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" If the vertical angle of a triangle be bisected by a straight line which also cute 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... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 147
by John Playfair - 1856 - 318 pages
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 382 pages
...ratio as the arcs which sab. tend them ; and so also have the sectors. PROPOSITION B. THEOREM. If an angle of a triangle be bisected by a straight line,...likewise cuts the base ; the rectangle, contained by th# sides of the triangle, is equal to the rectangle, contained by the segments of the base, together...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...angle. . . . . . . 240 C. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. . . . . . . . . . ....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...PROPOSITION C. THEOREM. If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...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 sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle circumscribing the triangle. Having given n points...
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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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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...quadrilateral inscribed in a circle intersect at right angles. 101. The rectangle contained by two sides of a triangle is equal to the rectangle contained by the segments of the third side made by a line bisecting the opposite angle, plus the square of the bisecting line. 102....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878 - 398 pages
...ratio as the arcs which subtend them ; and so also have the seciora. PROPOSITION B. THEOREM. If an angle of a triangle be bisected by a straight line,...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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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...BA.AC-BD.DC+AD\ Proposition 29. Theorem.—If from any angle of a triangle a perpendicular be drmvn to the base, the rectangle contained by the sides of...the triangle, is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...inscribed. 6. Triangles and parallelograms of the same altitude are to one another as their bases. 7. If an angle of a triangle be bisected by a straight line,...base, together with the square of the straight line which bisects the angle. 8. The angle subtended at the centre of a circle by an arc which is equal...
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 396 pages
...and BE, CD are joined by lines meeting in F. Prove that AF produced bisects BC. 11. If the vertical angle of a triangle be bisected by a straight line...the segments of the base, together with the square on the straight line which bisects the angle. 12. If two straight lines be parallel, and one of them...
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