Proposition X.23 — A straight line commensurable with a medial straight line is…

Proof

Commensurability preserves the medial property: scaling a medial by a rational ratio leaves it medial.

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Depends on (2)

X.21Proposition X.21The rectangle contained by rational straight lines commensurable in square only is irrational, and the side of the…
XIII.3Definition XIII.3A medial straight line is the mean proportional between two rational straight lines commensurable in square only.

Required by (dependents) (1)

X.24Proposition X.24The rectangle contained by medial straight lines commensurable in length is medial.

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