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" Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 83
by Euclides - 1816 - 528 pages
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...D. Which was to be done. PROP. XXXV. THEOR. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD cut one another in the point E, within the circld ABCD; the rectangle contained by AE, EC shall be...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equal to the given angle DQEF PEOP. XXXV. THEOR. IF two straight lines within a circle cut one another, the rectangle contained by the segments of one of them, is equal or equivalent to the rectangle contained by the segments of the other. * Let the two straight lines...
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Algebra Applied to Geometry: To Determine the Position of a Point at Rest ...

X. Y. Z. - Equations - 1843 - 96 pages
...Circumference and Point of intersection are equal 91 8*. If two Lines within a Circle cut one another the Rectangle contained by the Segments of one of...Rectangle contained by the Segments of the other, (Euclid 35, 3.) - - - 92 Problems ..... 93 Answers to the Loci, (p. 31) ... 96 ERRATA. The Studen1...
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Proceedings

Scotland free church, gen. assembly - 1847
...GEOMETRY AND PRACTICAL MATHEMATICS. !• If two chords in a circle intersect each other, prove that the rectangle contained by the segments of one of them is equal to the rectangle contained by tbe segments of the other. • Prove that similar triangles are to each other as the squares of their...
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An elementary treatise on algebra. [With] Key

James Thomson - 1844
...the part of it without the circle. (Euc. III. 36. Cor.) 8. If two chords cut one another in a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. (Euc. III. 35.) Let ABC be the required triangle, and let the leg AC or BC = x. Then (Euc. I. 47.)...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...given angle DQEF PROPOSITION XXXV. THEOREM. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD, cut one another in the point E, within the circle ABCD. Then the rectangle contained by AE, EC shall...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...given angle D : which was to be done. PROP. XXXV. THEOR. — If two chords of a circle cut one another, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. In the circle ABCD, let the two chords AC, BD cut one another in the point E : the rectangle AE.EC...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Thomson - Algebra - 1845 - 292 pages
...the part of it without the circle. (Euc. III. 36. Cor.) 8. If two chords cut one another in a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. (Euc. III. 35.) Let ABC be the required triangle, and let the leg AC or BC =x. Then (Euc. 1.47.) AB...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of...in the point E : the rectangle contained by AE, EC shall be equal to the rectangle contained by BE, ED. If AC, BD pass, each of them, through the centre,...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846
...Z — given ZC. PROP. LXII. THEOR. 35. 3Eu. If two straight lines within a circle cut one another, the rectangle contained by the seg-ments of one of...contained by the segments of the other. Let the two str. lines AC, BD cut each other in E within 0 ABCD: then AE. EC = BE. ED. Fig. 4. 1st. Let AC, BD...
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