| Euclid - 1845 - 199 páginas
...which AB is at right angles. Therefore, if two straight lines, &c. QED PROPOSITION IX. THEOR. — Two **straight lines, which are each of them parallel to...straight line, and not in the same plane with it, are** par<Mel to one another. Let AB, CD be each of them parallel to EF, and not in the same plane with it... | |
| Euclides - 1845
...parallel to BE. Therefore AD and CF are each of them equal and parallel to BE. But straight lines that are **parallel to the same straight line, and not in the same plane with it, are parallel to one another** : (xi. 9.) therefore AD is parallel to CF ; and it is equal to it; (i. ax. 1.) and AC, D.Fjoin them... | |
| Euclid, James Thomson - 1845 - 352 páginas
...(XI. 4) to the plane BDE in which those lines are. Wherefore, if one, &c. PROP. IX. THEOR. — Two **straight lines -which are each of them parallel to the same straight line, and** are not both in the same plane with it, are parallel to one another. Let AB, CD be each of them parallel... | |
| Euclides - 1846
...plane to which AB is at right angles. Wherefore, If two straight lines S$ca ED PROP. IX. THEOR. Two **straight lines, which are each of them parallel to...plane with it, are parallel to one another. Let AB,** CD be each of them parallel to EF, and not in the same plane with it : AB shall be parallel to CD.... | |
| Dennis M'Curdy - 1846 - 138 páginas
...the other is also at right angles to the same plane. Recite p. 6 of this; ax. 11 of b. 1. 8 Th. Two **straight lines, which are, each of them, parallel to the same straight line,** though not both in the same plane with it, are parallel to each other. Recite p. 4, 7, 6 of this. 9... | |
| Euclid, John Playfair - 1846 - 317 páginas
...AB, and are drawn through the same point D, which is impossible (11. Ax. 1.). PROP. VIII. THEOR. Two **straight lines which are each of them parallel to the same straight line,** though not both in the same plane with it, are parallel to one another. Let AB, CD be each of them... | |
| Samuel Hunter Christie - 1847
...plane MN. Therefore, if two straight lines, &c.: which was to be proved. • PROP. XIX. THEOR. Two **straight lines, which are each of them parallel to the same straight line, and not** both in one plane with it, are parallel to one another. Let AB, CD (fig. 25) be each of them parallel... | |
| Euclides - 1848
...angles to a plane ; the other also shall be at right angles to the same plane. PROP. IX. THEOREM. Two **straight lines which are each of them parallel to...the same plane with it, are parallel to one another.** PROP. X. THEOREM. If two straight lines meeting one another be parallel to two others that meet one... | |
| 1863
...the equal angles are homologous sides. Cut a given straight line in extreme and mean ratio. 4. Two **straight lines which are each of them parallel to the same straight line,** but not in the same plane with it, are parallel to one another. 5. If 48 men working eight hours a... | |
| Euclides - 1853
...right angles: therefore GH is parallel (i. 28) to AC, and for like reason FK is parallel to AC. Now **straight lines which are each of them parallel to the same straight line** are parallel (i. 30) ; therefore GH, FK are parallel. In the same manner it may be shewn that GF, HK... | |
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