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Updated: May 20, 2025
Yet the polygons and curves were always regarded as distinct lines, differing inappreciably, but different. The careful study of the period to which we refer led to a new discovery, that every curve may be considered as composed of infinitely small straight lines. For, by the definition which assigns to a point position without extension, there can be no tangency of points without coincidence.
Thus our logic is valid as infinitesimal analysis, just as the geometry of the straight line allows us to define each state of curve. It is thus, for example, that vitality maintains a relation of momentary tangency to the physico-chemical structure. If we study this relation and analogous relations, this fact remains indisputably legitimate.
To begin with, he could not decide whether, on their wedding day, there ever had been any real spiritual tangency between them. Reed said not; but Reed had been young, at the time of his earlier acquaintance with them, and so incapable of forming any stable judgment.
While in his social relations the young man is seeking points of tangency with those in his own plane, in his religious experience he seeks to come into relation with his God; that is, with the power that exists in the plane above his own.
We can then conceive all the intricacies of tangency. In particular we can conceive an abstractive set of which all the members have point-contact at the same event-particle. It is then easy to prove that there will be no abstractive set with the property of being covered by every abstractive set which it covers.
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