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" If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
The Elements of Euclid, containing the first six books, with a selection of ... - Side 6
av Euclides - 1874
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Journal of the Michigan Schoolmasters' Club, Volum 22;Volumer 31-40

Michigan Schoolmasters' Club - 1894
...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

Florian Cajori - 1896 - 304 sider
...relatively to each other, namely, in proving proposi1 The parallel-postulate is : " If a straight line meet two straight lines, so as to make the two interior...lines, being 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...
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Studies in Deductive Logic: A Manual for Students, by W. Stanley Jevons

William Stanley Jevons - 1896 - 304 sider
...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 being continually produced shall at length meet upon that side on which are the...
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A History of Elementary Mathematics: With Hints on Methods of Teaching

Florian Cajori - 1896 - 304 sider
...less than two right angles, these straight lines, being 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, different numbers are assigned to the "axioms." Tims, the parallel-postulate...
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MATHEMATICAL ESSAYS AND RECREATIONS

HERMANN SCHUBERT - 1899
...Magnitudes which coincide with one another are equal to one another. Eleventh axiom: If a straight line meet two straight lines so as to make the two interior...lines, being 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...
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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
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length...
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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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The Monist, Volum 13

1903
...conception of parallelism. So it was formulated axiomatically as follows : " If a straight line meet two straight lines, so as to make the two interior...the angles which are less than two right angles." This dogmatic statement (now commonly called "the axiom of parallels") was naturally transferred by...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length...
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