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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. "
Elements of Geometry - Page 54
by Adrien Marie Legendre - 1825 - 224 pages
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Extremal Combinatorial Problems and Their Applications

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...
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Analytical Geometry

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...
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Applied Analysis

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...
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Information Relative to the Appointment and Admission of Cadets to the ...

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.) ((>)...
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The New Geometry: Form One

G. P. West - Geometry - 1965 - 362 pages
...its locus is a circle having for centre the mid-point of AB. 13. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 14. Show that, if AX, BY are medians of AABC, AX2 - BY2 = | (AC2 - BC2)....
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Report of the Examinations Conducted by the Council of Higher Education ...

Newfoundland Council of Higher Education - 1919 - 180 pages
...having each of the base angles double of the vertical angle. 4. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 5. If the base and vertical angle of a triangle are given, prove the locus...
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modern geometry

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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School Certificate Mathematics

Mathematics - 1965 - 232 pages
...that BC = CP. Given that AB = AC = 2BC, show that AP* = 6BC*. 2. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 3. APQ is a triangle and PQ is produced to B and C so that BP=PQ= QC. Prove...
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Paractical Geometry Based on the Various Geometry Books by Godfrey and Siddons

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...
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Elementary Geometry Plane (Classic Reprint)

James McMahon - 2018 - 244 pages
...its locus is a circle, having for centre the mid-point of AB. tEx. 1142. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. tEx. 1143. In any quadrilateral the sum of the squares on the four sides...
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