 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 ... - Seite 154von Samuel H. Winter - 1877 - 413 SeitenVollansicht - Über dieses Buch
 | Robert Simson - 1806 - 546 Seiten
...: 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 Seiten
...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 Seiten
...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 - 1827 - 546 Seiten
...; 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 - 1833 - 332 Seiten
...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 Seiten
...: 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 - 1837 - 180 Seiten
...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 - 1838 - 434 Seiten
...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 - 1841 - 214 Seiten
...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 Seiten
...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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