 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...PROPOSITION XIV. THEOEEM. In any triangle, the sum of the squares described on two sides is equivalent to twice the square of half the third side, plus twice the square of the line drawn from the middle point of that side to the vertex of the opposite angle. 102 For, on BC,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...PROPOSITION XIV. THEOREM. In any triangle, the sum of the squares described on two stdes is equivalent to twice the square of half the third side, plus twice the square of the line drawn from the middle point of that side to tl1e vertex of the opposite angle. Let ABC be any... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...method for determining the kind of triangle, when its sides are given (BI, T. XXXV., S.). THEOREM XvH. In any triangle, the sum of the squares of any two...equal to twice the square of half the third side, increased by twice the square of the line drawn from the middle of this third side to the opposite... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...THEOREM. In any triangle, the sum of the squares described on two s'det is equivalent to twice tJte square of half the third side, plus twice the square of the line drawn from the middle point of that side to the vertex of thi opposite angle. Let ABC be any triangle,... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...method for determining the kind of triangle. when its sides are given (BI, T. XXXV., S.). THEOREM XV1I. In any triangle, the sum of the squares of any two...sides is equal to twice the square of half the third aide, increased by twice the square of the line drawn from the middle of this third side to the opposite... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...described on the third side. PROPOSITION XIV. THEOREM. In any triangle, the sum of the squares described on two sides is equal to twice the square of half the third side increased by twice the square of the line drawn from the middle point of that s'ide to the vertex of... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...2bn (205). m2 + p2 = b~- + n2 +p* + 26n. a2 =&2 + c2 + 26n. 213. Proposition XIV.— Theorem. 1. /n any triangle, the sum of the squares of any two sides is equivalent to twice the square of half the third side, plus twice the square of the inedial line to... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...is a right angle (converse of 12). xv. Theorem. In any triangle, the sum of the squares described on two sides is equal to twice the square of half the third side, plus twice the square of the line drawn from the middle point of that side to the vertex of the opposite angle. HYPOTH. In the triangle... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...d' + 2 cd - - Th. VIII. .-. a - = b' - d ' + c' 2 + d' + 2 cd = 6" + e " + 2 c d. QED THEOREM XIV. In any triangle, the sum of the squares of any two...half the third side, plus twice the square of the medial line to that side. Let a, b, c, be the sides of a triangle, and m the medial line from C to... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...described on the third side. PROPOSITION XIV. THEOREM. In any triangle, the sum of the squares described on two sides is equal to twice the square of half the third side, increased by twice the square of the line drawn from the middle point of that side to the vertex of... | |
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In every triangle the sum of the squares of two sides is equal to twice the square of half the third side plus twice the square of the median drawn to the third side. 
