| Walter William Rouse Ball - 1908 - 522 sider
...usually stated iu the form that if a straight line meets two straight lines, so as to make the sum of **the two interior angles on the same side of it taken together less than two right angles,** then these straight lines being continually7 produced will at length meet upon that side on which are... | |
| James Byrnie Shaw - 1918 - 206 sider
...approach also, that is, in non-Euclidean geometry. Euclid had among his postulates one which read thus : **If a straight line meet two straight lines so as to...lines, being 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... | |
| Robert T. Browne - 1919 - 395 sider
...mankind. The parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads as follows: **"If a straight line meet two straight lines so as...lines being continually produced, shall at length meet** upon that side on which are the angles which are less than two right angles." On this postulate hang... | |
| 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... | |
| 1886
...of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is: — "If a straight line meets **two straight lines, so as to make the two interior...lines being continually produced shall at length meet** upon that side on which are the angles which are less than two right angles." In other words, if the... | |
| Roberto Bonola - 1955 - 389 sider
...parallels cut hy a transversal make equal alternate angles, he hrings m the unwieldly postulate or axiom: " **If a straight line meet two straight lines, so as...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
...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...continually produced, shall at length meet on that** side on which are the angles which are less than two right angles" (the famous "parallel postulate");... | |
| I. N. Herstein, Irving Kaplansky - 1978 - 246 sider
...up to this point has prepared us for the astonishing final axiom. AXIOM 12. If a straight line meets **two straight lines, so as to make the two interior...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 in Figure... | |
| 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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