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" BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to... "
The complete measurer: or, The whole art of measuring, containing the ... - Page 47
by Thomas Keith - 1817
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National Society's Monthly Paper

1855 - 264 pages
...segment of a circle are equal to one another; 10. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. ALGEBRA. (Second Section.) 1. Simplify a-[6 + e-{d+6-(e+26-fl+d}}] 2. If *=-— show that (x+a) (x+$)+(c-*)...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...that if PS and PC be drawn making any constant angle with AH and AC, the locus of P is a circle. 7. If two straight lines within a circle cut one another, the rectangle contained by the segment* of one of them is equal to the rectangle contained by the segments! of the other. With a point...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...angle DBE is equal to the angle BCD in the alternate segment of the circle. LXVIII.— EUCLID III. 35. If two straight lines within a circle cut one another...rectangle contained by the segments of the other. Let the two straight lines AC, BC within the circle ABCD cut one another in the point E, the rectangle...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...another within a circle ; as Prop. 35, bk. iii. , "if two straight lines cut one another within a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. " 4. By this proposition the method may be demonstrated of finding the value of an Adfected Quadratic...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...which joins them shall fall within the circle. 2. If two straight lines cut one another within a circle the rectangle contained by the segments of one of...rectangle contained by the segments of the other. VOLUNTARY PORTION. about the equal angles proportionals, the triangles shall be equiangular, and shall...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...circle ABC containing an angle equal to the given angle D. PBOPOSITION XXXV. THEOREM. If two chords in a circle cut one another, the rectangle contained...rectangle contained by the segments of the other. Given the two chords AC and BD, within the circle ABCD, cutting one another in the point E ; to prove...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...PROPOSITION XXXV. THEOREM. If two straight lines cut one another within a circle, the rectangle contained btf the segments of one of them, is equal to the rectangle contained by the si'gmrnh of the other. Let the two straight lines AC, BD, cut one another in the point E, within...
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Guide to the army - competitive examinations

Alexander Hadden Hutchinson - 1861 - 128 pages
...his army consist before the battle ? Euclid. 1. If two straight lines cut one another within a circle the rectangle contained by the segments of one of...rectangle contained by the segments of the other. 2. If a point be taken within a circle, from which there fall more than two equal straight lines to...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...BC. QE r. PBOP. 35. — THEOK. (Very Important.) If two st. lines eut one another within a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. Cox. 10, I. 12, I. 1, III. Pst. 1. DEM. Def. 15, I. 3, III. 47, I. Axs. 1, 2, 3, I. 36, 1. Parlms....
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...BAC has been cut off, containing an angle equal to the given angle DQEF PROPOSITION 35.— THEOREM. If two straight lines within a circle cut one another,...rectangle contained by the segments of one of them shall be equal to tlte rectangle contained by the segments of the other. (References— Prop. I. 12,...
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