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. 1876 Excerpt: ...polygon. Construct a triangle equivalent to the given polygon (263), then, a square equivalent to the given triangle (264, 2). 266. Proposition XLIV--Problem. To construct a square equivalent to the sum of two or more given squares, or to the difference of two given squares. 1. Let l, m, n, be the sides of the given ...
Read More
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. 1876 Excerpt: ...polygon. Construct a triangle equivalent to the given polygon (263), then, a square equivalent to the given triangle (264, 2). 266. Proposition XLIV--Problem. To construct a square equivalent to the sum of two or more given squares, or to the difference of two given squares. 1. Let l, m, n, be the sides of the given squares.. Take AB = l, and per-m l, pendicular to AB draw BC = m, and draw AC. Then, AC2 = l2 + m2 (209). Perpendicular to AC, draw CD = n, also draAV AD. Then, AD"1 = AC2 + n = Z2 + m2 + n 2. Let l and m be the sides of two given squares. Take AB = m, and draw BC perpendicular to AB. With A as center and l as radius, describe an arc cutting BC in C. 267. Corollary. To construct a square equivalent to tlie sum of any number of given polygons, or to the difference of two given polygons. Construct squares respectively equivalent to the given polygons (265), then, a square equivalent to the sum or difference of these squares (266). 268. Proposition XLV--Problem. On a given line to construct a rectangle equivalent to a given rectangle. Let E be the given rectangle, a its attitude, b its base, and b' a s .""' the given line. Find a fourth i-h proportional, a!, to V, b, and a (253). Then, a' is the altitude of the required rectangle R. For, b': b:: a: a', .. a'b' = ab. But, R=a'b', R = ab, .-. R = R. 269. Proposition XLVI.--Problem. Given the area of a rectangle and the sum of two adjacent sides, to construct the rectangle. Let s2 be the given area, AB the sum of two adjacent sides of the required rectangle. On AB as a diameter construct a semi-circumference. At A erect a perpendicular to AB equal to s, and at its extremity draw CD parallel to AB. At D, one point of the intersection of this parallel with the circumference, let fall the p...
Read Less