 | Hastings Berkeley - Mathematics - 1910 - 279 pages
...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 - Science - 1917 - 526 pages
...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 - Mathematics - 1918 - 222 pages
...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 - Hyperspace - 1919 - 426 pages
...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 - Geometry, Solid - 1921 - 216 pages
...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 pages
...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... | |
 | John Neville Keynes - Logic - 1928 - 580 pages
...proposition and its contrapositive ; for example, between Euclid's twelfth axiom, " 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 that are less than two right angles," and the second part of the... | |
 | John Whitehead, L. F. Whitehead - Dagbani language - 1928 - 514 pages
...lines cannot enclose a space Ii. AU right angles are equal to one another. I2. If a straight line meet two straight lines, so as to make the two interior...it taken together less than two right angles, these two straight lines being continually produced shall at length meet on that side on which are tht angles... | |
 | Franklin D. Jones - Machinery - 1928 - 1254 pages
...a space, n. All right angles are equal to one another. 12. If a straight line intersects two other straight lines, so as to make the two interior angles...side of it taken together less than two right angles, then these straight lines, if continually produced, must meet upon the side on which the angles are... | |
 | Science - 1906 - 600 pages
...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... | |
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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... 
