 | Euclides - 1821 - 294 páginas
...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 páginas
...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... | |
 | Andrew Bell - 1837 - 290 páginas
...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 - 1855 - 628 páginas
...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 páginas
...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 páginas
...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 - 1862 - 532 páginas
...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 - 1863 - 504 páginas
...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 - 1868 - 340 páginas
...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 páginas
...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... | |
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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. 
