Definition·Untested·2605.00009

Definition X.3

With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and incommensurable respectively, some in length only, and others in square also, with an assigned straight line. Let 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.

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X.19Proposition X.19The rectangle contained by rational straight lines commensurable in length is rational.
X.21Proposition X.21The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the…

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