 | Euclides - 1821 - 294 pages
...PROP, 11. THEOR, In every quadrilateral Jigure (ABCD) 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 fine (EF) joining the points of bisection of the did' gonals. .. 23. Join EA, ED. Then the sum of the... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...PROPOSITION XVI. — THEOREM. 249. 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 straight line that joins the middle points of the diagonals. Let А В С D be any quadrilateral, the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...PROPOSITION XVI. — THEOREM. 249. 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 straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the _C... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...PROPOSITION XVI. — THEOREM. 249. 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 straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the diagonals... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION XVI. — THEOREM. 249. 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 straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the diagonals... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...AC* = DP. 63. Corottary I. 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. For, let E and F be the middle points of the diagonals... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...63. Corollary I. In any quadrilateral, the sum of the squares of the four sides is equal to the sura of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. For, let E and F be the middle points of the diagonals... | |
 | 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... | |
 | 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,... | |
 | 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,... | |
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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. 
