 | James Smith - 1870 - 634 pages
...Young, a living " recognised Mathematician" gives the exercise in the following terms : — Prove that " 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 line joining the middle points... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...a diameter at its extremity is a tangent to the circumference. 4. Prove that In every parallelogram the sum of the squares of the four sides is equal to the sum of the squares of the diagonals. ENGLISH. GRAMMAR. And is this Yarrow? This the stream Of which my fancy cherished... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...Subtracting the second equation from the first, we have X DP; that is, 2d. AB' — 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 times the square of the line joining the middle points of the diagonals.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...first, we have B* — ^C* = 2(BD + DC) X DP; _ 2d. AB* — 'AC* = 2BC X DP. that is, 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 square of the line joining the middle points... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...second equation from the first, we have X DP; that is, 2d. AB* — 1C* = 2BC X DP. 63. Corollary 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 times the square of the line joining the middle points of the diagonals.... | |
 | Euclid - Geometry - 1872 - 284 pages
...of the squares of AP and PD 3 equal to double the square of AO and double the square of PO ; hence, the sum of the squares of the four sides is equal to four times the square of BP, four times the square of AO. and four times the square of PO, that is,... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...BD*; hence, finally, AB* + BC* + CD* + DA* = AC* + BD* + 4EF*. 64. Corollary II. In a parallelogram, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals. For if the quadrilateral in the preceding corollary is a parallelogram, the... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...AB2+AC2=2AD2 + 2DB2. Therefore, in any triangle, etc. PROPOSITION XV. THEOREM. In every parallelogram, the sum of the squares of the four sides is equal to the sum of the squares of the diagonals. Let ABCD be a parallelogram, of which the A p diagonals are AC and BD; the... | |
 | Elias Loomis - 1880 - 456 pages
...as a system of lines passing through a common point at an infinite distance. PROPOSITION VIII. 12. 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 which joins the middle points of the... | |
 | Charles Scott Venable - 1881 - 380 pages
...the square of the diameter. 1 6. In any quadrilateral 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 straight line which joins the middle points of these diagonals. 17. The sum of the squares on 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. 
