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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... "
A Supplement to the Elements of Euclid - Page 367
by Daniel Cresswell - 1819 - 410 pages
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 366 pages
...inside or outside. 21. 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. 22. The...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...circles, &c. 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 Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...PROPOSITION B. THEOREM. 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 - Euclid's Elements - 1837 - 332 pages
...PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likewise cuts the Lose; 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 stra ght line bisecting the angle. Let ABC...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

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...
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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
...&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: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...together with the square of AD. 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...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...the rectangle BD, DC, together with the square of AD. Wherefore., if an angle, &c. QED PROPOSITION C. THEOREM. If from any angle of a triangle a straight...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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