 | Absalom Peters, Selah Burr Treat, John Holmes Agnew - 1841 - 622 σελίδες
...measurement embodied in words. Those which declare that two straight lines cannot inclose a space, and that two straight lines which cut one another cannot both be parallel to a third, are in reality the only ones which express characteristic properties of space, and these it... | |
 | Thomas Gaskin - 1847 - 301 σελίδες
...VI.) 1. IN some treatises on Geometry it is laid down as an axiom more evident than Euclid's 12th, that two straight lines which cut one another, cannot both be parallel to the same straight line. Shew that this is only a disguise of Euclid's axiom. Give an instance to shew how some of the fundamental... | |
 | Robert Potts - 1860 - 380 σελίδες
...originate ? What other assumptions have been suggested and for what reasons ? 69. Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc. I. 29. 70. From Euc. i. 27, shew that the distance... | |
 | Euclides - 1864 - 448 σελίδες
...originate ? What other assumptions have been suggested and for what reasons ? 69. Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc. I. 29. 70. From Euc. I. 27, shew that the distance... | |
 | Euclides - 1864 - 262 σελίδες
...originate ? What other assumptions have been suggested and for what reasons ? 69. Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc. i. 29. 70. From Euc. i. 27, shew that the distance... | |
 | Robert Potts - 1865 - 528 σελίδες
...originate ? What other assumptions have been suggested, and for what reasons ? 74. Assuming as an axiom that " two straight lines which cut one another, cannot both be parallel to the same straight line"; deduce Euclid's twelfth axiom as a corollary of Euc. i. 29. 15. From Euc. I. 27, shew that the distance... | |
 | Robert Potts - 1868 - 434 σελίδες
...originate ? What other assumptions have been suggested and for what reasons ? 69. Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc. I. 29. 70. From Euc. I. 27, shew that the distance... | |
 | Euclides - 1871 - 136 σελίδες
...many modern writers on Geometry propose, as more evident to the senses, the following Postulate : " Two straight lines which cut one another cannot BOTH be parallel to the same straight line." If this be assumed, we can prove Post. 6, as a Theorem, thus: Let the line EF falling on the lines... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...many modern writers on Geometry propose, as more evident to the senses, the following Postulate : " Two straight lines which cut one another cannot BOTH be parallel to the same straight line." If this be assumed, we can prove Post. 6, as a Theorem, thus: Let the line EF falling on the lines... | |
 | Euclides - 1874 - 120 σελίδες
...part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. Two straight lines which cut one another cannot both be parallel to a third straight line. PEOPOSITION 1. PROBLEM. To describe an equilateral triangle on a given finite... | |
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Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc. 
