 | Frederick Augustus Griffiths - 1839 - 348 pages
...three angles of any triangle taken together are equal to two right angles, or 180°. The difference of the squares of two sides of a triangle is equal to the product of their sum and difference. The sides of a triangle are proportional to the sines of their... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...XvH. In any triangle, the sum of the squares of any 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 of this third side to the opposite angle. c If CD is drawn bisecting AB, we shall have AC2 + BC2 = 2AD2... | |
 | Frederick Augustus Griffiths - Artillery - 1859 - 426 pages
...three angles of any triangle, taken together, are equal to two right angles, or 180°. The difference of the squares of two sides of a triangle is equal to the product of their sum, and difference. The sides of a triangle are proportional to the sines of... | |
 | André Darré - 1872 - 226 pages
...are related to each other as the squares of the contiguous sides. 19. The sum of the squares of any two sides of a triangle is equal to twice the square of the line drawn from the vertex of the angle which the sides contain to the middle point of the opposite... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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 the opposite angle. Let ABC be any triangle, and EA a line drawn... | |
 | John Reynell Morell - 1875 - 220 pages
...coincides with the middle of the straight line which joins the two fixed points. 109. The difference of the squares of two sides of a triangle is equal to twice the product of the third side by the projection of the medial line of this last side on its direction.... | |
 | George Shoobridge Carr - Mathematics - 1880
...(p—q). [П. 12, 13, The following cases are important : — (i.) When p = q, 62+c2 = 2q*+2d2; ie, the sum of the squares of two sides of a triangle is equal to twice the square of half the base, together with twice the square of the bisecting line drawn from the vertex. (ii.) When... | |
 | Charles Scott Venable - 1881 - 380 pages
...square of the opposite side ; and if it is obtuse, the sum will be less. PROPOSITION XIV. THEOREM. The sum of the squares of two sides of a triangle is equivalent to twice the square of the median to the third side together with twice the square of half... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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 the opposite angle. AB~" + AC2 = 2BE2 + 2EA*. Draw AD perpendicular... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...(pq). [II. 12, 13. The following cases are important : — (i.) When p = q} Ъ*+с* = 2ç2+2tf ; ie, the sum of the squares of two sides of a triangle is equal to twice the square of half the base, together with twice the square of the bisecting line drawn from the vertex. (ii.) When... | |
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The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side. 
