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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 22:10, 11 April 2009
, 22:10, 11 April 2009→Selection 11
==Selection 11==
==Selection 11==
===The Signs for Multiplication (concl.)===
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<p>The conception of multiplication we have adopted is that of the application of one relation to another. So, a quaternion being the relation of one vector to another, the multiplication of quaternions is the application of one such relation to a second.</p>
<p>The conception of multiplication we have adopted is that of the application of one relation to another. So, a quaternion being the relation of one vector to another, the multiplication of quaternions is the application of one such relation to a second.</p>
<p>Even ordinary numerical multiplication involves the same idea, for 2 × 3 is a pair of triplets, and 3 × 2 is a triplet of pairs, where "triplet of" and "pair of" are evidently relatives.</p>
<p>Even ordinary numerical multiplication involves the same idea, for <math>~2 \times 3~</math> is a pair of triplets, and <math>~3 \times 2~</math> is a triplet of pairs, where ''triplet of'' and ''pair of'' are evidently relatives.</p>
<p>If we have an equation of the form:</p>
<p>If we have an equation of the form:</p>