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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... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 180
af Euclides - 1816 - 528 sider
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 sider
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 sider
...&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...
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Geometrical Propositions Demonstrated, Or, a Supplement to Euclid: Being a ...

William Desborough Cooley - 1840 - 106 sider
...; 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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 sider
...&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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 sider
...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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 sider
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 338 sider
.... 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 sider
...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....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 sider
...&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...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 sider
...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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