 | Benjamin Greenleaf - 1862 - 518 sider
...A square circumscribed about a given circle is double a square inscribed in the same circle. 28. If the sum of the squares of the four sides of a quadrilateral be equivalent to the sum of the squares of the two diagonals, the figure is a parallelogram. 29. Straight... | |
 | Benjamin Greenleaf - 1861 - 638 sider
...A square circumscribed about a given circle is double a square inscribed in the same circle. 28. If the sum of the squares of the four sides of a quadrilateral be equivalent to the sum of the squares of the two diagonals, the figure is a parallelogram. 29. Straight... | |
 | Benjamin Greenleaf - 1863 - 504 sider
...A square circumscribed about a given circle is double a square inscribed in the same circle. 28. If the sum of the squares of the four sides of a quadrilateral be equivalent to the sum of the squares of the two diagonals, the figure is a parallelogram. 29. Straight... | |
 | Benjamin Greenleaf - 1868 - 340 sider
...A square circumscribed about a given circle is double a square inscribed in the same circle. 28. If the sum of the squares of the four sides of a quadrilateral be equivalent to the sum of the squares of the two diagonals, the figure is a parallelogram. 29. Straight... | |
 | Euclid - 1872 - 284 sider
...under the greater segment and the difference of the segiii'ui s is equal to the square of the less. XX. The sum of the squares of the four sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals.... | |
 | William Frothingham Bradbury - 1877 - 262 sider
...ADXED . Adding these equations, observing that AD = DC, we have = 2 Z7? + 2 U172 THEOREM XXXI. 73 1 The sum of the squares of the four sides of a quadrilateral is equivalent to the sum of the squares of its diagonals plus four times the square of the line joining... | |
 | Cornell University - 1880 - 868 sider
...roots both of whole numbers and of fractions. 12. Find the fifth root of 14348907. II. GEOMETRY. 1. The sum of the squares of the four sides of a quadrilateral is equal to the sum of the squares of the two diagonals and four times the square of the line that joins the middle points of... | |
 | William Frothingham Bradbury - 1880 - 260 sider
...— 1ADY.ED ~ {- 2 DCXED Adding these equations, observing that AD = DC, we have THEOREM XXXI. 73 • The sum of the squares of the four sides of a quadrilateral is equivalent to the sum of the squares of its diagonals plus four times the square of the line joining... | |
 | John Casey - 1886 - 262 sider
...DE = BC ; .-. AD = DE ; hence (2) AC2 + CE2 = 2AD2 + 2DC2; but CE2 = BD2 ; .-. AC2 + BD2 = 2 AD2 + 2DC2 = sum of squares of the four sides of the parallelogram....sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals.... | |
 | John Casey - 1888 - 279 sider
...produce AD to meet CE. Now, AD = BC (xxxiv.), and DE = BC ; .-. AD = DE ; hence (2) AC2 + CE2 = 2AD2 + 2DC2 ; but CE2 = BD2 ; .-. AC2 + BD2 = 2AD2 + 2DC2...— The sum of the squares of the four sides of a of the squares of its diagonals plus four times the square of the line joining the middle points of... | |
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The sum of the squares of the four sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. 
