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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: The Errors by which Theon, Or Others, Have Long ... - Page 169
by Robert Simson - 1827 - 513 pages
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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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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 222 pages
...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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Introduction to Plane Trigonometry

Thomas Grenfell Vyvyan - 1882 - 150 pages
...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...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 pages
...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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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 pages
...parallel. 11. 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. II....
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Examinations Papers

1885 - 522 pages
...divisions of this paper.) I. — 1. 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. 2. Prove that the tangent to a parabola at any point is the bisector of the angle which the focal distance...
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Weekly problem papers, with notes. [With] Solutions

John James Milne - 1885 - 392 pages
...cos (A - )}. 5. If the vertical 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 two lines equally inclined to the bisector, one terminated by the base and the other by the rircum-uircle....
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 pages
...extended to each of the escribed circles of the triangle ACB. 5. The rectangle contained by two sides of a triangle is equal to the rectangle contained by the perpendicular and the diameter of the circumscribed circle. For, let CE be the diameter. Join AE. Then the triangles ACE, DCB are equiangular...
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