 | Jacques Ozanam - Mathematics - 1803 - 548 pages
...respecting any kind of quadri. lateral figures whatever. THEOREM v. In every quadrilateral figure whatever, the sum of the squares of the four sides, is equal to the sum of the squares of the two diagonals, plus four times the square of the line which joins the middle of these... | |
 | William Nicholson - Natural history - 1809 - 726 pages
...the contiguous sides in, if only impelled by the force corresponding thereto. 6. In any trapezium, the sum of the squares of the four sides is equal to the §um of the squares of the two diagonals together with four times the square of the distance between... | |
 | Edward Augustus Kendall - Encyclopedias and dictionaries - 1811 - 482 pages
...diagonals of every parallelogram is equal to the sum of the squares of the four sides. 4. In any trapezium, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals, together with four times the square of the distance between the middle... | |
 | Edward Augustus Kendall - 1811 - 474 pages
...diagonals of every parallelogram is equal to, the sum of the squares of the tour sides. 4 In any trapezinm, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals, together with four times the square of the distance between the middle... | |
 | William Nicholson - Natural history - 1819 - 424 pages
...of the contiguous sides in, if only impelled by the force corresponding thereto 6. In any trapezium, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals, together with four times the square 01 the distance between the middle... | |
 | William Nicholson - Natural history - 1819 - 426 pages
...the contiguous sides in, if only impelled by the force corresponding thereto. 6. In any trapezium, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals, together with four times the square of the distance between the middle... | |
 | Euclides - 1821 - 294 pages
...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... | |
 | Jacques Ozanam - 1840 - 850 pages
...Whence by adding we heve Ac3 + Bcs = 2A D2-f- 2o c2. THEOREM V. /я every quadrilateral figure whatever, the sum of the squares of the four sides, is equal to the sum of the squares of the two diagonals, plus Jour times the square of the line shich joins the middle of these... | |
 | Scottish school-book assoc - 1845 - 444 pages
...both sides. PROPOSITION XLV. — THEOREM. In any parallelogram the diagonals AD bisect each other, and the sum of the squares of the four sides is equal to the squares of the two diagonals. v AD is || to BC, the Z.ADE is = the £CBE, and the ^DAE is = the Z.ECB;... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...perpendicular AD. Then, And, BE~DC Hence, by adding and observing that EB and EC are equal, we have Cor. 1. In any 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... | |
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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 times the square of the line joining the middle points of the diagonals. 
