 | Paul Carus - 1893 - 722 Seiten
...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... | |
 | Michigan Schoolmasters' Club - 1894 - 556 Seiten
...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... | |
 | Florian Cajori - 1896 - 338 Seiten
...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... | |
 | William Stanley Jevons - 1896 - 344 Seiten
...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... | |
 | Florian Cajori - 1896 - 324 Seiten
...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... | |
 | Hermann Schubert - 1899 - 163 Seiten
...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... | |
 | Charles Austin Hobbs - 1899 - 266 Seiten
...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.... | |
 | Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 330 Seiten
...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... | |
 | Joseph John Findlay - 1902 - 494 Seiten
...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... | |
 | 1903 - 748 Seiten
...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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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... 
