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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: The Errors by which Theon, Or Others, Have Long ... - Page 169
by Robert Simson - 1827 - 513 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...an angle, PROPOSITION C. TREOn. — If from any angle of a triangle a straight line be Sr N. drawn perpendicular to the base, the rectangle contained...AD the perpendicular from the angle A to the base ItC : the rectangle HA, AC shall be equal to the rectangle contained by AD and the diameter of the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...PROP. B. THEOR. See N. 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 - 1836 - 488 pages
...if an angle, &c. QED PROP. C. THEOR. Book VI. from any angle of a triangle a straight line be drawn perpendicular to the base ; the rectangle contained...the perpendicular, and the diameter of the circle descri: bed about the triangle. \Let ABC be a triangle, and AD the perpendicular from the angle A to...
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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 Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...have the sectors. B. 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, to. gether with the square of the straight line bisecting the angle. C. If...
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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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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 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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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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