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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; viz. the first six books, together with the eleventh ... - Page 165
by Euclides - 1834
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...inscribed circle, we may ghew that the rectangle contained by the sum of the perpendiculars and the sum of the sides of the triangle, is equal to the rectangle contained by the sum of the sides, and the sum of the radii of the inscribed and circumscribed circles. 20. Let...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...sectors. PROP. 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 equal to the rectangle contained by the segments of the base, together with the square of the straight line, which bisects the angle. PROP....
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...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 equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle. LET abc...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...PROPOSITION B. THEOR. 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 equal loathe rectangle contained by the segments of the base, together with the square of the straight line...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...are equal to the three sides of the triangle. 6. If from the angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...contained by the perpendicular and the diameter of the circumscribing circle. 7. Draw a straight line perpendicular to a given plane from a given point above...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...+DA2. PROP. C. THEOR. If from any anglt of a triangle a straight line be drawn perpendicular to tht base; the rectangle contained by the sides of the...contained by the perpendicular, and the diameter of thc circle described about the triangle. Let ABC be a triangle, and AD the perpendicular from the angle...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...extreme and mean ratio. 3. If an angle of a triangle he 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. Section...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...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 - 264 pages
...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 - 230 pages
...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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