 | William Chauvenet - 1871 - 380 sider
...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...the opposite angle plus the square of the bisector. Let AD bisect the angle A of the triangle ABC; then, ABX AC=DBX DC + DA*. For, circumscribe a circle... | |
 | William Chauvenet - 1871 - 380 sider
...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 from the vertex... | |
 | William Chauvenet - 1872 - 382 sider
...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...the opposite angle plus the square of the bisector. Let AD bisect the angle A of the triangle ABC; then, AB X AC= DBXDC + DA\ For, circumscribe a circle... | |
 | William Chauvenet - 1872 - 382 sider
...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 sider
...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... | |
 | 1876 - 646 sider
...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 from the vertex... | |
 | Aaron Schuyler - 1876 - 384 sider
...bisector. 8. The rectangle of any two sides of a triangle is equivalent to the rectangle of the external segments of the third side formed by the bisector of the opposite exterior angle, minus the square of the bisector. 9. The area of a triangle is equal to the product... | |
 | George Albert Wentworth - 1877 - 416 sider
...Show that as PA is to PK so is CF to CE, and so also is PH to PB. PROPOSITION XVIII. THEOREM. 299. In any triangle the product, of two sides is equal...side formed by the bisector of the opposite angle together with the square of the bisector. 4 /'""^TV V /V-" It! //"/ V; i Let Z BA C of the AA BC be... | |
 | George Albert Wentworth - 1877 - 436 sider
...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...third side formed by the bisector of the opposite anyle together with the square of the bisector. . ! Dí Let ¿BAC ofthe A ABC be bisected by the straight... | |
 | George Albert Wentworth - 1877 - 416 sider
...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 to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex... | |
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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. 
