 | 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... | |
 | Benjamin Martin - Science - 1755 - 532 pages
...the Reâangle 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—... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 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... | |
 | 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;... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 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... | |
 | 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... | |
 | Euclides - 1840 - 192 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... | |
 | 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,... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 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,... | |
 | 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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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. 
