| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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