 | George Washington Hull - 1807 - 408 pàgines
...quadrilateral form a parallelogram. 262. The perimeter of the parallelogram formed by joining the middle points of the four sides of any quadrilateral is equal to the sum of the diagonals of the quadrilateral. 253. The difference of the squares of two sides of any triangle is... | |
 | Euclides - 1821 - 294 pàgines
...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 pàgines
...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 - 1855 - 628 pàgines
...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 - 1862 - 532 pàgines
...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 pàgines
...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 pàgines
...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 pàgines
...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... | |
 | Edward Olney - 1872 - 96 pàgines
...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 is equivalent... | |
 | Edward Olney - 1872 - 102 pàgines
...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, the product... | |
| |
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. 
