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" The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 156
by Euclides - 1821
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Universal Arithmetick, Or, A Treatise of Arithmetical Composition and ...

Isaac Newton, Edmond Halley - Algebra - 1720 - 312 pages
...having reduc'd, AD = v/2 ЛС? -f 2 ABq — - В Cq. Whence, by the by, in any Parallelogram, the Sum 01 the Squares of the Sides is equal to the Sum of the Squares of the Diagonals. PROBLEM VIII. Having given the Angles of the Trapex>ium ABCD, alfo its Perimeter...
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The General Magazine of Arts and Sciences: Philosophical, Philological ...

Benjamin Martin - Science - 1755 - 536 pages
...the ReÔangle of the tranfvers and conjugate Diameters, (Set Ellipfis " Stone's DifiioaaryJ and the Sum of the Squares of the Sides is equal to the Sum of the Squares of the tranfverfe and conjugate Diameters j thai is, с Ь — xy, and o* + ┐╗ zz iZJ╗ i—...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...observing that EB = EC, we shall have AB + AC = ZAE + ZEB. 195. Corollary. In every parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. For the diagonals AC, BD (^.113), mutually bisect each PV. 113. other in...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...corresponding members, and observing that EB=EC, we shall have IB 195. Corollary. In every parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. AB + BC = 2AE + 2BE ; the triangle ADC gives likewise AD+DC= '2J~E + '2DE;...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...observing that EB = EC, we shall have IB + AC = 2J1E + 2EB. 1 95. Corollary. In every parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. the triangle ADC gives likewise AD 4 DC = adding the corresponding members...
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Geometrical Propositions Demonstrated, Or, a Supplement to Euclid: Being a ...

William Desborough Cooley - Geometry - 1840 - 106 pages
...squares of AC and CD (s. Prop. 64), together with four times ofFG. square PROP. LXVII. In a trapezium (ABCD), the sum of the squares of the sides is equal to the sum of the squares of the diagonals together with four times the square of the line (FG) joining their middle...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...of the bisecting line, and twice the square of half of the bisected side. 65. In a parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. 66. In a parallelogram the sum of the squares of the lines drawn from its...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...square of half the bisected side. (Euclid, ii. 12, 13. Cape, iii. 65.) 30. In a parallelogram, the sum of the squares of the sides is equal to the sum of the squares of the diagonals. (Euclid, ii. 13. Cape, iii. 65. Cor.) 31. If from the angles of a triangle,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...AC X BD sin AOD. 5. In any quadrilateral, the sum of the squares of the four sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the distance between the middle points of the diagonals ; that is, If the quadrilateral is a parallelogram,...
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National Society's Monthly Paper

1856 - 376 pages
...straight lines drawn from a given point in one of the sides. SECT. III. — 1. In a parallelogram the sum of the squares of the sides is equal to the sum ofthe squares of the diagonals. 2. If two straight lines intersect in a circle, the difference of their...
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