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 IX.

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.

[illustration] diagram

A Demonstration.

Definitions and terms.

A Circle is a Geometrical Figure comprehended

with one line, as E F G H E, termed the Periphe∣ria 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 infi∣nite, and if any one be terminated at both ends with the Circumference, it is called the Diame∣ter, 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.