 If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another...  Euclid's Elements of Geometry - Page 248edited by - 1893 - 504 pagesFull view - About this book
 | John Playfair - Geometry - 1836 - 148 pages
...other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre ; it is evident, that AE, EC,... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...other.* Let the two straight lines AC BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre ; it is evident, that AE, EC,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E ; the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre, it is evident that AE, EC,... | |
 | Euclid - Geometry - 1845 - 218 pages
...other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E ; the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre, it is evident that AE, EC,... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E ; the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre, it is evident that AE, EC,... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED. If AC, BD pass each of them through the centre, so that E is the centre; it is evident, that AE, EC,... | |
 | Euclides - 1853 - 146 pages
...the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E: the rectangle contained by AE, EC, is equal to the rectangle contained by BE, ED. If AC, BD, pass each of them through the centre, so that E is the centre; it is evident that AE, EC,... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...other. Let the two straight lines AC, BD, 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 each of them through the centre, so that E is the centre, it is evident that AE, EC,... | |
 | Euclides - 1856 - 168 pages
...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 to the rectangle contained by BE, E D. First, if AC, CD intersect in the centre of the circle, it is evident that AE, EC, EB, ED being... | |
 | Euclides - 1860 - 288 pages
...segments of the other. Let the two chords AC, BD, within the circle ABCD, cut one another in the point K; the rectangle contained by AE, EC is equal to the rectangle contained by DE • KB. Join FA, FB, FC, and FD, F being the centre. Then in the isosceles triangle AFC, the square... | |
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