 | Euclides - 1821 - 294 σελίδες
...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... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...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 the middle points of the diagonals.... | |
 | Charles Davies - 1854 - 436 σελίδες
...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 joining tl1e middle points of the diagonals.... | |
 | William Somerville Orr - 1854 - 534 σελίδες
...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... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
...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 join1ng the middle points of the diagonals,... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...E С XED, we have ABS + ACa = 2 1~E8 + 2 E~B2PROPOSITION XV. — THEOREM. 248. In any parallelogram the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals. Let А В С D be any parallelogram, the diagonals of which are AC, BD ; then the... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...EBXED to ECXED, we have AB2 + AC2 = 2 AE2 + 2 EBaPROPOSITION XV. — THEOREM. 248. In any parallelogram the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals. Let ABCD be any parallelogram, the diagonals of which are AC, BD ; then the sum... | |
 | Benjamin Greenleaf - 1863 - 504 σελίδες
...to ECXED, we have AB2 + AC2 = 2 AE2 + 2 EB2. PROPOSITION XV. — THEOREM. 248. In any parallelogram the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals. Let ABCD be any parallelogram, DC the diagonals of which are AC, BD ; then the sum... | |
 | Benjamin Greenleaf - 1868 - 340 σελίδες
...EBXEDtoECXED, we have AB2 + AC2 = 2 AE2 + 2 E~B2. PROPOSITION XV. — THEOREM. 248. In any parallelogram the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals. Let ABCD be any parallelogram, the diagonals of which are AC, BD ; then the sum... | |
 | Benjamin Greenleaf - 1869 - 516 σελίδες
...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... | |
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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. 
