Quote: rational and irrational as commensable or incommensurable magnitudes

Quotation

BOOK TEN DEFINITIONS I 1. Those magnitudes are said to be commensurable which are measured by the same measure, and those incommensurable which cannot have any common measure. ... 3. With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and incommensurable respectively ... Let then the assigned straight line be called rational, and those straight lines which are commensurable with it, whether in length and in square or in square only, rational, but those which are incommensurable with it irrational.   Google-1   Google-2

Published before 1923

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