 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 of the bisector.  Annual Statement - Page 531876Full view - About this book
 | Richard Townsend - Geometry, Modern - 1863 - 328 pages
...therefore pd = bc, qd — ca, rd = ab, and therefore generally — In every triangle the product of any two sides is equal to the product of the diameter of the circumscribing circle into the perpendicular on the third side from the opposite vertex. This property... | |
 | 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...circumscribed circle by the perpendicular let fall upon the tidrd side from the vertex of the opposite angle. Let AB, AC, be two sides of a triangle ABC, AD the... | |
 | William Chauvenet - Geometry - 1871 - 380 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 product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.... | |
 | William Chauvenet - Geometry - 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 product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.... | |
 | 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 the qnaru of... | |
 | William Chauvenet - Geometry - 1875 - 390 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...third side from the vertex of the opposite angle. Let AB, AC, be two sides of a triangle AB C, AD the perpendicular upon BC, AE the diameter of the circumscribed... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...the above equality BD XD С for ED XAD, then BAX AC = ВD X DC + Tff. PROPOSITION XIX. THEOREM. 300. In any triangle the product of two sides is equal...third side from the vertex of the opposite angle. Let ABC be a triangle, and AD the perpendicular from A to B С. Describe the circumference ABC about... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...equality BDXD С for EDXAD, then BAX AC = BDX DC+Tl?. PROPOSITION XIX. THEOREM. 300. In any triangle ihe product of two sides is equal to the product of the...third side from the vertex of the opposite angle. Let ABC be a triangle, and AD the perpendiculai ¿rom A to B С. Describe the circumference ABC about... | |
 | 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 the square of... | |
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