 If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.  Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ... - Page 154by Samuel H. Winter - 1877 - 413 pagesFull view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...: therefore EF is parallel to GH. Wherefore, if two parallel planes, Sec. QED B PROP. XVII. THEOR. IF two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B ; C,... | |
 | John Mason Good - 1813 - 714 pages
...parallel planes be cut by another plaue, their common sections with it are parallels. Prop. XVII. Theor. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Prop. XVIII. Theor. If a straight line be at right angles to a pbue, every plane which passes through... | |
 | Euclides - 1816 - 588 pages
...parallel : Therefore EF is parallel to GH. Wherefore, if two parallel planes, &c. QED PROP, XVII. THEOR. IF two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD, be cut by the parallel planes GH, KL, MN, in the points A, E, B; C,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...; therefore EF is parallel to GH. Wherefore, if two parallel planes, &c. QED PROP. XVII. THEOR. Jf two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B ; C,... | |
 | John Martin Frederick Wright - Astronomy - 1833 - 332 pages
...1. FIND the present worth of 897/- 15*. 6|rf. due' nine months hence at 3| per cent. per annum. 3. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. 3. Multiply */( - a) by */( - 6.) 4. In the expansion of (a + bx + cx* + dx3 + &c.)M, write down the coefficient... | |
 | Euclid - 1835 - 540 pages
...: Therefore EF is parallel to GH. Wherefore, " if two parallel planes," &c. QED PROP. XVII. THEOR. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F,... | |
 | A. Bell - Conic sections - 1837 - 180 pages
...plane EH, is equal to the inclination of the plane CD to the same plane EH. PROPOSITION XVL THEOEEM. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD, be cut by the parallel planes GH, KL, MN, in the points A, E, B ; C,... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...parallel : therefore EF is parallel to GH. Wherefore, if two parallel planes, &c. QED / PROP. XVII. THEOR. IF two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F,... | |
 | Thomas Grainger Hall - Geometry, Descriptive - 1841 - 214 pages
...planes AB, CD, meet if produced, which is contrary to the hypothesis. INTRODUCTION. PROPOSITION XVIII. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let AB, CD, be cut by the parallel planes GH, KL, MN, in the points A, E, B; c, F, D; then AE : EB... | |
 | Euclides - 1842 - 316 pages
...equal to the inclination of the plane CD to the same plane EH. Therefore, &c. QED PROP. XVII. THEOR. IF two straight lines be cut by parallel planes : they shall be cut in the same ratio. Let the straight lines A в, c D be cut by the parallel planes GH, KL, MN, in the points A, E, B ;... | |
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