¼Cash Debitor to John T [...]urrowgood 39 l 10 s. received in full of all de­mands to this day3910 
 Moneys received (for goods sold at time before due) upon rebate.   
¼Cash Debitor to John Benning 24 l. Received in full24  
6/4Profit and Losse debitor to Dito John 1 l 17 s 6 d for payment before due1176
Anno 1658. 12 Febr. in London.
 Moneys gained by Exchange.   
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 is218−4
 To discharge a debt by Assignment.   
4/3Thomas Spilman debitor to William Lane for my Assignment, poid h [...]m in full of his debt3611−4
 Debt sold to another from whom it was not due.   
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 for50  
6/3Profit and loss debitor to Dito Tho­mas 32 l 3 s 4 d lost by the sale of his bill32−3−4
 Febr. 19. 1659. Part of a debt lost by a Bankrupt and the rest received.   
Cash debitor to Abraham Bland 259 l 7 s 4 d being but ⅔ Received in full of a debt of 387 l 11 s ⅔258−7−8
6/3Profit 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.   
7/2Voyage 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 account80  
7/2Dito Voyage consigned to Dito Hans debitor to Spanish Tobaco 440 l for so Pot [...]en's w [...]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.
 Charges for a voyage, or otherwise.   
7/1Dito voyage debitor to Cash 9 l 16 s for charges upon the Fustians and To­baco, for Fraight, Custom and Excise, &c.916 
 Goods ensured.   
7/1Dito voyage debitor to Cash 7 l 16 s for insurance of Dito Fustians and To­bacco, paid John Mazoone at 30 s per cent. is716 
 Feb. 22. 1658. Money received for fraight of a ships part.   
Cash debitor to Ship the Sampson of London, for fraight received of John Wright Master thereof, for my ½ share3538
 Money or goods given away to any person.   
7/2Profit and Losse debitor to Fustians 1 l 2 s 8 d for one piece given to A.B.   
6/1Profit and losse debitor to Cash 12 l given towards the relief of a fire at Enfield in the County of Middlesex128
 Gratuities received.   
Cash debitor to Profit and Losse for 200 l received for a Legacy given m [...] by A. M.12  
 Febr. 28. 1658. Commodities formerly shipt to another Countrey, and advice of the sale thereof.   
7/7Hans Butterbox at Amsterdam, my ac­count currant, debitor to voyage to Amsterdam 613 l 15 s 4 d. as appear [...] by his account sent me, and dated at Amsterdam, Novemb. 25. instant, be­ing the neat proceed of my goods sol [...] there613154
Anno 1658. 28 Febr. in London.
 Commodities received to sell for another mans account in Commission.   
7/1Hans 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:
For Fraight, at 1 s per qu.050000
For Custom, at 1 s 6 d per q.071000
For Excise, at 6 d per qu.021000
For Porterage, Literage and Cartage, at 6 d per qu.021000
For Meaters allowance001500
 Commission Goods sold.   
1/7Cash debitor to Hans Butterbox his account of Wheat for 100 quarters so [...]d to John Sutton Junior at 58 s per qu. is290  
 Provision for Commodities sold.   
 7/6Hans Butterbox his account of Wheat debitor to profit and losse for my pro­vision for the said Wheat at 12 d per l.1410 
 March 3. 1658. The proceed of commodities paid by bill of Exchange.   
8/ [...]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 deducted2575 
Anno 1658. 24. March in London.
 Commodities bought for Companies Accounts.   
8/8Tobacco in Company between John Mazoon and my self debitor 210 l fo 30 hh of Vi [...]ginia each ½, the whole a [...] 7 l per hh is210  
Cash debitor to John Mazoon his ac­count by me in Company for his ½ part received105  
 Commodities sold for Company Account.   
Cash debitor to Tobacco in Compa­ny between John Mazoon and my sel [...] each ½ for 30 hh sold to Henry Beak at [...]0 l per hh.300  
8/ [...]Tobacco in Company debi [...]or to John Mazoon his account by me in company 45 l for ½ advance45  
8/ [...]Tobacco in Company debitor to pro­fit and loss 45 l for my ½ of advanc [...] gain by the sale of the Tobaccoes45  
8/4John Mazoon his account by me in Company debitor to dito John his ac­count proper 150 l, v [...]z. for his prin­cipall brought in, and gaines thereof made good upon his particular ac­count150  
Anno 1659. 25 March in London
 Order of Balancing.   
2/9Balance debitor to Hans Butterbox my account currant 613 l 15 s 4 d. due to me in ready money613154
4/9John Mazoone debitor to Balance 455 l. due to him by conclude455  
4/9Barnaby Clemens debitor to balance 300 due to him 5 March last, by my obligation300  
9/5Balance debitor to Edw: Price 101 l 10 s due to me the 30 of April next10110 
6/9John Malthorse debitor to balance 304 l 10 s due the 29 of April next43010 
7/6Voyage to Amsterdam debitor to profit and loss 76 l 3 s 4 d. gained by sale of goods there7634
Hans Butterbox his account of Wheat debitor to his account currant 256 l 5 s. being the neat proceed of his wheat2565 
9/2Balance debitor to Fustians 142 l 16 s for 126 pieces remaining unsold, at 22 s 8 d per piece14216 
2/6Fustians debitor to profit and losse 61 l 9 s 4 d gained by the sale of 73 pieces6194
2/6Spanish Tobacco debitor to profit and loss 146 l 13 s 8 d gained by the sale of 10 Potacoes146134
9/2Balance debitor to Colchester Sayes 34 l 6 s 8 d for 20 pieces unsold, at 34 s per piece368
9/2Balance debitor to Couchaneal 184 l 1 s 3 d for 11 C 3 qu. 74 pound, at 15 l 10 s per C. unsold−18413
[...]/6Couchaneal debitor to profit and loss 5 l 5 s gained by the sale of 3 C55 
9/5Balance debitor to Lead 204 l 11 s 3 d for 95 Pigs wa. 13 tun 12 C 3 q. at 15 s per cent. resting unso'd204113
9/5Balance debitor to Claret wine 60 l for 5 tuns, at 12 l per tun resting un­sold60  
9/5Balance debitor to Sugars 43 l 11 s 4 d ½ for 24 C o qu. 23 pound, at 36 shillings per cent. being unsold43114 ½
Sugars debitor to profit and loss 1 l 16 s gained by the sale of 6 C.116 
9/6Balance debitor to Province Oyles 9 l 3 s for 1 Cask taken content un­sold93 
6/6Profit and loss debitor to Interest reckoning 3 l lost by giving of interest for money3  
9/3Balance debitor to Ship the Sampson of London 200 l for my ⅛ part thereof200  
[...]/6Ship Sampson debitor to profit and losse 35 l 3 s 8 d. gained by fraight3538
9/3Balance debitor to the Nags head at Rumford 350 l for the principal worth of it350  
9/1Balance debitor to Cash 1561 l 4 s 1 d resting in hand15614½

THE LEAGER: NUMBER A. Anno Dom. 1659. in LONDON.

The forme of the Kalender belonging to the Leager.
  • [Page]A
    • Abrah: Bland. fol. 1
  • B
    • John Benning. 4
    • Hans Butterbox my account currant. 7
    • Dito Butterbox his ac­count of Wheat. 7
    • Dito Butterbox his ac­count currant. 8
    • Ballance. 9
  • C
    • Cash. fol. 1
    • Couchaneale. 2
    • Barnaby Clemens. 4
    • Jane de Clare. 4
  • D
  • E
  • F
    • Fustians. fol. 2
  • G
    • Tho: Goodman. fol. 3
  • H
    • House Nags head. f. 3
  • I
    • Interest reckoning. f. 6
  • K
  • L
    • William Lane. fol. 3
    • Lead 5
  • M
    • John Mazoon. fol. 4
    • John Malthorse. 6
    • John Mazoon his ac­count by me in compa­ny. 7
  • N
  • O
    • Oyles Province. fol. 6
  • P
    • Edward Price. fol. 5
    • Simon Peters. 6
    • Profit and Loss. 6
  • Q
  • R
  • S
    • Stock. fol. 1
    • Sayes. 2
    • Ship Sampson. 3
    • Thomas Spilman. 4
    • Sugars. 5
  • T
    • Tobacco. fol. 2
    • John Thurrowgood. 4
    • Tobacco in Company for John Mazoone and my self each ½. 8
  • V
    • Voyage to Amsterdam. fol. 7
  • W
    • Wines Clarret. fol. 5
    • James Wilson. 5
  • X
  • Y
  • Z
  Cash Debitor.    
16581First Jan. to stock for severall coins amounting to Sterling mo­ney1− 800  
 33 Dito to Fustians for 13 pieces sold to John Deport at 30 s per piece22414 
  15 Dito to John Benning, recei­ved in part425176
 419 Dito to Edward Price recei­ved to clear a Truck5309 
  29 Dito to John Malthorse recei­ved at interest at 6 per cent. per an.6−300  
 530 Dito to Simon Peters being so much borrowed of him 50  
  9 Feb. to John Thurrowgood re­ceived in full demand43910 
  Dito to John Benning received in full upon rebate 24  
 612 Dito to profit and loss fo [...] gain in exchange of 100 Dollars62184
  2 Dito to Thomas Goodman, re­ceived of William Short in full350  
  19 Dito to Abraham Bland being 13 s 4 d per l for 387 l 11 s3−258074
 722 Dito to Ship Sampson for my ⅛ part for fraight 35038
  Dito [...]o profit and loss for a Legacy [...]eiv'd, given me by A. M.6−200  
 829 Dito to H. Butterb. his account of Wheat for 100 qu. sold at 58 s per qua [...]e [...] [...]7−290  
 924 Mar [...], to John Mazoon his account by me in company for his part received8−105  
  - Dito to Tobacco in company for 30 [...]at 10 l per hh −300  
  Contra Creditor. LSD
1658315 Jan. by Lead for 95 Pigs wa. 13 T. 12 C. 3 qui at 15 s per C.5204 [...]13
 5- Dito by James Wilson for ⅓ of his debt paid him in part51825 ½
  30 Dito by Edw. Price delivered him upon interest at 6 per c. 3 mo.5100  
  - Dito by profit and loss for house-keeping for 3 moneths650  
 52 Feb. by Jane de Clare, paid him in full of all demands460  
 5- Dito by James Wilson paid him in full of all demands536411
 719 Dito by Voyage to Amsterd. paid charges of Fustians & Tobac.7916 
 7- Dito by dito voyage for Insu­rance at 30 s per cent.7716 
 722 Dito by profit and loss given in relief for a fire612  
 828 Dito by H. Butterb. his account of Wheat at the receit for charges7185 
 83 March, by H. Butterb. his account currant remitted him by bills82575 
 924 Dito by Tobac. in Company, paid in full for 30 hh at 7 l per hh821011 
1659925 Dito by balance resting in Cash91524192 ½
  Stock Debitor.    
165821 Jan. to Barnaby Clemens by my Obligation due 15 March4300 6
 2Dito to Thomas Spilman due to him on demand436114
 2Dito to John Mazoon payable on demand4305  
1659 25 March, to balance for con­clude carried thither9235941
  Contra Creditor.    
165811 Jan. by Cash for severall Coins of money amounting to Sterling money1800  
  - Dito by Fustians for 200 pie­ces cost 22 s 8 d per piece2226134
  - Dito by Spanish Tobaco for 10 Potatoes wa. net. 880 pound, at 6 s 8 d per pound22936 [...]
  - Dito by Colchester Sayes, for 20 pieces unsold at 34 s per piece23468
  - Dito by Couchancal for 14 C 3 qu. 14 po. at 15 l 10 s per C.2230113
  - Dito by Ship the Sampson of London, for my ⅛ part3200  
  - Dito by house the Nags-head at Rumford, for what it cost3350  
  - Dito by Abraham Bland, for his Obligation due the last instant338711 
  - Dito by Thomas Goodman for his Bill382034
  - Dito by William Lane being the rest of an old account336114
1659 25 March, by profit and losse gained by this 3 moneths trading6359122
  Fustians Debitor.    
165811 Jan. to stock for 200 pieces which cost 22 s 8 d per Piece1226134
1659 25 March to profit and loss gai­ned by the sale of 73 Pieces661094
  Spanish Tobaco Debitor.    
165811 Jan. to stock for 10 Potacoes wa. net. 880 pound, at 6 s 8 d per pound129364
1659 25 March to profit and loss gai­ned by the sale of dito Tobaco6146138
  Colchester Sayes Debitor.    
165811 Jan. to stock for 20 Pieces cost 34 s per piece134068
  Couchaneale Debitor.    
165811 Jan. to stock for 14 C. 3 qu. 14 pound, at 15 l 10 s per C.1230113
1659 25 March to profit and loss gai­ned by sale of 3 C.6505 
  Contra Creditor.    
165833 Jan. by Cash for 13 pieces sold to John Deport at 38 s. pe [...] piece124114 
 3- Dito by John Thoroughgood of Chester for 20 pieces at 39 s per pi ce t 30 dayes43910 
 619 Feb. by voyage to Amsterdam to be sold for my account, 40 pie­ces at 40 s. per piece780  
 722 Dito by profit and loss for one piece given away to A. B.6128
1659 25 March by balance for 126 pieces unsold at 22 s. 8 d. per piece914816 
  Contra Creditor.    
1658619 Feb. by voyage to Amsterd. consigned to Hans Butterbox to be sold for my use 10 Potacoes of Spanish Tobaccoe wa. net. 880 pound, at 10 s. per po.7440  
  Contra Greditor.    
1659 25 March by ballance for 20 pieces resting uns [...]d, which cost 34 s. per piece93468
  Contra Creditor.    
1658315 Jan. by John Benning for 3 C. at 17 l. 5 s. per C. ½ instant, rest at 6 moneths45115 
1659 25 March by ballance for 11 C. 3. qu. 14 pound unsold, cost 15 l. 10 s. per C.914813
  Ship the Sampson Debitor.    
165811 Jan. to stock for my ⅛ part, which cost me1200  
1659 25 March, to Profit and Losse gained by fraight63538
  House the Nags head at Rumford Debitor.    
165811 Jan. to stock for the principle it cost me1350  
  Abraham Bland Debitor.    
165821 Jan. to stock for his bond da­ted 5 Decemb. last, due the last of this moneth138711 
  Thomas Goodman Debitor.    
165821 Jan. to stock for his bill to be paid on demand18234
  William Lane of Ipswich Debitor.    
165821 Jan. to stock, being the rest of an old Account136114
  Contra Creditor.    
1658722 Feb. by Cash received for my ⅛ part for fraight13538
1659 25 March, by Balance for my ⅛ part thereof9200  
  Contra Creditor.    
1659 25 March by Ballance for the principall it cost9350  
  Contra Greditor.    
1659619 Feb. by Cash received at 13 s 4 d per l for 20 s126474
 16- Dito by Profit and Loss lost by him when he failed612338
  Contra Creditor.    
1658612 Febr. by Cash received of Will: Short in full of my said debt150  
 6Dito by Profit and Loss lost by the sale of my said debt to dito William63234
  Contra Creditor.    
1658612 Feb. by Tho: Spilman order'd to receive of dito William436114
  Barnaby Clemens Debitor.    
1659 25 March to balance due to him by my obligation the 5 of March last9300  
  Thomas Spilman Debitor.    
1658612 Feb. to William Lane for my [...]ssignment336114
  John Mazoon Debitor.    
1659325 March to balance due to him by conclude9455  
  John Thoroughgood Debitor.    
165833 Jan. to Fustians for 20 pieces [...]t 39 s. per piece, to be paid with­ [...]n 30 dayes23910 
  John Benning Debitor.    
1658315 Jan. to Couchaneal for 3 C. neat, at 17 l. 5 s. per C. ½ instant rest at 6 moneths25115 
  Jane de Clare Debitor.    
165852 Feb. to Cash paid in full of all demands160  
  Contra creditor.    
165821 Januar. by stock payable 5 March next1300  
  Contra creditor.    
165821 Jan. by stock payable on demand136114
  Contra credito.    
165821 Jan. by stock payable on de­mand1305  
 824 March by his account by me in company8150  
  Contra cred tor.    
165859 Feb. by Cash received in full of all demands13910 
  Contra creditor.    
1658315 Jan. by Cash paid in part125176
 59 Feb. by Cash received in full upon rebate 24  
  - Dito by profit and loss allow­ed for payment before due61176
  Contra creditor.    
1658315 Jan. by Claret wines being 5 Tun, at 12 l. per Tun560  
  Lead Debitor.    
1658315 Jan. to Cash paid for 95 Pigs wa. 13 Tun 12 C. 3 qu. at 15 s per C.12041 [...]3
  Clarret Wines Debitor.    
1658315 Jan. to Jane de Clare for 5 [...]uns at 12 l per tun460  
  Sugars Debitor.    
1658415 Jan. to James Wilson for 30 C. 0 qu. 23 pound neat at 36 s per C. ⅓ instant, rest at 9 moneths55474 ½
1659 25 March to Profit and Losse gained by the sale of 6 C neat6116 
    5634 ½
  James Wilson Debitor.    
1658415 Jan. to Cash for ⅓ paid him in part.11825 ½
 52 Feb. to Cash paid in full of all demands 3641
    5474 ½
  Edward Price Debitor.    
1658419 Jan. to Sugars for 2 hh wa. neat 6 C. at 42 s per C.51212 
 530 Dito to Cash dd. him upon interest at 6 l per C.1100  
  - Dito to Interest-reckoning for allowance of dito C l. for 6 mo­neths6112 
    1 [...]42 
  Contra Creditor.    
1659 25 March by Ballance for 95 Pigs resting unsold9204113
  Contra Creditor.    
1659 25 March by Ballance resting unsold, 5 tuns at 12 l per tun960  
  Contra Creditor.    
1658419 Jan. by Edward Price for 6 C. at 42 s per C. in barter51212 
1659 25 March by Ballance for 24 C 0 qu. 23 l resting unsold94 [...]114 ½
    5634 ½
  Contra Creditor.    
1658415 January by Sugars for 30 C. 0 qu. 23 l. neat at 36 s per C. ⅓ instant, rest at 1 moneth55474 ½
  Contra Creditor.    
1658419 Januar. by Province Oyles 1 Cask received content693 
  Dito by Cash paid in full satis­faction of dito truck139 
1659 25 March by Ballance due to me 30 April next91010 
  Province Oyles debitor.    
16584To Edward Price for 1 Cask taken content593 
  John Malthorse debitor.    
1659 25 March to Ballance due to him 29 April next930410 
  Interest reckoning debitor.    
1658429 Jan. to John Malthorse for 3 moneths allowance of 300 l. at 6 per cent. for 3 moneths6410 
  Simon Peters debitor.    
1659 25 March to Ballance due upon demand950  
  Profit and loss debitor.    
1658530 Jan. to Cash paid A B. my servant for 3 moneths house-kee­ping150  
  9 Feb. to John Benning allowed for payment before due41176
 612 Dito to Thomas Goodman lost by sale of his debt to Will: Short.33234
  19 Dito to Abraham Bland lost by taking 13 s. 4 d. per l. when h [...] failed312938
 722 Dito to Fustians for 1 piece given to A.B.2128
  - Dito to Cash given towards the relief of a Fire at Enfield in [...]he County of Middlesex112  
1659 25 March to Interest reckoning lost by the same63  
  - Dito to Stock gained by this 3 moneths trading1359122
    5 [...]9194
  Contra Creditor. LSD
1659 25 March by Ballance for one Cask unsold993 
  Contra Creditor.    
1658429 Jan. by Cash received upon interest at 6 per cent. for 3 months1300  
  - Dito by Interest reckoning for 3 moneths allowance for 300 l. at 6 per cent.6410 
  Contra Creditor. 30410 
1658529 Jan. by Edward Price for al­lowance of 100 l. for 3 moneths at 6 per cent5110 
1659 25 March by Profit and Losse lost per summe63  
  Contra Creditor. 410 
1658530 Jan. by Cash borrowed and payable on demand150  
  Contra Creditor.    
1658612 Feb. by Cash gained by ex­change of 100 Dolars for Eng. mo.12184
 722 Dito by dito given as a Le­gacy by A. M. 200  
 828 Dito by Hans Butterbox hi [...] account of Wheat for my provisi­on at 12 d. per l.71410 
  24 March by Tobaccoe in com­pany for ½ of my advance845  
1659 25 Dito by voyage to Amsterd. gained by the sale of goods there77634
  - Dito by Fustians gained by the sale of 73 pieces26194
  - Dito by Spanish Tob. gained by the sale of 10 Potacoes 14 [...]138
  - Dito by Couchaneale gained by the sale of 3 C. 55 
  - Dito by Sugars gained by the sale of 6 C. 116 
  - Dito by Ship the Sampson gai­ned by fraight33538
  Voyage to Amsterdam configned to Hans Butterbox Deb.    
1658619 Feb. to Fustians for 40 Pie­ces at 40 s per Piece280  
  - Dito to Spanish Tobacco for 10 Potacoes neat 880 pound at 10 s per pound, to be sold for my account 440  
 7- Dito to Cash for charges upon the Fustians and Tobacco1916 
  - Dito to Cash for Insurance John Mazoon at 30 s per cent. 716 
1659 25 March to Profit and Losse gained by sale of dito goods67634
  Hans Butterbox at Amsterdam my Account currant debitor.    
165872 Feb. to Voyage to Amsterdam for the neat Proceed of my goods there7613154
  Hans Butterbox at Amsterdam his account of Wheat Deb.    
1658828 Feb. to Cash for charges at the receit of 100 quarters1185 
  - Dito to Profit and Losse for my provision at 12 d per l.61410 
1659 25 March to dito Hans his ac­count currant for the neat pro­ceed thereof82575 
  Contra creditor.    
1658728 Feb. by Hans Butterbox my account currant761315 
  Contra creditor.    
1659 25 March by Ballance due to me in ready mony9613154
  Contra creditor.    
1658829 Feb. by Cash for 100 quar­ters sold to John Sutton at 58 s per qu.1290  
  Hans Butterbox at Amsterdam his account currant debitor.    
165883 March to Cash remitted him payable by Simon Newman of Am­sterdam12575 
  Tobaccoe in company for John Ma­zoon and my self debitor.    
1658924 March to Cash for 30 hh. at 7 l. per hh.8210  
  - Dito to John Mazoon for his ½ advance 45  
  - Dito to profit and loss for my ½ of advance645  
  John Mazoon his account by me in company debitor.    
1658924 March to dito John his ac­count proper for principall and gains4150  
  Contra creditor.    
1659 25 March by dito his account of wheat, being the neat proceed the [...]eof72575 
  Contra creditor.    
1658924 March by Cash for 30 hh. sold to John Brown at 10 l per hh.1300  
  Contra creditor.    
1658824 March by Cash received for his ½ part110 [...]  
 924 March by Tobaccoe in com­pany his ½ advance845  
  Balance Debitor.    
1659525 March, to Hans Butterb. my account currant due in ready mon.761354
  - Dito to Edward Price due to me 30 April next510110 
  - Dito to Fustians for 126 pie­ces resting unsold, at 22 s 8 d per piece214216 
  - Dito to Colchester Sayes for 20 pieces unsold 3468
  - Dito to Couchaneal for 11 C. 3 q. 14 l at 15 l to s per C. unsold218413
  - Dito to Lead for 95 piggs re­maining unsold5204113
  - Dito to Clarret Wines for 5 tuns, at 12 s per tun unsold 60  
  - Dito to Sugars for 24 C. 0 qu. 23 l unsold, at 36 s per C. 4311
  - Dito to Province Oyles for one Cask unsold693 
  - Dito to Ship Sampson for my ⅛ part thereof3200  
  - Dito to House Nags head at Rumford for the principal worth 350  
  - Dito to Cash resting in bank11524192 ½
  Contra Creditor.    
1659 25 March, by John Mazoon due to him by conclude4455  
  - Dito by Barnaby Clemens for my obligation due 5 March last 300  
  - Dito by John Malthorse due to him 29 April next630410 
  - Dito by Simon Peters due on demand 50  
  - Dito by Stock for difference, there being my present estate123594 

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