| John Dougall - 1810
...the square of the whole line AB, or 6 X6 = 36. PROP. XVTII. for. t, Plate 2. The square constructed **on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares** constructed or the two sides containing the right angle. Let ABC be a trianale, having a right angle... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...— BC) = AB2 — BC*. LFGI E JJ 57 PROPOSITION XI. THEOREM. The square described on the hypotenuse **of a right-angled triangle is equivalent to the sum of the squares described on the** two sides. Let the triangle ABC be rightangled at A. Having formed squares on the three sides, let... | |
| George Lees - 1826 - 272 pages
...another as the squares of their corresponding sides. Cor- 2. The rectilineal figure described upon **the hypothenuse of a right-angled triangle, is equivalent to the sum of the** similar rectilineal figures described upon the sides containing the right angle. i •;.•_,, PROP.... | |
| James Hayward - Geometry - 1829 - 218 pages
...- ; and multiplying both sides by a, we have a2 = 62 -f- c8, that is — The square described upon **the hypothenuse of a right-angled triangle, is equivalent to the sum of the squares described** upon the other two sides. 173. We may demonstrate this truth from the areas immediately, without referring... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal **to the sum of the squares described on the other two sides** of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...LCBI 78 GEOMETRY, PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled **triangle is equivalent to the sum of the squares described on the other two sides. Let** the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A,... | |
| Charles Davies - Geometrical drawing - 1840 - 252 pages
...4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal **to the sum of the squares described on the other two sides.** Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB... | |
| Scotland free church, gen. assembly - 1847 - 552 pages
...makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal **to the sum of the squares described on the other two sides,** these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...equal to > — ; (See Appendix, Problem IV.) PROP. VII. THEOREM. The square described on the hypotenuse **of a right-angled triangle is equivalent to the sum...the squares described on the other two sides. Let** the triangle be Fig. 64. KDI, right angled at I. Describe squares on KD, KI, DI ; then we have to prove... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...the other two sides; in other words, BC^AB'-f-AC". Therefore, The square described on the hypolhcnuse **of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides.** Cor. 1. Hence, by transposition, the square of one of the sides of a right-angled triangle is equivalent... | |
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