 | William Somerville Orr - Science - 1854 - 534 pages
...the circumference to the four corners of the parallelogram, will always amount to the same sum. 7. In any quadrilateral the sum 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 linn joining the middle points... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...AB°•=oAE*+EB*+1EBxED (p. 13). Hence, by adding and observing that EB and EC are equal, we have ED C 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 tlte line... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...sine of the angle included between them ; that is, the area of ABCD is equal to 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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...12). And, B~ Fl1 C (P. 13). Hence, by adding and observing that EB and EC are equal, we have (lor. 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 tf1e line... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 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 А В С D be any quadrilateral, the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 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 _C... | |
 | 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
...any finite quantity, say 60. Find the values of the sides of the quadrilateral O y VR, and prove that the sum of the squares of the four sides, is equal to the area of the circle X Z. I must premise, that if you, Sir, were to assert that the solution of this... | |
 | James Smith - Circle-squaring - 1869 - 459 pages
...any finite quantity, say 60. Find the values of the sides of the quadrilateral O y VR, and prove that the sum of the squares of the four sides, is equal to the area of the circle X Z. I must premise, that if you, Sir, were to assert that the solution of this... | |
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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. 
