| 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 - 536 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 - 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... | |
| 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 - 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... | |
| 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 - 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... | |
| 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 - 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,... | |
| 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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