 | Charles Butler - Mathematics - 1814 - 528 pages
...If two straight lines cut one another, and the rectangle contained by the segments of one of them, be equal to the rectangle contained by the segments of the other, the circumference which passes through three of the extremities of the two given straight lines, shall... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...be equal to one another. (LXXV.) To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line. (LXXVI.) If a given circle be cut by any number of circles, which... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...another. PROP. LXXXI. 106. PROBLEM. To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line. Let AB and L be two given finite straight F Gr E lines : It is required... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...part ; (m) being whole or fractional. 11. To divide a given line into two such purls, that the square of the one shall be equal to the rectangle contained by the other and a given line. 12. A straight line being given in magnitude and position ; to draw to it,... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...part ; (m) being whole or fractional. 11. To divide a given line into two such parts, that the square of the one shall be equal to the rectangle contained by the other and a given line. 12. A straight line being given in magnitude aud position ; to draw to it,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...IF two chords of 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. In the circle ABCD, let the two chords AC, BD cut one another in the point E : the rectangle AE.EC is... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...straight lines within a circle cut each other, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. • In case 1st, E is the centre of the 0, and evident that AE x EC = BE x ED. it is Steps of the Demonstration... | |
 | Euclides - 1838 - 264 pages
...cut off, containing an angle equal to the given angle 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 them is equal to the rectangle contained by the segments of the other. Let the two straight... | |
 | Euclides - Geometry - 1841 - 378 pages
...cut off, containing an angle equal to the given angle 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 them is equal to the rectangle contained by the segments of the other. Let the two straight... | |
 | Scottish school-book assoc - 1845 - 444 pages
...PROPOSITION LXV — THEOREM. If two chords, AB, CD, cut one another in a point E, within a circle A CD, the rectangle contained by the segments of the one...rectangle contained by the segments of the other. That is, the rectangle AE-EB=CE-ED. Join CA and BD, then the Z.CAE is = the Z.BDE ; for they stand... | |
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If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other. 
