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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 - Side 145
av Euclid - 1838 - 416 sider
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...one and equal to another given rectilineal figure. 6. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle...diameter of the circle described about the triangle. The rectangle contained by the two sides can never be less than twice the triangle. EUCLID. BOOKS I....
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National Society's Monthly Paper

1856
...the ratio compounded of the ratios of their sides. 3. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle...the perpendicular, and the diameter of the circle deseribed about the triangle. SECT. II. — I . If the line bisecting the vertical angle of a triangle...
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Elements of Geometry and Conic Sections

Elias Loomis - 1857 - 226 sider
...external segments. PROPOSITION XXIX. THEOREM. If an angle of a triangle be 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 of the...
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Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 sider
...external segments. PROPOSITION XXIX. THEOREM. If an angle of a triangle be 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 of the...
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Parliamentary Papers, Volum 7

Great Britain. Parliament. House of Commons - 1859
...similar to another given rectilineal figure. 4. If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle...diameter of the circle described about the triangle. 5. Given the perimeter and the angles of a triangle ; required to construct it geometrically. Required...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 sider
...the radius of the circle. 2. 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 straight line which bisects the angle. If...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - 1859
...triangles of the same circle. 8. 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 straight line which bisects the angle. 9....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 sider
...Wherefore, if an angle, &c. UKI). PROPOSITION C. THEOREM. If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle...perpendicular from the angle A to the base BC. The rectangle .B^, AC shall be equal to the rectangle contained by AD and the diameter of the circle described about...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...together with the square on AD. PROPOSITION C. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle...diameter of the circle described about the triangle. Given a triangle ABC, and AD the perpendicular from the angle A to the base BC ; to prove that the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 317 sider
...sector PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likewse cuts the base; the rectangle contained by the sides of the triangle is equal to th« rectangle contained by the segments of the base, together with the square of the straight line...
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