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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 ... - Pągina 154
per Euclides - 1821
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Universal Arithmetick, Or, A Treatise of Arithmetical Composition and ...

Isaac Newton, Edmond Halley - 1720 - 272 pągines
...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 - 1755
...the Reāangle 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* + æ» zz iZJ» i—...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 pągines
...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 - 1825 - 224 pągines
...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...: Translated from the French for the Use of the ...

Adrien Marie Legendre - 1825 - 224 pągines
...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 - 1840 - 94 pągines
...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
...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
...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 - 1855 - 592 pągines
...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
...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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