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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 366
by Daniel Cresswell - 1819 - 410 pages
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...bisect an angle of a triangle, and likewise cut the base ; the rectangle contained by the sides is equal to the rectangle contained by the segments of the base, together with the square of the bisecting line. Given ABC a triangle, and AD a straight line bisecting the angle BAC : then BAX AC=BDX...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...opposite Verniers. PROP. LXXVIII. THEOR. If an angle of a triangle be bisected by a straight line which cuts the base; the rect-angle contained by the sides of the triangle is eyual to the rectangle contained by the seyments of the base, together with, flu Let ABC be a bisect...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...QED PROP. B. THEOR. 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 shall be equal to the rectangle contained by the segments of the base, together with the square of...
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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
...angle. PROP. 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. PROP. D. THEOREM. The...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...etc. QED 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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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...base, together with the square of the straight line which bisects the angle. Section 3. 1. Show that equal triangles on equal bases have equal altitudes,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 340 pages
...sector EHF PROP. 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...the rectangle contained by the segments of the base, togfther with the square of the straight line bisecting tlte angle. Let ABC be a triangle, and 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...to the rectangle contained by the segments of the ha;e, together with the square of the straight line which bisects the angle. SECT. III.— 1. Show...
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