 | Edward Olney - Geometry - 1872 - 96 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. 676. COR. — The sum of the squares of the sides of a parallelogram is equivalent... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...trisect the sides, etc. 675- In nny 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, the product... | |
 | 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, the product... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...the sum of the squares of its diagonals. Verify this by the case of the square. 13. Prove that the sum of the squares of the sides of a •quadrilateral is equal to the sum of the squares of its diagonals, with four times tlie square of the line joining their points of bisection.... | |
 | 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 be the... | |
 | 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... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...This the student can easily prove for himself. It is clearly a particular case of (II. 4.).] 3. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of its diagonals, together with four squares of the line joining the middle points of the diagonals.... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...if r, the radius of the sphere, be equal to OA, the sum of the 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.... | |
 | United States. War Department - 1895 - 1000 pages
...coefficients and sum of the same coefficients with alternate signs. 3. Geometry. — No. 2 — The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals, increased by four times the square of the segment which unites the middle... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...PROPOSITION VJLU. 12. In any quadrilateral, the sum of the squares of the four sides is equal to the gum 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 be the... | |
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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. 
