| 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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