 The sum of the squares of the four 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 mid-points of the diagonals.  Analytic Geometry - Page 16by Wallace Alvin Wilson - 1915Full view - About this book
 | George Washington Hull - Geometry - 1807 - 408 pages
...quadrilateral form a parallelogram. 262. The perimeter of the parallelogram formed by joining the middle points of the four sides of any quadrilateral is equal to the sum of the diagonals of the quadrilateral. 253. The difference of the squares of two sides of any triangle is... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the other two sides. 34. The sum of the squares of the sides of any quadrilateral is equivalent to the sum of the squares of the diagonals, increased by four times the square of the line joining the centers of the diagonals. 35. If, from any point in a circumference, perpendiculars be let fall on... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...the other two sides. 34. The sum of the squares of the sides of any quadrilateral is equivalent to the sum of the squares of the diagonals, increased by four times the square of the line joining the centers of the diagonals. 35. If, from any point in a circumference, perpendiculars be let fall on... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the other two sides. 34. The sum of the squares of the sides of any quadrilateral is equivalent to the sum of the squares of the diagonals, increased by four times the square of the line joining the centers of the diagonals. 35. If, from any point in a circumference, perpendiculars be let fall on... | |
 | Sir William Henry Maule - 1872 - 314 pages
...conic sections ? Try this problem of Euler, which I intended to propose to you, but think I forgot : The sum of the squares of the four sides of any quadrilateral figure = the sum of the squares of its diagonals + four times the square of the line joining the middle... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...projection of m on 6. AL ^ — ! — r ^o 2 = Then, Also, (212). GEOMETRY— BOOK 111. 214. Corollaries. 1. The sum of the squares of the four sides of any quadrilateral is equivalent to the sum of the squares of the diagonals, plus four times tlie square of the line joining... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...the second equality from the first. Then AT? - ,ГС2 = 2 B С XM D. PROPOSITION XII. THEOREM. 339. The sum of the squares of the four sides of any quadrilateral is equivalent to the sum of tl'e squares of the diagonals together with four times the square of the line... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...PROPOSITION XIV. THEOREM. 344. In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals, increased by four times the square of the Ihte joining the middle points of the diagonals. B Let E and F be the middle [joints of the diagonals... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...Draw DE, making Z CDE=ZADB. The A ABD and CDE are similar. Also the A BCD and ADE are similar. 239. The sum of the squares of the four sides of any quadrilateral 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... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...and ADE are similar. 239. The sum of the squares of the four sides of any quadrilateral 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. HINT. Join the middle points F, E, of the diagonals. Draw EB and ED.... | |
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