## Regressive 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, eie3ï¿½e2e3e4 = 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. - Deduction is analysis when it is
**regressive**from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles. - Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first
**regressive**order of Aristotle - P-M, S-P, S-M. - He re-defines analysis in the very opposite way to the ancients; whereas they defined it as a
**regressive**process from consequence to ground, according to Wundt it is a progressive process of taking for granted a proposition and deducing a consequence, which being true verifies the proposition. - But his account of the first is imperfect, because in ancient analysis the more general propositions, with which it concludes, are not mere consequences, but the real grounds of the given proposition; while his addition of the second reduces the nature of analysis to the utmost confusion, because hypothetical deduction is progressive from hypothesis to consequent facts whereas analysis is
**regressive**from consequent facts to real ground.