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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: With Notes - Page 172
by John Radford Young - 1827 - 208 pages
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Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - Geometry, Non-Euclidean - 1891 - 142 pages
...cut by a transversal make equal alternate angles, he brings in the un wieldly postulate or axiom: " If a straight line meet two straight lines, so as...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles." Do you wonder that succeeding...
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Educational Review, Volume 3

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...to one another," is not required for use before proposition 14 of his first book. Also the axiom, " If a straight line meet two straight lines, so as...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles," is not required till proposition...
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Science, Volume 20

Science - 1892 - 444 pages
...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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Science, Volume 20

Science - 1892 - 448 pages
...at least one which is not axiomatic.1 This is the axiom of parallel?, 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 oh that side on...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...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, Volume 3

Paul Carus - Electronic journals - 1893 - 720 pages
...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...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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Journal of the Michigan Schoolmasters' Club, Volume 22; Volumes 31-40

Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...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 - Mathematics - 1896 - 336 pages
...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...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 - Logic - 1896 - 344 pages
...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 - Circle-squaring - 1899 - 163 pages
...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...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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