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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. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Pągina 156
per Euclides - 1821
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - 1872 - 102 pągines
...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,...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pągines
...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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 pągines
...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...
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A Synopsis of Elementary Results in Pure and Applied Mathematics, Volum 1,Part 1

George Shoobridge Carr - 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...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pągines
...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...
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Elements of Plane Geometry

Franklin Ibach - 1882 - 208 pągines
...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...
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Wentworth & Hill's Exercise Manuals: Geometry, Edició 3

George Albert Wentworth - 1884 - 264 pągines
...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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A Synopsis of Elementary Results in Pure Mathematics: Containing ...

George Shoobridge Carr - 1886 - 1036 pągines
...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...
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Exercise Manuals, Edició 3

George Albert Wentworth - 1889 - 276 pągines
...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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Principles of Plane Geometry

James Wallace MacDonald - 1894 - 76 pągines
...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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