 | Webster Wells - Geometry - 1899 - 450 pages
...277, 2 AC x AE = ABi + AC2 - BC2 ; and in like manner a value may be found for 2 BC x BD.) 79. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. (§ 279, I.) 80. To construct a triangle similar to a given triangle, having... | |
 | 1899 - 166 pages
...perpendicular let fall on it from the opposite angle, and the acute angle. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 2 Of two straight lines drawn to a circle from a given point the one which... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...the cases in which AQ falls without the triangle, or coincides with AP. 25. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 26. In any quadrilateral the squares on the diagonals are together equal... | |
 | 1900 - 650 pages
...the square on the segment between the points of section, B. 7. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. 8. If from the vertical angle of a right-angled triangle a perpendicular... | |
 | J. Elliott - Geometry - 1902 - 290 pages
...length of the median AD, 4;r 2 = 26 2 +2c 2 -a 2 EXERCISES. 1. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 2. ABC is any triangle. BC is divided at D so that BD is twice CD. Prove... | |
 | Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...its locus is a circle, having for centre the mid-point of AB. Ex. 1 142. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 1 143. In any quadrilateral the sum of the squares on the four sides... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...the cases in which AQ falls without the triangle, or coincides with AP. 25. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals, 26. In any quadrilateral the squares on the diagonals are together equal... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...other, the square on their common chord is equivalent to three times the square on the radius. 922 The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. 923 If the mid-points of two adjacent sides of a parallelogram are joined,... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...other, the square on their common chord is equivalent to three times the square on the radius. 922 The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. 923 If the mid-points of two adjacent sides of a parallelogram are joined,... | |
 | George William Myers, William Rockwell Wickes, Ernest August Wreidt, Ernst Rudolph Breslich - Geometry - 1907 - 90 pages
...the sides. 7. Using the notation and relations suggested by Fig. 38, prove, algebraically, that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. FIG. 38 8. Find the base, b, and the altitude, a, of a parallelogram whose... | |
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The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 
