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If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Elements of geometry, based on Euclid, books i-iii - Side 9
av Edward Atkins - 1876 - 119 sider
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Science, Volum 20

1892
...at least one which is not axiomatic.1 This id the axiom of parallels, which reads as follows : — " If a straight line meet two straight lines so as to...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 sider
...that all right angles are equal, admits of proof, and is therefore perhaps out of place as an Axiom.] 12. If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet...
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The Monist, Volum 3

Paul Carus - 1893
...Eighth axiom : Magnitudes which coincide with one another are equal to one another. Eleventh axiom : If a straight line meet two straight lines so as to...continually produced, shall at length meet on that side on which are the angles which are less than two right angles. Twelfth axiom : Two straight lines...
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Journal of the Michigan Schoolmasters' Club, Volum 22;Volumer 31-40

...any center with any radius. 4. That all right angles are equal. 6. If a straight line meet two other straight lines so as to make the two interior angles on the same side of it together less than two rig~ht angles, these two straight lines being continually produced shall at...
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A History of Elementary Mathematics: With Hints on Methods of Teaching

Florian Cajori - 1896 - 304 sider
...figures to be moved relatively to each other, namely, in proving proposi1 The parallel-postulate is : " If a straight line meet two straight lines, so as...continually produced, shall at length meet on that side on which are the angles which are less than two right angles." In the various editions of Euclid,...
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Studies in Deductive Logic: A Manual for Students, by W. Stanley Jevons

William Stanley Jevons - 1896 - 304 sider
...Give the logical opposites, converse and contrapositive, of Euclid's (so-called) twelfth axiom — If a straight line meet two straight lines, so as to make the interior angles on the same side of it taken together less than two right angles, those straight lines...
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MATHEMATICAL ESSAYS AND RECREATIONS

HERMANN SCHUBERT - 1899
...Eighth axiom: Magnitudes which coincide with one another are equal to one another. Eleventh axiom: If a straight line meet two straight lines so as to...continually produced, shall at length meet on that side on which are the angles which are less than two right angles. Twelfth axiom: Two straight lines...
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The Elements of Plane Geometry

Charles Austin Hobbs - 1899 - 240 sider
...exterior angles are parallel. Proposition 32. Theorem. 43. If two straight lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the two straight lines are parallel. Consult Prop. 4 and Prop. 30. COB....
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Bok 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 sider
...another, are equal. 10. Two straight lines cannot enclose a space. 11. All right angles are equal. 12. If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet...
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Principles of Class Teaching

Joseph John Findlay - 1902 - 442 sider
...proposition (it is numbered as the first part of Proposition 28) : — If a straight line meet two other straight lines, so as to make the two interior angles on the same side supplementary, the lines will never meet, although produced ever so far. You can prove it by assuming...
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