 If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes,...  Pure Mathematics - Seite 82von Leslie Leland Locke - 1909 - 324 SeitenVollansicht - Über dieses Buch
 | Karl Fink, Wooster Woodruff Beman, David Eugene Smith - 1900 - 360 Seiten
...following axiom : "If all the points of a straight line are divided into two classes such that every point of the first class lies to the left of every point of the second, then there exists one point and only one which effects this division of all points into two classes,... | |
 | Richard Dedekind - 1901 - 138 Seiten
...following principle : "If all points 'of the straight line fall into two classes such that every point of the first class lies to the left of every point...severing of the straight line into two portions." As already said I think I shall not err in assuming that every one will at once grant the truth of... | |
 | 1914 - 758 Seiten
...the principle : " If all the points of a line are separated into two classes such that every point of the first class lies to the left of every point...exists one and only one point which produces this separation." More generally, I might refer to the conflict between analysis and geometry in the development... | |
 | Alfred North Whitehead - 1907 - 87 Seiten
...and is as follows : "If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point...severing of the straight line into two portions." It is of course to be understood that the dividing point itself belongs to one of the two classes.... | |
 | Euclid - 1908 - 550 Seiten
...edition 1905, p. u). " If all points of a straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, there exists one and only one point which produces this division of all the points into two classes,... | |
 | Godfrey Harold Hardy - 1908 - 449 Seiten
...that the first class of points does include points besides x = 0. Then it is clear that every point of the first class lies to the left of every point of the second class. Hence there is a point A (x = R, say) which divides the two classes, and may itself belong to either... | |
 | 1910 - 516 Seiten
..."emendation" (pp. 279 — 280) is Dedekind's original axiom. into two classes such 1 1 IM, t every point of the first class lies to the left of every point...class, then there exists one and only one point which generates this division; that is to say, there is one and only one point (of the first class) which... | |
 | Paul Carus - 1916 - 666 Seiten
...Dedekind" after long meditation to be: If all the points of L fall into two classes such that every point of the first class lies to the left of every point...class, then there exists one and only one point which generates this division. This, as Dedekind emphasized, will probably be considered as evidently true... | |
 | Ernst Cassirer, William Curtis Swabey, Marie Taylor (Collins) Swabey - 1923 - 488 Seiten
...when all the points of a straight line are divided into two classes, in such a manner that every point of the first class lies to the left of every point of the second class, there exists one and only one point of the straight line which produces this division of all the points,... | |
 | Paul Carus - 1924 - 652 Seiten
...Cantor-Heine-Meray. He writes : "If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point...severing of the straight line into two portions." " (See p. 11 of the English translation.) "I am not in the position to bring forward any proof of its... | |
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