| Euclides - 1855 - 230 páginas
...». . . XI. 10. . XI. 2. . . XI. 5.. . XI. 35. , XI. 35, cor. XI. 3. . XI . 19. If two straight lines **are each of them parallel to the same straight line, and -not in the same plane with it.** If two straight lines meeting one another be parallel to two others that meet one another, and are... | |
| Euclides - 1855 - 270 páginas
...plane to which AB is at right angles. Therefore, if two straight lines, &c. QED PROP. IX. THEOREM. 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. Let AB and CD he each of them parallel... | |
| John Playfair - 1855 - 336 páginas
...and are drawn through the same point D, which is impossible (11. Ax. 1.). V PROP. VIII. THEOR. Two **straight lines which are each of them parallel to the same straight** lint, though not both in the same plane with it, are parallel to one another. Let AB, CD be each of... | |
| Eucleides - 1860 - 396 páginas
...t angles to the same plane. XI. 10. . XL 2.. . XL 5.. XL 35, cor. HYPOTHESES. If two straight lines **are each of them parallel to the same straight line, and not in the same plane with it.** If two straight lines meeting one another be parallel to two others that meet one another, and are... | |
| War office - 1861 - 12 páginas
...similarly described figures on the sides containing the right angle. 2. Two straight lines which are each **parallel to the same straight line, and not in the same plane with it, are parallel to one another.** 3. A square is inscribed in another square so that its angular points divide the sides of the latter... | |
| Euclides - 1864 - 448 páginas
...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, DF join them towards... | |
| University of Calcutta - 1864
...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 - 1865 - 402 páginas
...is at rig-ht angles, (xi. 4.) Therefore, if two straight lines, &c. QE D PROP. IX.— THEOREM. Two **straight lines which are each of them parallel to...not in the same plane with it, are parallel to one** anotfier. (References— Prop. i. 11 ; xi. 4, 6, 8.) Let AB, CD be each of them parallel to EF and... | |
| Robert Potts - 1865 - 528 páginas
...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, DFjoin them towards... | |
| Euclid, Isaac Todhunter - 1867 - 426 páginas
...to which AB is at right angles. Wherefore, if two straight lines &c. QED PROPOSITION 9. THEOREM. Two **straight lines which are each of them parallel to...plane with it, are parallel to one another. . Let AB** and CD be each of them parallel to EF, and not in the same plane with it : AB shall be parallel to... | |
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