 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...of the four sides of a quadrilateral figure is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. PROPOSITIONS IN EUCLID WHICH MAY BE SET TO BE WRITTEN OUT WITH THE EIDERS. NtJMBER OF RIDER. 1 2 3... | |
 | Seth Thayer Stewart - Geometry - 1891 - 426 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. 101. Prove that, if the squares of the sides of a quadrilateral are together equivalent to the squares... | |
 | Seth Thayer Stewart - Geometry - 1893 - 262 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. I. Assume the construction, E and F being middle points of the diagonals. 2. Ä W + /TO5 = 2 DT2 +... | |
 | John Casey - Geometry - 1895 - 216 pages
...squares of the four sides of a quadrilateral is equal to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. ~~~~~^-o Dem.— Let ABCD be the quadrilateral, E, F the middle points of the diagonals. Now, in the... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...sum of the squares of the sides of any quadrangle equals the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals. 5. Show that in a trapezoid, the sum of the squares of the diagonals equals the sum of the squares... | |
 | George Albert Wentworth - Geometry - 1896 - 296 pages
...the four sides of any quadrilateral is. equal to the sum of the squares of the diagonals increased by four times the square of the line joining the middle points of the diagonals. Let ABCD be a quadrilateral, and EF the line joining the middle points of the diagonals AC and BD.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...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. 157 Hint.— Apply § 355, I. to the triangles ABC, ADC, and BED, and combine equations thus obtained.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...of the four sides of a quadrilateral is equivalent to the sum of the squares of its diagonals plus four times the square of the line joining the middle points of the diagonals. Appl. Prove AI? + B(f + Cff + DA* = AC* + BD* + 4 EF~ Cons. Draw BF and DF Dem. AB * +BC * = 2AF *... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...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. '57 Hint.— Apply § 355, I. to the triangles ABC, ADC. and BED, and combine equations thus obtained.... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...the four sides of any quadrilateral is equal to the sum of the squares of the diagonals, increased by four times the square of the line joining the middle points of the diagonals. 256. If one of the parallel sides of a trapezoid is double the other, each diagonal will cut off one... | |
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... by four times the square of the line joining the middle points of the diagonals. 
