| Euclides - 1821 - 294 sivua
...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 sivua
...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 sivua
...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 sivua
...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 sivua
...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 sivua
...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,... | |
| War office - 1858 - 578 sivua
...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... | |
| John Hymers - 1858 - 292 sivua
...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... | |
| Benjamin Greenleaf - 1862 - 532 sivua
...— 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 sivua
...— 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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