 | Sir John Leslie - 1809 - 522 Seiten
...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 - 734 Seiten
...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 - 1817 - 456 Seiten
...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 - 1822 - 394 Seiten
...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 a right-angled...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... | |
 | James Hayward - 1829 - 218 Seiten
...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... | |
 | Adrien Marie Legendre - 1830 - 344 Seiten
...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 - 1833 - 168 Seiten
...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 - 1838 - 382 Seiten
...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 - 1840 - 262 Seiten
...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 Seiten
...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... | |
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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. 
