 | William Chauvenet - Geometry - 1871 - 380 pages
...parallelogram, the diagonals bisect each other, and the distance EF is zero. PROPOSITION XX.— THEOREM. 65. In any triangle, the product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the tidrd side... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...are similar, and give AB : AE = AD : AC, whence, AB X AC = AE X AD. PROPOSITION XXI.— THEOREM. 66. In any triangle, the product of two sides is equal to the produd of the segments of the third side formed by the bisector of the opposite angle plus the square... | |
 | United States Naval Academy - 1874 - 888 pages
...drawn, the angent is a mean proportional between the whole secant and its external segment. 'rove that in any triangle the product of two sides is equal to the product of the segnents of the third side formed by the bisector or the opposite angle together with... | |
 | 1876 - 646 pages
...which cuts off upon the line the greater distance from the foot of the perpendicular. Corollaries. 2. In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...Show that as PA is to PK so is С F to CE, and so also is PH to PB. PROPOSITION XVIII. THEOREM. 299. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite anyle together with... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...X AE. EXERCISE. If AB = 8, AC = 12, AD = 6, find diameter of the circumscribed circle. XL. Theorem. In any triangle, the product of two sides is equal to the product of the segments of the third side made by a line bisecting the opposite angle, plus the square... | |
 | Benjamin Gratz Brown - Geometry - 1879 - 68 pages
...the bisector of an angle divides the opposite side into segments proportional to the adjacent sides. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...above equality BOX DC for EDX AD, then BAX AC = BD XD С + AD\ '5. ED PROPOSITION XIX. THEOREM. 300. In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...constant). .-. AB x AC= AI? + DB x DC. Whence AD* = AB x AC— DB x DC. a ED PROPOSITION XXIV. THEOREM. 350. In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side. -.A Let ABC... | |
 | Yale University - 1892 - 200 pages
...which cuts off upon the line the greater distance from the foot of the perpendicular. Corollaries. 2. In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side... | |
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In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side. 
