 | Pierce Morton - 1830 - 584 ページ
...Therefore, &c. PROP. 41. The squares of the four sides tf a quadrilateral are together greater than the squares of its diagonals, by four times the square of the straight line which joins the middle points of the diagonals. Let А В С D be a quadrilateral, and... | |
 | 1835 - 684 ページ
...Therefore, SEC. PROP. 41. The squares of the four sides of a quadrilateral are together greater than the squares of its diagonals, by four times the square of the straight line which joins the middle points of the diagonals. Let А В С D be a quadrilateral, and... | |
 | Adrien Marie Legendre - 1852 - 436 ページ
...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 Davies, William Guy Peck - 1855 - 628 ページ
...the squares of the two diagonals is equivalent to the sum of the squares of the four sides diminished by four times the square of the line joining the middle points of .he diagonals ; that is, AC* + BD»o AB» + BC1 + CD3 + DA1 - 4EF1. If the quadrilateral is a parallelogram,... | |
 | War office - 1858 - 578 ページ
...(2*-3)0-5) = 103. 3. Show that the squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square...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 ページ
...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... | |
 | James Smith - 1869 - 492 ページ
...of the squares of the four sides is equal to the sum of the squares of the diagonals, together with four times the square of the line joining the middle points of the diagonals" Now, when the diameter of the circle Z=8,then, — £---* = — = 7, and this is the length of the... | |
 | James Smith - 1869 - 459 ページ
...the squares of the four sides is equal to the sum of the squares of the diagonals •, together with four times the square of the line joining the middle points of the diaOA 4- AH gonals? Now, when the diameter of the circle Z = 8,then, - — 4—+_3 — L ="7 and this... | |
 | James Smith - 1870 - 634 ページ
...of the squares of the four sides, is equal to the sum of the squares of the diagonals, together with four times the square of the line joining the middle points of the diagonals^ JM Wilson, Mathematical Master of Rugby School, and the most recent author of a Treatise on " Elementary... | |
 | Ephraim Chambers - 1870 - 872 ページ
...sum of the squares of its diagonals is equal to the sum of the squares of the sides, together with four times the square of the line joining the middle points of the diagonals ; if it can Ъе inscribed in a circle (ie, if its four corners are in the circumference of any circle),... | |
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... by four times the square of the line joining the middle points of the diagonals. 
