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" If from the vertical 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... "
A Supplement to the Elements of Euclid - Page 326
by Daniel Cresswell - 1819 - 410 pages
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1878 - 398 pages
...seciora. 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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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
...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...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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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...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 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. 11. Prove that the circle...
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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
...PROPOSITION c. THEOREM:. If from the vertical 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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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 456 pages
...bisected by a line which 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 ofthe bisecting line. Let ABC be a triangle, and let the angle BAC be bisected by the straight line...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 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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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 is equal to the rectangle contained by the perpendicular end the diameter of the circli described about the triangle. • Let ABC be a triangle,...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 286 pages
...not, let B, E, F, and H be on the same circle. Let the student prove an impossibility. Proposition 28. Theorem. — If an angle of a triangle be bisected...segments of the base, together with the square of the line bisecting the angle. Let ABC be a triangle, and let the angle BA C be bisected by the straight...
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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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