| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...contained by either of the equal sides, and the projection of the base upon that side. 18. The square on the hypotenuse of a right-angled triangle is equal to four times the area of the triangle, together with the square on the difference of the two sides. 19. Produce a given... | |
| Euclides - 1874 - 342 pages
...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 is equal to four times the area of the triangle together with the square on the difference of the sides. 28. In any triangle,... | |
| Daniel W. Fish - 1874 - 320 pages
...solved by the use of the following principle, which is demonstrated in geometry. 423. PRINCIPLE. — The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. WRITTEN EXERCISES. 1. The two sides of a right-angled... | |
| William Alexander Willock - Circle - 1875 - 196 pages
...joining their points of bisection. 14. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the bisectors of the sides drawn from the vertices of the triangle. 15. Prove that the sum of the squares... | |
| Richard Wormell - 1876 - 268 pages
...the difference of the squares of AD, D С. 112. Three times the sum oí the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angle. 113. The squares on the diagonals... | |
| John Homer French - Arithmetic - 1876 - 358 pages
...Geometrical Principles, but the illustration is not an analysis of the principle. Geometrical ^Principles. I. The square of the hypotenuse of a rightangled triangle is equal to the sum of the squares of the other two sides. II. The diameter of a circle : the circumference : :... | |
| Robert Potts - Geometry - 1876 - 446 pages
...area, and the line bisecting the base, construct the triangle.. '* IV. 30. Shew that the square on the hypotenuse of a right-angled triangle, is equal to four times the area of the triangle together with the square on the difference of the sides. 31. In the triangle ABC,... | |
| Isaac Todhunter - Spherical trigonometry - 1879 - 176 pages
...be inscribed in the two solids. 10. The sum of the squares of the four diagonals of a parallelepiped is equal to four times the sum of the squares of the edges. 11. If with all the angular points of any parallelepiped as centres equal spheres be described,... | |
| John Casey - Geometry - 1882 - 186 pages
...4EF 2 +4FB 2 = AC 2 +BD 2 + 4EF 2 . Prop. 6. — Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the lines bisecting the sides of the triangle. Dem. — Let D, E, F be the middle points of the sides.... | |
| Samuel Constable - Geometry - 1882 - 222 pages
...inscribed in the triangle ABC. 16. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the bisectors. square of half the base plus twice the square of the bisector of that base, we have, if... | |
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