| 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... | |
| 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... | |
| 1847
...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 - 96 pages
...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... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...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... | |
| Charles Davies - Geometrical drawing - 1846 - 240 pages
...triangle equal to ? 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 rightangled triangle, right-angled at C, then will the square D, described on AB,... | |
| James Bates Thomson - Arithmetic - 1846 - 336 pages
...principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal **to the sum of the squares described on the other two sides.** (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3... | |
| James Bates Thomson - Arithmetic - 1847 - 422 pages
...30. 34967ft-. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal **to the sum of the squares described on the other two sides.** (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following... | |
| James Bates Thomson - Arithmetic - 1847 - 422 pages
...contains 25 sq. ft. Hence, the square described on the hi/pothenuse of any right-angled triangle, is equal **to the sum of the squares described on the other two sides.** DBS. Since the square of the hypothenuse BC, is 25, it follows that the , or 5, must be the hypothenuse... | |
| James Bates Thomson - Arithmetic - 1848 - 422 pages
...575-580.] SQUARE ROOT. 371 578. The square described on the hypothenuse of a rightangled triangle, is equal **to the sum of the squares described on the other two sides.** (Thomson's Legendre, B. IV. 11, Euc. I. 47.) The truth of this principle may be seen from the following... | |
| |