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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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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 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 similar to the whole triangle, and to one another. The perpendicular...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...square that lies without the circle. 2. If from any angle of a triangle a perpendicular be let fall on the base, the rectangle contained by the sides of...diameter of the circle described about the triangle. The sides of a right-angled triangle are 1*5 and 2 feet respectively, find, without the use of Trigonometry,...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...equiangular pentagon. 4. 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. 5....
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
... CAF, AG2 = BG . GC ,xi B А . AC PROP. C.— THEOR. If from any angle of a triangle a st. line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangk is equal to the rectangle contained by the perpendicular and the diameter of the circle described...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863 - 482 pages
...their intersection may be inscribed in a circle. 5. 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. 6. From each of -two opposite angular points of a parallelogram lines are drawn to the points of bisection...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...base ; the rectangle contained bg the sides of the triangle is equal to the rectangle contained bg the perpendicular and the diameter of the circle described...AD the perpendicular from the angle A to the base BC. The rectangle .B.4, ACshull be equal to the rectangle contained by AD and the diameter of the circle...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...an angle of a triangle be bisected by a straight line that cuts the base, the rectangle containedby 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. ACB...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...B. THEOREM. If an angle of a triangle be bisected by a straight line which likewise outs the bast ; 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 line which bisects tlw angle. Let...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...THEOREM. 7y an angle of a triangle be bisected by a straight tine which lihewise cuts the base ; then the rectangle contained by the sides of the triangle is equal to ihc rectangle contained by the segments of the base, together with the square of the straight line...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...B. THEOREM. Jf 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 segments of the base, together with the square on the straight line which bisects the angle. Let...
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