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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. "
Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... - Side 11
av John William Withers - 1905 - 192 sider
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The American Eclectic, Volum 2

Absalom Peters, Selah Burr Treat, John Holmes Agnew - 1841 - 622 sider
...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...
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The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - 1847 - 301 sider
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 sider
...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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 sider
...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...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 sider
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 sider
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 sider
...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...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871 - 136 sider
...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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 376 sider
...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...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 sider
...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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