 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 ... - Σελίδα 154των Samuel H. Winter - 1877 - 413 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Robert Simson - 1806 - 546 σελίδες
...: 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 σελίδες
...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 σελίδες
...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 σελίδες
...; 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 σελίδες
...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 σελίδες
...: 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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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