| Lewis Sergeant - 1873
...one angle of a parallelogram is a right angle, so is each of the others. Proposition 47. — Theorem. **The square on the hypotenuse of a right-angled triangle is equal to** the squares on the sides. If C is the right angle in ABC, the square on AB = the squares on AC, CB.... | |
| Euclides - 1874 - 342 pages
...points, is equal to the sum of the squares on the other two sides and on the diagonals. 27. Prove that **the square on the hypotenuse of a right-angled triangle...together with the square on the difference of the** sides. 28. In any triangle, if a line be drawn from the vertex bisecting the base, the sum of the squares... | |
| James Frederick Ferrier - Philosophy - 1875 - 532 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, **The square on the hypotenuse of a right-angled triangle is equal to** the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot... | |
| Robert Potts - Geometry - 1876 - 446 pages
...triangle, the area, and the line bisecting the base, construct the triangle.. '* IV. 30. Shew that **the square on the hypotenuse of a right-angled triangle,...together with the square on the difference of the** sides. 31. In the triangle ABC, if AD be the perpendicular let fall upon the side BC; then the square... | |
| Euclides - 1884 - 434 pages
...opposite an obtuse angle of a triangle is greater than the squares on the other two sides. 15. Five times **the square on the hypotenuse of a right.angled triangle is equal to four times the** sum of the squares on the medians drawn to the other two sides. 16. Three times the square on a side... | |
| Education - 1884
...and a diagonal is 8,545 feet ; determine whether the parallelogram is a rectangle. By Euclid I. 47, **the square on the hypotenuse of a rightangled triangle is equal to** the sum of the squares on the sides. Here the diagonal corresponds with the hypotenuse. Now 75842 +... | |
| Euclides - 1884 - 182 pages
...each side of which shall be equal to a given straight line." 9. Give the proposition equivalent to : " **The square on the hypotenuse of a right-angled triangle is equal to** the sum of the squares upon the other two sides." 10. In the construction to XLVIII., show that it... | |
| John Trowbridge - 1884 - 408 pages
...have forgotten the philosophical proofs. Thus we can by actual measurement ascertain the truth that **the square on the hypotenuse of a right-angled triangle is equal to** the sum of the squares on the base and altitude of the triangle, and, knowing this fact, we can make... | |
| George Shoobridge Carr - Handbooks, vade-mecums, etc - 1886 - 1040 pages
...— The complements of the parallelograms about the diameter of a parallelogram are equal. I. 47. — **The square on the hypotenuse of a right-angled triangle is equal to** the squares on the other sides. I. 48. — The converse of 47. BOOK II. II. 4. — If a, b are the... | |
| James Frederick Ferrier - Philosophy - 1888 - 744 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, **The square on the hypotenuse of a right-angled triangle is equal to** the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot... | |
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