 | Paul Carus - 1894 - 698 páginas
...said to himself: "Can I prove this plain, straightforward, simple, if somewhat inelegant theorem : If a straight line meeting two straight lines, make...where the angles are less than two right angles." [Williamson's translation; Postulate 5, P. Tannery and Heiberg, Axiom n in Gregory.] And let not the... | |
 | Robert T. Browne - 1919 - 426 páginas
...BA indefinitely produced. The parallel-postulate is stated in the nonEuclidean geometry as follows: "If a straight line meeting two straight lines make...being produced indefinitely will meet each other on this side where the angles are less than two right angles." It is stated by MANNING* in the following... | |
 | 1893 - 562 páginas
...alternate angles, he brings in the unwieldy assumption thus translated by Williamson (Oxford, 1781): "n. And if a straight line meeting two straight lines...where the angles are less than two right angles." Hundreds of mathematicians have tried to relieve Euclid's geometry of this assumption by deducing it... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1893 - 554 páginas
...alternate angles, he brings in the unwieldy assumption thus translated by Williamson (Oxford, 1781): "n. And if a straight line meeting two straight lines...where the angles are less than two right angles." Hundreds of mathematicians have tried to relieve Euclid's geometry of this assumption by deducing it... | |
 | Julius Thomas Fraser - 1990 - 552 páginas
...that if a straight line falling on two straight lines makes the angles, internal and on the same side, less than two right angles, the two straight lines, being produced indefinitely, meet on the side on which are the angles less than two right angles. 40 By default, if the two angles,... | |
 | Shiing-Shen Chern, G. Tian, Peter Li - 1996 - 734 páginas
...under partial support of NSF grant DMS-87-01609 679 548 680 SHIING-SHEN CHERN [October the same side, less than two right angles, the two straight lines, being produced indefinitely, meet on the side on which are the angles less than two right angles." a + ß < 180° FIG. 3 Euclid... | |
 | Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - 1907 - 212 páginas
...(Williamson's translation, Oxford, 1781): 11. And if a straight line meeting two straight lines makes those angles which are inward and upon the same side...being produced indefinitely will meet each other on that side upon which the angles are less than two right angles (.Fig. /, Angle A + Angle B less than... | |
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And that, if a straight line falling on two straight lines make the angles, internal and on the same side, less than two right angles... 