 | 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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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... 
