 | Samuel Constable - Geometry - 1882 - 222 pages
...OBC, OCA, OAB. It will be found by addition that the squares OB, 00, OA cancel.] 2. Prove that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. [See Prop. 12. It is necessary, also, for the solution of this theorem and... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...squares on AB and AC is double the sum of the squares on BD and DA. QED Ex. 23. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 24. The sum of the squares on the sides of any quadrilateral 'WM ,'•... | |
 | Mathematical association - 1884 - 146 pages
...squares on AB and AC is double the sum of the squares on BD and DA. QED Ex. 23. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 24. The sum of the squares on the sides of any quadrilateral is greater... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...that prove that the middle point of AD is equally distant from B and C. 5. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. PEOP. XI.— PROBLEM. To divide a given finite line (AB) into two segments... | |
 | Euclides - 1885 - 340 pages
...that prove that the middle point of AD is equally distant from B andC. 6. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. PEOP. XI.— PROBLEM. To divide a given finite line (AB) into two segments... | |
 | New York (State). Department of Public Instruction - 1887 - 268 pages
...triangle, when the altitude, the vertical angle, and one of the sides are given. 4. Prove that the sura of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. 5. Describe a circle which shall pass through three given points not in the... | |
 | 1887 - 644 pages
...hase and on the line joining the vertex to the middle point of the base. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 2. Angles in the same segment of a circle are equal to one another. Two chords... | |
 | George Albert Wentworth - 1889 - 276 pages
...to twice the product of the third side and the projection of the median upon the third side. 22. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals (Ex. 19.) 23. The sum of the squares of the sides of any quadrilateral is... | |
 | George Albert Wentworth - 1889 - 264 pages
...to twice the product of the third side and the projection of the median upon the third side. 22. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals (Ex. 19.) 23. The sum of the squares of the sides of any quadrilateral is... | |
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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. 
