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

PROBLEME VIII.

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 Arithme∣tick.

The Theorem.

With the breadth of any rectangled figure given, di∣vide the square inches contained in a foot, the quoti∣ent 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 neces∣sary, but of no necessity whether longer or short∣er, for this length will contain a foot of board, al∣though 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 mea∣sure 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

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 Ru∣ler 22 2/13 inches; at 6 ¾ take 21 ⅓ inches, at 7 you will find 30 4/7 inches, and thus proceeding in quar∣ters 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 quar∣ters 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 how∣soever not considerable in things of this nature, for if they should be continued to 4 feet, the differ∣ence betwixt 47 and 48 inches in this square mea∣sure will be but 3/47 parts of an inch; these propor∣tionals found, you may inscribe them upon a Ru∣ler, with figures to them, and so made ready and apt for common use, if exactnesse be requi∣red, make use of the Problemes delivered you be∣fore.

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, & fre∣quently 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

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 in∣ches 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 quar∣ters, &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.

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