 | Sir John Leslie - 1809 - 522 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1828 - 346 σελίδες
...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 - 1829 - 228 σελίδες
...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 - 1830 - 344 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1840 - 262 σελίδες
...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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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. 
