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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 ... - Side 180
af Euclides - 1816 - 528 sider
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879 - 376 sider
...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 - 1879 - 282 sider
...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 sider
...to the whole 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,...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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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 sider
...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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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 sider
...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 geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 sider
...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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Introduction to Plane Trigonometry

Thomas Grenfell Vyvyan - 1882 - 150 sider
...point of BC, shew that 62 =cs+ -JCHAPTER XII. CIRCLES RELATED TO THE TRIANGLE. 46. To find the radius of the circle described about the triangle. Let ABC be a triangle: describe a circle about it, and draw BD perpendicular to BC to meet the circle in D : join CD. (See...
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Geometrical Exercises for Beginners

Samuel Constable - 1882 - 222 sider
...last.] 13. Prove that the rectangle contained by a side of this square and a line equal to the sum of the sides of the triangle is equal to the rectangle contained by the sides. 14. Inscribe a square in any triangle; and prove that the rectangle contained by a side...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 sider
...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 segments of the base, together with the square on the straight line which bisects the angle. Let...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 sider
...to that included by them. If from the vertical angle of a triangle a perpendicu1ar be drawn to tJie base, the rectangle contained by the sides of the...by the perpendicular and the diameter of the circle circumscribed about the triangle. A Let ABC be a triangle, AD the perpendicular from A on the base...
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