 | 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... | |
 | 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...that joins the middle points of the diagonals. Let А В С D be any quadrilateral, the diagonals of which are AC, DB, and EF a straight lino joining... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagf>nu/s, plus four times the square of the straight line that...the diagonals. Let ABCD be any quadrilateral, the __C diagonals of which are AC, DB, and EF a straight line joining their middle points, E, F ; then... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diag-- onals, plus four times the square of the straight line that joins the middle points of the diagonals. Let AB CD be any quadrilateral, the diagonals of which are AC, DB, and EF a straight line joining their... | |
 | 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...the diagonals. Let ABCD be any quadrilateral, the _C diagonals of which are AC, DB, and EFa straight line joining their middle points, E, F ; then the... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 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...quadrilateral, the diagonals of which are AC, DB, and EP a straight line joining their middle points, E, F ; then the' sum of the squares of AB, BC, CD,... | |
 | 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...F ; then the sum of the squares of AB, BC, CD, AD is equivalent to AC2 + BD2 + 4 EF2. A Join ^ B and ED ; then in the triangle ABC, AB2 + B~C2 = 2TE2... | |
 | 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... | |
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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. 
