Sentence Examples


  • A characteristic feature of the calculus is that a meaning can be attached to a symbol of this kind by adopting a new rule, called that of regressive multiplication, as distinguished from the foregoing, which is progressive.
  • For instance, if n= 4, E r = e l e 3, Es= e 2 e 3 e 4 , we have IErIE8 = (-e2e4) (- e 1) = ele2e4 = l e3, consequently, by the rule of regressive multiplication, eie3�e2e3e4 = e3.
  • Applying the distributive law, we obtain, when r+s>n, ArB 8 = EaErE i 3E 8 = E(a(3)ErEs, where the regressive products E r E B are to be reduced to units of species (r+s-n) by the foregoing rule.
  • In the course of reducing such expressions as (AB)C, (AB){C(DE)} and the like, where a chain of multiplications has to be performed in a certain order, the multiplications may be all progressive, or all regressive, or partly, one, partly the other.
  • Further, he perceived that the difference between the progressive and regressive orders extends from mathematics to physics, and that there are two kinds of syllogism: one progressing a priori from real ground (I) Some M is P.

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