| Charles Butler - 1814
...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 - 1817 - 436 Seiten
...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 - 1819 - 410 Seiten
...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 - 1819 - 377 Seiten
...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 - 1819 - 377 Seiten
...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 - 1837 - 390 Seiten
...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 - 1837
...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
...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 - 1841
...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... | |
| 1845
...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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