 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...a triangle is equivalent to the rectangle contained by the diameter of the circumscribed circle and the perpendicular drawn to the third side from the vertex of the opposite angle. BOOK IT. scribed about the triangle ; then will ABXAC be equivalent to AD X CE. For,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...a triangle is equivalent to the rectangle contained by the diameter of the circumscribed circle and the perpendicular drawn to the third side from the vertex of the opposite angle. BOOK IV. A scribed about the triangle ; then will ABXAC be equivalent to AD X CE. For,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...a triangle is equivalent to the rectangle contained by the diameter of the circumscribed circle and the perpendicular drawn to the third side from the vertex of the opposite angle. BOOK IV. scribed about the triangle ; then will ABXAC be equivalent to ADX 0 E. For,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...a triangle is equivalent to the rectangle contained by the diameter of the circumscribed circle and the perpendicular drawn to the third side from the vertex of the opposite angle. BOOK IV. scribed about the triangle ; then will ABXAC be equivalent to AD X t!E. For,... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...triangle, the product of two sides equals the product of the diameter of the circumscribed circle and the perpendicular drawn to the third side from the vertex of the opposite angle. Let a O be circumscribed about the A ABC, and let CD be a diameter and CE a _L to AB.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...triangle, the diameter of the circumscribed circle is equal to the product of any two sides divided by the perpendicular drawn to the third side from the vertex of the opposite angle. PROPOSITION XXXII. THEOREM. 299. In any triangle, the product of any two sides is equal... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...and mean ratio. See Proposition XIX., and Book II., Proposition VII. Proposition XXI. A Theorem. 232. In any triangle, the product of any two sides is equal to the product of the perpendicular to the third side from the opposite angle by the diameter of the circumscribed... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...and mean ratio. See Proposition XIX., and Book II., Proposition VII. Proposition XXI. A Theorem. 232. In any triangle, the product of any two sides is equal to the product of the perpendicular to the third side from the opposite angle by the diameter of the circumscribed... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...chord DE cuts the chord AB at F, and the chord AC at G, prove that the angles AFG and AGF are equal. 6. In any triangle the product of any two sides is equal...perpendicular drawn to the third side from the vertex of the opposite angle. 7. Two triangles having an angle of one equal to an angle of the other, are to each... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...proportional (ยง 281). PROPOSITION XXXIII. TJIEOBEM. 286-. In any triangle, the product of any two sides w equal to the diameter of the circumscribed circle,...perpendicular drawn to the third side from the vertex of the opposite angle. Ii Let AD be the diameter of the circumscribed circle A CD of the triangle ABC, and... | |
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In any triangle, the product of any 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. 
