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" If the vertical angle of a triangle be bisected by a straight line which also cute 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 on the straight... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 147
by John Playfair - 1856 - 318 pages
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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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the sector BGC to the sector EHF. Wherefore, in equal circles, etc. QED PROPOSITION B. THEOR. If an angle of a triangle be bisected by a straight line...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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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 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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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...figure. 2. To cut a given straight line in extreme and mean ratio. 3. If an angle of a triangle he bisected by a straight line which likewise cuts the...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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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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...&c. QED PROP. С. 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 AB С be a triangle,...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...sides of the triangle. 6. If from the 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 circumscribing circle. 7. Draw a straight line perpendicular...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...cor. . VI. 3. VI. 2. VI. A. (p. 76). If several parallels be drawn to the base of a triangle. If an angle of a triangle be bisected by a straight line, which likewise cuts the base. • Idem If a straight line bisects both the angle and base of a triangle. If from any angle of a triangle...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...Shew that each of the complements of the parallelograms is a mean proportional between them. 6. If an angle of a triangle be bisected by a straight line,...the rectangle contained by the sides of the triangle ia equal to the rectangle contained by the segments of the base, together with the square of the straight...
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