| Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...the rhomboid BE, and the rhomboid BF is equivalent to the trapezoid ABCD. BOOK II. PROP. XIV. THEOR. **The square described on the hypotenuse of a right-angled triangle, is equivalent to the** squares of the two sides. Let ACB be a triangle which is right-angled at B; the square of the hypotenuse... | |
| John Dougall - 1810
...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... | |
| Sir John Leslie - Geometry - 1817 - 454 pages
...perpendiculars branching from the great line to each remarkable flexure of the extreme boundary. PROP. X. THEOR. **The square described on the hypotenuse of a right-angled triangle, is equivalent to the** squares of the two sides. / Let the triangle ABC be right-angled at B ; the square described on the... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...square described on BC : hence we have (AB+BC) x (AB — BC) = AB2 — BC*. LFGI E JJ 57 PROPOSITION XI. **THEOREM. The square described on the hypotenuse of...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... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...proposition is equivalent to the algebraical formula ,(a+b) (a — 6)*=a2 — 62. '-• THEOREM. 1 86. **The square described on the hypotenuse of a right-angled...equivalent to the sum of the squares described on the** two sides. Let the triangle ABC be right-angled at A. Having formed squares on the three sides, let... | |
| James Hayward - Geometry - 1829 - 228 pages
...both sides by #, we have « 2 =: b 2 + c 2 , that is — 7Vtc 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... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...proposition is equivalent .to the algebraical formula, (a + V) (a — 6)=«2 — 62. v THEOREM. 186. **The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of** tJie squares described on the two sides. Let the triangle ABC be right-angled at A. Having formed squares... | |
| 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, on the hypothenuse,.... | |
| 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... | |
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