| 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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