| John Dougall - 1810 - 580 pages
...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... | |
| James Hayward - Geometry - 1829 - 172 pages
...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,... | |
| 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 of the squares** described on the other two sides. Let the triangle be Fig. 64. KDI, right angled at I. Describe squares... | |
| 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... | |
| Almon Ticknor - Measurement - 1849 - 144 pages
...therefore AC, BD, are bisected at the point 0. Fig. 25. 26. The square described on the hypotenuse **of a right-angled triangle is equivalent to the sum of the squares** described on the other two sides. (Pig. B) Fig. A. Let the triangle ABC be right-angled at A. Having... | |
| Charles Davies - Logic - 1850 - 375 pages
...class will be common to every individual of the class. For example : " the square on the hypothenuse **of a right-angled triangle is equivalent to the sum of the squares** described on the other two sides," is a proposition equally true of every right-angled triangle: and... | |
| A. M. LEGENDRE - 1852
...algebraical formula, (a+b)x(ab)=o?-b*. PROPOSITION XI. THEOEEM. The square described on the hypothenuse **of a right-angled triangle is equivalent to the sum of the squares** described on the two other sides. Let BCA be a right-angled triangle, right-angled at A : then will... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1854 - 432 pages
...expressed by the algebraical formula, 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 BCA be a right•angled triangle, right•angled at A : then... | |
| GEORGE R. PERKINS - 1856
...COMPARISON OF SQUARES CONSTRUCTED ON CERTAIN LINES. THEOREM XXIX. The square constructed on the hypotenuse **of a right-angled triangle, is equivalent to the sum of the squares** constructed respectively on the other two sides. This Theorem is not a fundamental one, like Theorem... | |
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