| Adrien Marie Legendre - 1822 - 394 σελίδες
...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... | |
| 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 - 1836 - 394 σελίδες
...CB I X . IP C VI £ J D a » I j B PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on tlte other two sides, Ixet the triangle ABC be right nngled at A. Having described squares on the three... | |
| Adrien Marie Legendre - 1837 - 376 σελίδες
...the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on tha 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, the perpendicular AD, which... | |
| Adrien Marie Legendre - 1838 - 382 σελίδες
...b)—a9 — b3. D K LCBI 78 GEOMETRY, PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum...Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A, on the hypothenuse,. the perpendicular AD, which... | |
| 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... | |
| Francis Henney Smith - 1841 - 46 σελίδες
...indebted for the important proposition which forms the 47th of Euclid, that the square on the hypothenuse of a right angled triangle, is equivalent to the sum of the squares on the other two sides ; and also that of all plane bodies, the circle has the greatest area under... | |
| Scotland free church, gen. assembly - 1847 - 554 σελίδες
...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 - 1844 - 108 σελίδες
...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 KDI, right angled at I. Describe squares onKD, KI, DI ; then we have to prove that the square KDCA... | |
| James Bates Thomson - 1844 - 268 σελίδες
...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 a right-angled triangle is equivalent... | |
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