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" 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... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 55
by Euclides - 1840
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...the arch EF, so is the seetolh BGC to the sector EHFb. Wherefore, in equal 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 of the triangle is equal to the rectangle...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...so is the sector BGC to the sector EHF. Wherefore, in equal circles, &c. QED 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...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...which the circumferences on which they stand have to one another : so also have the 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 equal to the rectangle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...straight line, &c. QED PROP. HI. THEOR. IF the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another : And if the segments...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 490 pages
...and FL, and it is manifest, that the segment CL is equal to the segment BK. PROP. LV. 64. THEOREM. If an angle of a triangle be bisected by a straight line, which also cuts the base, the rectangle, contained by the sides of the triangle, is equal to the rectangle contained by the segments...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...angles by the straight line AD. Therefore, if the angle, &c. Q,. ED PROP. A. THEOR. If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced ; the segments between the bisecting line and the extremities of the base have the same ratio...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...the arch EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, &c. Q, ED 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 ist equal to the rectangle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...circumference EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, &c. Q, ED 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...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...triangle and the three angles to construct it. PROPOSITIONS IN PLANE GEOMETRY. 1816. 1 . IF the exterior angle of a triangle be bisected by a straight line which also cuts the base produced, the segments between the bisecting line and the extremities of the base, have the same ratio...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...and FL, and it is manifest, that the segment CL is equal to the segment BK. PROP. LV. 64. THEOREM. If an angle of a triangle be bisected by a straight line, which also cutis the base, the rectangle, contained by the sidea of the triangle. is equal to the rectangle contained...
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