 | 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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If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... 
