 | Euclides - 1821 - 294 σελίδες
...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 σελίδες
...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... | |
 | George Clinton Whitlock - 1848 - 338 σελίδες
...squares- of the sides of a (138) quadrilateral, exceeds the sum of the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. Cor. 4. The sum of the squares of the sides of a parallele- (139) gram, is equal to the sum of the... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...quadrilateral, the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals, plus four times the square of the line joining the middle points of the diagonals. Let ABCD be a quadrilateral, AC, BD, the diagonals, and EF a line join- D^ ing the middle points E... | |
 | Charles Astor Bristed - 1852 - 470 σελίδες
...THE squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. 2. The coefficient of x' in the expansion of (1 -fx) (l+cz) (1 + c'x) (1 + c'x)..., the number of factors... | |
 | Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...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,... | |
 | John Hymers - 1858 - 292 σελίδες
...sides of a quadrilateral figure is greater than the sum of the squares of its diagonals by TRIO. 20 four times the square of the line joining the middle points of the diagonals. 61. When a quadrilateral is capable of having both a circle inscribed in it and one circumscribed about... | |
 | War office - 1858 - 578 σελίδες
...the squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. 4. The faces of a pyramid on a square base are equilateral triangles, and each side of the base is... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...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 σελίδες
...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... | |
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The sum of the squares of the 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 middle points of the diagonals. 
