 | Emil G. Milewski - Mathematics - 1998 - 932 pages
...= 2|Zl|2 + 2|z2|2 (1) What is the relationship between this identity and the following theorem? The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. Solution: The left-hand side of eq.(l) can be transformed to 2 = zi-z2 Z2Z2... | |
 | B.S. Stechkin, V.I. Baranov - Computers - 2007 - 207 pages
...satisfying the inequality d(k; X) > 1. If X is a Hilbert pace, then the parallelogram law holds in it: the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. Hence, if X is a Hilbert space, then d2(k; X) + <*>2(2, A;; X) — 4, and... | |
 | Izu Vaisman - Mathematics - 1997 - 300 pages
...common point (the orthocenter of the triangle). 1.4.2. Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum of the squares of the lengths of its diagonals. 1.4.3. Prove the theorem of three perpendiculars: let a be... | |
 | John K. Hunter, Bruno Nachtergaele - Mathematics - 2001 - 460 pages
...reader. D The relation (6.4) is called the parallelogram law. Its geometrical interpretation is that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals (see Figure 6.1). As the polarization formula (6.5) shows, an inner product... | |
 | Military Academy, West Point - 906 pages
...trisected at the points where they cross the sides of the original triangle. No S.— Theorem: The sum of the squares of the sides of a parallelogram is equal to the sum oí the squares (Wt. 10.) of the diagonals. No 9. — (a) Define a regular polygon. (Wt. 10.) ((>)... | |
 | 130 pages
...the mid-points of the sides BC, CA, AB of the triangle ABC, show that 4. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. ©amfcrtoge : PRINTED BY JOHN CLAY, MA AT THE UNIVERSITY PRESS Mathematics,... | |
 | British Columbia. Superintendent of Education - 1897 - 710 pages
...bisect their common tangent. 9. Trisect a given finite straight line. 10. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. ZOOLOGY. (For Second Class, Grade A.) Friday, July 10th; 1:30 pm to 3:30... | |
 | Thomas Hadyn Ward Hill - 190 pages
...Y^*. Similarly, for CG = AG = BG, for an equilateral triangle, Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. AB Ideas: (i) Sum of squares suggests Pythagoras' or Apollonius' Theorem.... | |
 | 480 pages
...OB2.) Ex. 66. In the figure of Ex. 55, OA2 + OD2 = OB2-t-OC2+4BC2. Ex. 67. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 68. In any quadrilateral the sum of the squares on the four sides exceeds... | |
 | Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - Geometry - 1963 - 198 pages
...points A, B remains constant ; prove that its locus is a circle. Ex. 31. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 33. The sum of the squares on the diagonals of a quadrilateral is equal... | |
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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. 
