| Royal Military Academy, Woolwich - Mathematics - 1853
..."Which was to be done. PROPOSITION XXXV. THEOR. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of...within the circle ABCD, cut one another in the point** K ; the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass... | |
| Euclides - Geometry - 1853 - 147 pages
...was to be done. PROPOSITION XXXV. — THEOREM. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of...segments of the other. LET the two straight lines** aС, bd, within the circle ab С d, cut one another in the point e ; the rectangle contained by ae,... | |
| Euclides - Geometry - 1853
...lines be drawn in the circle : then the rectangle contained by the segments of one of them shall be **equal to the rectangle contained by the segments of the other. Let** E be any point within the circle ABC, and through E let the straight lines AC, BD be drawn in the circle.... | |
| William Somerville Orr - Science - 1854
...the same, whatever chord (AB) be drawn through P ; .-.if two chords cut one another in any point P, **the rectangle contained by the segments of one of them is equal to** that contained by the segments of the other. Proposition XXXVI. — Let В be any point without a (.•ircle... | |
| John Playfair - Geometry - 1855 - 318 pages
...equal to the given angle D. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of...point E ; the rectangle contained by AE, EC is equal** tc the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is... | |
| John Playfair - Euclid's Elements - 1855 - 318 pages
...equal to the given angle D. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of...straight lines AC, BD, within the circle ABCD, cut** ona another in the point E ; the rectangle contained by AE, EC is equal U the rectangle contained by... | |
| 1855
...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-*)... | |
| Robert Potts - 1855
...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 A in the circumference of a circle ABC as centre a circle PBC is described cutting the... | |
| Euclides - 1856
...segment of the circle. LXVIII.— EUCLID III. 35. If two straight lines within a circle cut one another **the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC,** BC within the circle ABCD cut one another in the point E, the rectangle contained by AE, EC is equal... | |
| Euclides - 1858
...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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