 | George Shoobridge Carr - Mathematics - 1880
...MISCELLANEOUS PROPOSITIONS. 924 ТЬе sum of the squares of the sides of a 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. (922, i.) 925 COR. — The sum of the squares ^_ of... | |
 | Elias Loomis - 1880 - 456 pages
...as a system of lines passing through a common point at an infinite distance. PROPOSITION VIII. 12. In any quadrilateral, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four times the square of the line which joins... | |
 | Charles Scott Venable - 1881 - 380 pages
...the square of the diameter. 1 6. In any quadrilateral 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 straight line which joins the middle points of these diagonals. 17. The sum of the squares on the diagonals... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...DP. QED (260) (259) THEOREM X. 262. TJie sum of the squares of the sides of any quadrilateral equals the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. In the quadrilateral AB CD, let EF be the line joining... | |
 | George Albert Wentworth - 1884 - 264 pages
...of the diagonals (Ex. 19.) 23. 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. (Ex. 19.) 24. The sum of the squares of the diagonals... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...same squares is equal to or2. 924 The sum of the squares of the sides of a 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. (922, i.) 925 Сов. — The sum of the squares of... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...(1) and (2), we have AC2+ BC2= 2 A&+ 2 CD2. Subtracting (2) from (1), 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... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...I. In any quadrilateral (not a parallelogram) the sum of the squares of the four sides 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. COROLLARY II. In a parallelogram the sum of the squares... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...I. In any quadrilateral (not a parallelogram) the sum of the squares of the four sides 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. COROLLARY II. In a parallelogram the sum of the squares... | |
 | George Albert Wentworth - 1889 - 276 pages
...of the diagonals (Ex. 19.) 23. 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. (Ex. 19.) 24. The sum of the squares of the diagonals... | |
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In any quadrilateral the sum of the squares of the four sides 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. 
