| Robert T. Browne - 1919 - 395 sider
...parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads 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."** On this postulate hang all the "law and the prophets" of the non-Euclidean Geometry. In it are the... | |
| Charles Austin Hobbs - 1921 - 192 sider
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal **so as to make the two interior angles on the same side of** the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular... | |
| 1901
...far from "self-evident" it is the reader may judge for himself. "If a straight line meets two other **straight lines so as to make the two interior angles...it taken together less than two right angles, these** sides being continually produced shall at length meet on that side on which are the angles which are... | |
| 1906
...can not enclose a space. 11. All right angles are equal to one another. 12. 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. Modern objections to these... | |
| 1886
...equivalence of the three forms of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is: — **"If a straight line meets two straight lines, so as...the angles which are less than two right angles."** In other words, if the angle CAH + the angle ABD < 180°, then AC and />' l> will at length meet. This... | |
| Roberto Bonola - 1955 - 389 sider
...make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet **two straight lines, so as to make the two interior...less than two right angles, these straight lines,** heing continually produced, shall at length meet on that side on which are the angles which are less... | |
| University Council for Educational Administration - 1962 - 548 sider
...primitive terms, for example, "point"; defined terms, for example, "triangle"; axioms, for example, **"If a straight line meets two straight lines, so as to make** two interior angles on the same side of it taken together less than two right angles, these straight... | |
| I. N. Herstein, Irving Kaplansky - 1978 - 246 sider
...one another. But nothing up to this point has prepared us for the astonishing final axiom. AXIOM 12. **If a straight line meets 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. The axiom is illustrated... | |
| Ivor Grattan-Guinness, Gerard Bornet - 1997 - 236 sider
...4. And that all right angles are equal to one another. 5. And that if a straight line meet two other **straight lines so as to make the two interior angles...these straight lines being continually produced shall** meet on that side on which are the angles which are less than two right angles. 6. And that two straight... | |
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