 | John Dougall - 1810 - 734 pages
...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 - 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 three sides, let... | |
 | George Lees - 1826 - 276 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 - 168 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... | |
 | Thomas Dick - Education - 1833 - 458 pages
...branches of mathematical and physical science. That " a whole ia greater than any of its parts," — that " the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on its remaining sides," are facts, the one deduced from... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 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... | |
 | Charles Davies - Geometrical drawing - 1840 - 262 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 - 554 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 - 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 on KD, KI, DI ; then we have... | |
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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. 
