 | John Dougall - 1810 - 734 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 - 394 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 - 218 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 - 110 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 - 268 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 - 156 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 - 398 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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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 - Geometry - 1854 - 436 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 Roberts Perkins - Geometry - 1856 - 460 pages
...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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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. 
