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" If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the... "
A Supplement to the Elements of Euclid - Page 326
by Daniel Cresswell - 1819 - 410 pages
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...fi. ED PROP. C. THEOR. If from any angle of a triangle a straight line be drawn ' perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Geometrical Propositions Demonstrated, Or, a Supplement to Euclid: Being a ...

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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...circles, &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...square of the straight line bisecting the angle. Let ABC be a triangle, and let the angle BAC be bisected by the straight line AD; the rectangle BA, AC...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...BD.DC +DA2. PROP. C. THEOR. If from any angle of a triangle a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular, and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...to sectors. 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 equivalent to the rectangle contained by the segments of the base, together with the square of the...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...PROPOSITION C. THEOR. — If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...exterior angle, &c. PROP. D. THEOR. — If from an angle of a triangle a perpendicular be drawn to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. * From this proposition...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...QED PROPOSITION C. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base ; the rectangle 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 Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...rop 6" PROP. LXXIX. THEOR. If from any angle of a triangle a straight line be drawn perpendicular to the base; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a ^X and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...BD.DC +DAť. PROP. C. THEOR. If from any angltofa triangle a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular, and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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