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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; viz. the first six books, together with the eleventh ... - Page 165
by Euclides - 1834
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...sum of the co-efficients of the even terms. 11. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...by the perpendicular and the diameter of the circle circumscribing the triangle. Having given n points on the circumference of a circle, show that 3.4.5...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...external segments. PROPOSITION XXX. THEOREM. . If an angle of a triangle be bisected by a line lehich cuts the base, the rectangle contained by the sides of the triangle is equivalent to the rectangle contained by the segments of the base, together with the square of the...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...angle of a triangle a' straight line be drawn perpendicular to the base, the rectangle contained by tie sides of the triangle is equal to the rectangle contained...diameter of the circle described about the triangle. In the above figure, let ABC be a triangle, and let BE be the perpendicular from the angle B to the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878 - 398 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 eqvjil to the rectangle, contained by the segments of the base, together with the square on the line...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879 - 376 pages
...sq. on AD. III. 35. PROPOSITION C. THEOREM. If from any angle of a triangle a straight line be dravm perpendicular to the base, the rectangle, contained...circle described about the triangle. Let ABC be a A, and AD the _L from A to BC. Describe the ABC about the A ABC, III. B. draw the diameter AE, and...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...Proposition 28. Tlieorem.—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 of the base, together with the square of the line bisecting the angle. Let ABC be a triangle,...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...triangle the ratio of the base to a side. 10. If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...diameter of the circle described about the triangle. 11. Prove that the circle described through the middle points of the sides of a triangle passes also...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...another as their bases. 7. 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 which bisects the angle. 8....
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...X. 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 segments of the base, together with the square on the straight lino which bisects the angle. Let...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - Euclid's Elements - 1881 - 236 pages
...angle, &c. QED If from any angle of a triangle a straight line he drawn perpendicular to the bate ; the rectangle contained by the sides of the triangle...equal to the rectangle contained by the perpendicular end the diameter of the circli described about the triangle. • Let ABC be a triangle, and AD the...
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