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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 - 1842 - 332 pages
...therefore (def. 5. 5.) as the arc BC, is to the arc EF, so is the sector BGC to the sector EHF. 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 J>f 'the triangle is equal to the rectangle...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...Theorem, (Proportion,) angle BAC : angle DEF :: вc : DF. The same reasoning applies 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...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...equal to a given rectilineal angle. 12. 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 one to another ; and if the segments...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...circumference EF, so is the sector BGC to the sector EHF. Wherefore, in equal circles, &o. QBD 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...
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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
...arc BC is to EF, so is the sector BGC to EHF. Wherefore, in equal circles, &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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...sector BGC to the sector EHF. (v. def. 5.)' Wherefore, in equal circles, &c. QED PROPOSITION B. THEOREM. If an angle of a triangle be bisected by a straight line, nhich lilcewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...therefore DE is parallel to BC. Wherefore, If a straight line $c. QED PROP. III. THEOR. If the vertical angle of a triangle be bisected by a straight line...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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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...corrected by taking the half sum, or mean, between the readings of two opposite Verniers. PROP. LXXVIII. THEOR. If an angle of a triangle be bisected by a straight line which cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained...
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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
...(def. 5. 5.) as the arc BC, is to the arc EF, so is the sector BGC to the sector EHF. 149 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 Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...corrected by taking the half sum, or mean, between the readings of two opposite Verniers. PROP. LXXVIII. THEOR. If an angle of a triangle be bisected by a straight line which cuts the base; the rect-angle contained by the sides of the triangle is eyual to the rectangle contained...
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