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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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Circular[s] of Information, Utgaver 1-3

1890
...in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to make the two interior...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 Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...— Prove this proposition independently of Prop. 27. Ax. 12. — 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 right angles, these two straight lines being continually produced shall at length...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sider
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) so as to make the two interior angles on the same side together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st....
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The Teaching and History of Mathematics in the United States, Volumer 890-893

Florian Cajori - 1890 - 400 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." It has been validly urged against Euclid that this statement is far from being axiomatic....
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Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 sider
...make equal alternate angles, he brings in the un wieldly postulate or 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." Do you wonder that succeeding...
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Educational Review

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...required for use before proposition 14 of his first book. Also the 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," is not required till proposition...
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Science, Volum 20

1892
...axiomatic.1 This is the axiom of parallel?, which reads as follows : — " If a straight line meet two straight lines so as to make the two interior...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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Science, Volum 20

1892
...axiomatic.1 This id the axiom of parallels, which reads as follows : — " If a straight line meet two straight lines so as to make the two interior...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
...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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The Monist, Volum 3

Paul Carus - 1893
...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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