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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. 1814 Excerpt: ...D. Cor. 1, Hence the circumferences of circles are to one another as their diameters. Let the straight line X be equal to half the circumference of the circle ABD, and the straight line Y to Y-: . half the circumference of the circle GHL: And because the rectangles AO.X, and GP.Y are equal to the circles ABD and GHLd; therefore AO.X: GP.Y:: AD: d5.i.s..p. GL:: AO: GP; and alternately, AO.X: AO:: GP.Y: GP; whence, because rectangles that have equal altitudes are as their bases % X:: AO:: Y: GP, and e cagain alternately, X: Y:: AO: GP; wherefore, taking the doubles of each, the circumference ABD is to the circumference GHL as the diameter AD to the diameter GL. Cor. 2. The circle that is described upon the side of a right angled triangle opposite to the right angle, is equal to the two circles described on the other two sides. For the circle described upon SR is to the circle described upon RT as the square of SR to the square of RT; and the circle described upon TS is to the circle Supplement described upon RT as. the square of ST to the square of---RT. Wherefore, the circles described on SR; S.: '-.f.)gV an, d on ST are to the 1-; circle described on RT-s, . as the squares or oR and.of ST to the.square y ofRTf. But the squares Jg--;jp of RS and of ST are equal to the square of RT; therefore the circles described on RS and ST are equal to the circle described on Rt. f 24. 5. PROP. VII. THEOR. s ' i Equiangular paralldograms are to one another as the products of the numbers proportional to their sides....., Let AC and DF be two equiangular parallelograms, and let M, N, P and Q be four numbers, such that AB: BC:: M: N; AB: DE:: M: P, and AB: EF:: M: Q, and therefore ex aaquali, BC: EF:: N: Q. The parallelogram AC is to the parallelogram DF as MN to P...

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