| Charles Austin Hobbs - 1899 - 240 Seiten
...exterior angles are parallel. Proposition 32. Theorem. 43. If two straight lines are cut by a transversal **so as to make the two interior angles on the same side of** the transversal supplementary, the two straight lines are parallel. Consult Prop. 4 and Prop. 30. COB.... | |
| Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 Seiten
...another, are equal. 10. Two straight lines cannot enclose a space. 11. All right angles are equal. **12. If a straight line meet two straight lines so as to make the** interior angles on one side of it together less than two right angles, these straight lines will meet... | |
| Joseph John Findlay - 1902 - 442 Seiten
...proposition (it is numbered as the first part of Proposition 28) : — If a straight line meet two other **straight lines, so as to make the two interior angles on the same side** supplementary, the lines will never meet, although produced ever so far. You can prove it by assuming... | |
| 1903
...is only one form of the conception of parallelism. So it was formulated axiomatically 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." This dogmatic statement... | |
| Euclid - 1904 - 456 Seiten
...another, are equal. 10. Two straight lines cannot enclose a space. 11. All right angles are equal. **12. If a straight line meet two straight lines so as to make the** interior angles on one side of it together less than two right angles, these straight lines will meet... | |
| Ernst Mach - 1906 - 144 Seiten
...system is found the so-called Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : **"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." Euclid easily proves... | |
| Ernst Mach - 1906 - 144 Seiten
...system is found the so-called Fifth Postulate (also called the Eleventh Axiom and by some the Twelfth) : **"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." Euclid easily proves... | |
| Henry Heathcote Statham - 1907 - 281 Seiten
...248-252. t It may save some readers the trouble of referring to their Euclid to print the axiom here : " **If a straight line meet two straight lines so as to make the** interior angles on one side of it together less than two right angles, these straight lines will meet... | |
| Walter William Rouse Ball - 1908 - 522 Seiten
...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 Seiten
...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... | |
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