 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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.)... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | 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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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... 
