| 1892
...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... | |
| Euclid - 1892 - 518 sider
...that 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... | |
| Paul Carus - 1893
...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...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 lines... | |
| 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... | |
| Florian Cajori - 1896 - 304 sider
...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...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,... | |
| William Stanley Jevons - 1896 - 304 sider
...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... | |
| HERMANN SCHUBERT - 1899
...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...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 lines... | |
| 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.... | |
| Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 sider
...another, are equal. 10. Two straight lines cannot enclose a space. 11. All right angles are equal. **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... | |
| 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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