 | 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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Two straight lines which are each of them parallel to the same straight line, and not in the same plane with it, are parallel to one another. Let AB... 
