| Hastings Berkeley - 1910 - 279 Seiten
...are real Axioms of Direction. EUCLID'S Axiom of Parallels runs as follows : If a straight line meet **two straight lines, so as to make the two interior...are the angles which are less than two right angles.** The reason which made Euclid put the proposition in this complicated form is plain when we compare... | |
| William Thompson Sedgwick, Harry Walter Tyler - 1917 - 528 Seiten
...known as Axioms 11 and 12, — "All right angles are equal " ; and the famous parallel axiom : — **"If a straight line meets two straight lines, so as...make the two interior angles on the same side of it** together less than two right angles, these straight lines will meet if produced on that side." The... | |
| James Byrnie Shaw - 1918 - 222 Seiten
...non-Euclidean geometry. Euclid had among his postulates one which read thus : If a straight line meet **two straight lines so as to make the two interior...continually produced, shall at length meet upon that side** of the line on which are the angles which are less than two right angles. For ages mathematicians endeavored... | |
| Robert T. Browne - 1919 - 426 Seiten
...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 - 216 Seiten
...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 - 488 Seiten
...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 - 600 Seiten
...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 - 548 Seiten
...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 - 452 Seiten
...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 - 580 Seiten
...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... | |
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