| 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... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...points of a rectangle, the sums of the squares of those drawn to opposite angles are equal. 5. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of its diagonals, and four times the square of the line joining their middle points. 6. 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,... | |
| Euclides - 1860 - 142 pages
...former, we obtain DE2 + DF2 + FG= + GH2 + HK2 + KE2 = 3BC2 + 5BC2 = 8BC2. EXERCISE XVII. — THEOREM. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of its diagonals, and four times the square of the line joining their middle points. Let ABCD... | |
| Euclides - 1860 - 288 pages
...to eight times the square on the hypotenuse of the original triangle. 17. The sum of the squares on the sides of a quadrilateral is equal to the sum of the squares on its diagonals, and four times the square on the line joining their middle points. 18. 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,... | |
| 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,... | |
| 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,... | |
| 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,... | |
| 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... | |
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