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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 ... - Side 169
av Robert Simson - 1827 - 513 sider
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...geometers. PROP. B. THEOREM If any 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. Let...
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National Society's Monthly Paper

1855
...mean ratio. 3. If an angle of a triangle he bisected by a straight line which likewise cuts the hase, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the ha;e, together with the square of the straight line which bisects the angle. SECT....
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...triangle is isosceles. The rectangle under the sides of the triangle is equal to the rectangle under the perpendicular and the diameter of the circle described about the triangle. The triangles on each side of it are si mil at to the whole triangle, and to one another. Eaon of the...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...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 contained...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
...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 contained...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
...another given rectilineal figure. 4. 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. 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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