The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1740 Excerpt: ...Examp. Let there be a Parallelopipedon ABCD, (Fig. 35.) whose Breath is AB=8 Inches, Width AE=6 Inches, and from some Point H in one End let a Perpendicular be let fall on the other, let it meet the fame in P, and suppose HP=i2 Inches; then by the above Rule 8x 6 x 12=5176 Inches is the Measure of the Solid. Or, 1 on B set to 6 on A, against 8 on B, is 48 on A; against which bring 1 on B, then against 12 on B is 576 on A the Measure sought. Cor. Hence the Measure of every triangular' Prism, is equal to the Measure of a Perpendicular let fall from any Angle of its Base on its opposite Side, into half that Side, and this Product multiplied by the Height of the Prism. Thus, (Fig. 36.) Let ABD be a Prism whose Base ABC is a Triangle, from an Angle of which as C, let fall a Perpendicular on AB, meeting the fame in P, also let a Plane be drawn thro' any Line k k of the End D, perpendicular to the Base, and let it meet the fame in KK, and from any Point H of kk, a Line being let fall perpendicular onKK meeting the fame in then HQ is the Height of the Prism: Whence CPx-x HQJs the Measure thereof, which is evident from this Proposition, and Cor. 2. Prop. i.Cbap. 1. Cor. 4. If the Base was any regular Polygon, let the Area thereof be found by Corol. 4. Prop. 1. Chap. I. then this multiplied by the Height of the Prism, will be its Content. Examp. Let the Base be a Pentagon whose Side is 50, the fame with that Page 68. and let the Mea sure of a Line drawn from a Point in the End to the Base (Fig. 37.) be 12 Inches, then the Area of bf the Base is 4301,175, and that multiplied by 12, gives 51614,1 square Inches for the Measure of the pentagonal Prism ABEF. Also if the Area of the Base was any Conic Section, its Area may be found by one of the three last Propositions; th...