 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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 pages
...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... | |
 | James Smith - Mathematics - 1869 - 492 pages
...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 - Circle-squaring - 1869 - 459 pages
...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... | |
 | Ephraim Chambers - Encyclopedias and dictionaries - 1870 - 872 pages
...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),... | |
 | James Smith - 1870 - 634 pages
...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... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...AC* = DP. 63. Corottary I. In any quadrilateral, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals plus four...the preceding theorem, we have in the triangle ABC, IS* + BC2 = 2AE* + 2BE*, and in the triangle ADC, CD*+DA* = 2lE* + 2DE*, whence, by addition, IS* +... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...63. Corollary I. In any quadrilateral, the sum of the squares of the four sides is equal to the sura of the squares of the diagonals plus four times the...the preceding theorem, we have in the triangle ABC, IS' + BC' = 2AE* + 2BE', and in the triangle ADC, CD* + 5T = 2AE* + 2DE*, whence, by addition, IS2... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...trisect the sides, etc. 675- In nny 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... | |
 | Edward Olney - Geometry - 1872 - 96 pages
...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... | |
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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. 
