| Benjamin Franklin Finkel - 1888 - 481 Seiten
...assumption is a substitute for Euclid's famous eleventh (also called the twelfth) axiom which reads, **If a straight line meet two straight lines so as to make the two interior angles** *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together... | |
| 1890
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " **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... | |
| Florian Cajori - 1890 - 400 Seiten
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " **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... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 Seiten
...— 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... | |
| Edward Albert Bowser - 1890 - 393 Seiten
...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.... | |
| John Michels (Journalist) - 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... | |
| John Michels (Journalist) - 1892
...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 - 1892 - 518 Seiten
...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... | |
| 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... | |
| William Stanley Jevons - 1896 - 304 Seiten
...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... | |
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