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.

The Theorem.

Unto the squares of the two extreames or bases, adde the Geometrical mean square, which summe multiply by ⅓ part of the height, or ⅓ of the totall by the height, the product will be the Segments solid content requi∣red.

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 Seg∣ment.

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,

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 con∣troversie, 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.