 | Edward Olney - Geometry - 1872 - 102 pages
...trisect the sides, etc. 675- In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the line joining the centres of the diagonals. 677. In any quadrilateral which may be inscribed in a circle,... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...parallelogram, the diagonals bisect one another, and the line EF vanishes; therefore in a parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. EXERCISES ON BOOK II. 1. In a right-angled triangle, the square upon the... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...distance. PROPOSITION VIII. 12. In any quadrilateral, the sum of the squares of the four tides it equal to the sum of the squares of the diagonals plus four times the square of the line which joins the middle points of the diagonals. Let ABCD be any quadrilateral, and let E and F... | |
 | 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... | |
 | Charles Scott Venable - 1881 - 380 pages
...segments (parts) of the chords is equal to 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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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. 
