 | John Keill - Logarithms - 1723 - 444 pages
...by parallel Planes, they [hall be cut in the fame Proportion. LET two Right Lines AB, CD, be cut by Parallel Planes GH, KL, MN, in the Points A, E, B, C, F, D. I fay, as the Right Line AE is to the Right LneEB, foisCFtoFD. For let AC,BD, AD, bejoin'd: Let AD... | |
 | Euclid - Geometry - 1765 - 492 pages
...lines he cut by parallel planes, they will be cut in thejame ratio. For let two right lines AB, c D, be cut [by the parallel planes GH, KL, MN in the points A, E, B, c, F, D : I fay, as the right line AE is to EB, Co is c F to F D. For join Ac, BD, AD, let AD meet the plane... | |
 | John Keill - Geometry - 1772 - 462 pages
...by parallel Planes, tbej jhdl be cut in the fame Proportion. LE T two Right Lines AB, CD, be cut by parallel Planes GH, KL, MN, in the Points A, E, B, C, F, D. I fay, as the Right Line AE is to the Right LineEB, foisCFtoFD. For, let AC, BD, AD, be joined ; let... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...parallel planes, &c. QEDI PROP. XVI. THEOR. IF two straight lines be cut by parallel planes they will be cut in the same ratio. Let the straight lines AB,...parallel planes GH, KL, MN, in the points A, E, B, and C, F, D ; AE : EB : : CF : FD. Join AC, BD, AD ; let AD meet the plane KL in the point X, and join... | |
 | Euclid - Geometry - 1810 - 554 pages
...parallel planes, &c. QED B G PROP. XVII. THEOR. IF two straight lines be cut by parallel planes, thej shall be cut in the same ratio. Let the straight lines...parallel planes GH, KL, MN, in the points A, E, B; C, 'V, D: as AE is to EB, so is CF to FDJoin AC, BD, AD, and let AD meet the plane KL in the point X;... | |
 | 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 - 1814 - 560 pages
...Therefore JiF is parallel to GH. Wherefore, if two .parallel planes, &c. .QE !>• PROP. XVII. THEOR. IF two straight lines be cut by parallel planes, they...ratio. Let the straight lines AB, CD, be cut by the planes GH, KL, MN, in the points A, E, B; C, F, D: As AE is to EB. so is €F to ED. Join AC, BD, AD,... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...PROB. XVII. THEOREM. If two straight lines be eut by parallel^ planes, they shall be cut in the tarn» ratio. Let the straight lines AB, CD be cut by the parallel planes GH, EL, MN, in the poins A, E, B ; С, F, D: As AE is to ЕВ, so is CF to FD. Join AC, BD, AD, and let... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...planes ; the parts of the straight lines, which are intercepted by the planes, shall be to one another in the same ratio. let the straight lines AB, CD be cut by the parallel planes GH, K !.. MN in the points A, E, B, and С, F, D respectively: AE shall be to ЕВ as С F to F D. Join... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...x N D ^ 0 V ?>sx H^vl PROP. XVI. THEOR. If two straight lines be citl by parallel planes, they must be cut in the same ratio. Let the straight lines AB, CD he 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... | |
| |
THEOH.—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... 
