 | Euclides - 1838 - 264 pages
...QE o. PROP. B. THEOR. Jf an angle of a triangle be bisected by a straight line, which likewise cuts the base; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the segments of the base, together toith the square of the straight line which bisects the angle. Let... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...&c. QED PROP. B. THEOR. IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle.* Let ABC... | |
 | William Desborough Cooley - Geometry - 1840 - 106 pages
...; consequently, AD'AF = AF2+BF'FC, and since BA'AC =AD'AF, it follows, that BA'AC = AP + BF'FC, or the rectangle contained by the sides of the triangle, is equal to the square of the line bisecting the contained angle, together with the rectangle under the segments of... | |
 | Euclides - Geometry - 1841 - 378 pages
...&c. QED PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likewise cuts the base; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle. Let ABC... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...DA2. But ED. DA=BD.DC, therefore BA.AC = BD.DC +DA2. PROP. C. THEOR. If from any angle of a triangle a straight line be drawn perpendicular to the base...triangle, and AD the perpendicular from the angle A to the bake BC ; the rectangle BA.AC is equal to the rectangle contained by AD and the diameter of the circle... | |
 | Euclides - 1842 - 316 pages
...Wherefore, if an angle, &c. QED EUC. B. VI. OF GEOMETRY. PROP. C. THEOR. IF from any angle of a triangle a straight line be drawn perpendicular to the base...rectangle contained by the sides of the triangle is equivalent to the rectangle contained by the perpendicular and the diameter of the circle described... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
.... But ED. DA=BD.DC, therefore BA.AC = BD.DC +DA 2 . PROP. C. THEOR. If from any anglt of a triangle a straight line be drawn perpendicular to the base;...diameter of the circle described about the triangle. Describe (Prop 5. 4.) the circle ACB about the triangle, and draw its diameter AE, and join EC ; Because... | |
 | Euclides - 1845 - 546 pages
...square of AD. Wherefore., if an angle, &c. QED PROPOSITION C. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base...contained by the sides of the triangle is equal to Ike rectangle contained by the perpendicular and the diameter of the circle described about the triangle.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...&c. PROP. B. THEOB. — If an angle of a triangle be bisected by a straight line which likewise cuts the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the segments of the base, together with the square of tide straight line bisecting the angle. Let ABC... | |
 | Euclid - Geometry - 1845 - 218 pages
...PROPOSITION B. THEOR. — If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle. Let ABC... | |
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Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the... 
