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 II.

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 per∣fect 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 e∣qual 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 nei∣ther 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

remainder will be 16. the root 4. for the Perpendi∣cular 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 dimi∣nished by some common number, from whence di∣vers 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 ang∣led triangle, as A. B. C rectangled at B. and propor∣tional 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.