| 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... | |
| Euclides - 1833 - 304 pages
...PROP. 11. THEOR. In every quadrilateral figure (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 line (EF) joining the points of bisection of the diagonals. Fig. 23. Join EA and ED. Then the sum of the... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...AC X BD sin AOD. 5. In any quadrilateral, the sum of the squares of the four sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the distance between the middle points of the diagonals ; that is, If the quadrilateral is a parallelogram,... | |
| 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 of the quadrilateral... | |
| 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 of the quadrilateral... | |
| Edward Olney - Geometry - 1872 - 562 pages
...as does ADANOTHER DEM.— Lines through O parallel to the sides 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... | |
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