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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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Examination Christmas,1875

Education Department,London - 1876 - 1010 pages
...eight times either of the other two. 2. 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. If all the angles of...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...one another, the remaining sides shall be in a straight line. . . . . . . . . . . . . , . . . 240 Б. 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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...the same ratio as the arcs which subtend them ; and so also have the sectors. PROPOSITION B. THEOREM. If an angle, of a triangle be bisected by a straight line, which likeivise 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, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 pages
.... VL 3. ... Vi. A. (p. 76). HYPOTHESES. [f several parallels be drawn to the base of a triangle. [f an angle of a triangle be bisected by a straight line, which likewise cuts the base. Idem If a straight line bisects both the angle and base of a triangle. If from...
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Proceedings

Scotland free church, gen. assembly - 1876 - 1124 pages
...binomial theorem. 4. Find the sum of the series l H --- h -5-, etc., to infinity. x z1 If the vertical angle of a triangle be bisected by a straight line, which also счй the base, the segments of the base shall have the same ratio which the other eiclcs of the triangle...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...find the angles which this line makes with the two sides of the original triangle. 8. 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. If ABC be the triangle,...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 126 pages
...sides AB and AC of the given triangle. 8. 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. If ABC be the triangle,...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...the triangle, beyond the side opposite to tte obtuse angle. PROP, xxxix. THEOREM. (E. 6. 3). If any angle of a triangle be bisected by a straight line...which also cuts the base, the segments of the base hare to one another the same ratio which the adjacent sides have and the rectangle contained by the...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878 - 228 pages
...Describe a square about a given circle. 6. 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. Given the base and the...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 412 pages
...equiangular to a given triangle. 6. Define ratio, proportion, ex aequali, and part. 7. 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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