 | Isaac Newton, Edmond Halley - 1720 - 312 sider
...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 - 1755 - 532 sider
...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 - 1819 - 574 sider
...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... | |
 | Euclides - 1821 - 294 sider
...the circle of which this besecting line i» radius. PROP, 11. THEOR, In every quadrilateral Jigure (ABCD) the sum of the squares of the sides is equal to the sum of the squares of the diagonals, plus four times the square of the fine (EF) joining the points of bisection... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 sider
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 sider
...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;... | |
 | Euclid, James Thomson - 1837 - 410 sider
...bisect one another. PROP. C. THEOR. THE sum of the squares of the sides of a trapezium is equal to the sum of the squares of the diagonals, together with four times the square of the straight line joining the points of bisection of the diagonals. Let ABCD be a trapezium, having its... | |
 | Euclides - 1840 - 192 sider
...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... | |
 | Euclid, James Thomson - 1845 - 382 sider
...bisect one another. PROP. C. THEOB. — The sum of the squares of the sides of a trapezium is equal to the sum of the squares of the diagonals, together with four times the square of the straight line joining the points of bisection of the diagonals. Let ABCD be a trapezium, having its... | |
 | Alfred Wrigley - 1845 - 222 sider
...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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Prove that in any quadrilateral the sum of the squares of the sides is equal to the sum of the squares of the diagonals, increased by four times the square of the line joining the middle points of the diagonals. 
