| Charles Davies - Mathematics - 1867 - 186 pages
...example : when we prove 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,** we demonstrate the fact for all right-angled triangles. But in analysis, all numbers, all lines, all... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...the angle cannot be a right angle, since the square described on the first side would then be equal **to the sum of the squares described on the other two sides,** by I. 47 ; and the angle cannot be acute, since the square described on the first side would then be... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the angle cannot be a right angle, since the square described on the first side would then be equal **to the sum of the squares described on the other two sides,** by I. 47 ; and the angle cannot be acute, since the square described on the first side would then be... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...b) X (a — 6) = a2 — b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse **of a right-angled triangle is equivalent to the sum...the squares described on the other two sides. Let** ABC be a right-angled triangle, having the right angle at A ; then the square described on the hypothenuse... | |
| Robert Milligan - Apologetics - 1868 - 456 pages
...mankind. The mechanic does not think it necessary, to prove that 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,** every time that he attempts to square a building. It is enough for him to know that this truth has... | |
| Edward Brooks - Geometry - 1868 - 294 pages
...(« + &) (a THEOREM VI. 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. Let** ABC be a triangle, right-angled at B; then will For, construct squares on each of the sides, draw BD... | |
| Eli Todd Tappan - Geometry - 1868 - 436 pages
...demonstration from Euclid. 408. Theorem — The square described on the hypotenuse of a right angled **triangle is equivalent to the sum of the squares described on the** two legs. Let ABC be a right angled triangle, having the right angle BAC. The square described on the... | |
| Richard Wormell - Geometry, Modern - 1868 - 286 pages
...quadrilateral AFD E, and then a rectangle equivalent to the triangle. The square on the hypothenuse **of a right-angled triangle is equivalent to the sum of the squares** on the other sides. 148. Describe the squares on the sides (fig. 126), and through D, the right-angle,... | |
| Isaac Stone - Educational tests and measurements - 1869 - 278 pages
...twice the rectangle contained by the lines." P. VIII. B. IV. "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."** P. XI. B. IV. " In every quadrilateral inseribed in a circle, the rectangle of the two diagonals, is... | |
| Isaac Stone - Educational tests and measurements - 1869 - 272 pages
...twice the rectangle contained by the lines." P. VHI. B. IV. "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."** P. XI. B. IV. "In every quadrilateral inscribed in a cirele, the rectangle of the two diagonals, is... | |
| |