Proposition X.10 — To find two straight lines incommensurable, the one in lengt…

Proof

Take a non-square integer ratio (e.g.\

2 : 1

) and use it via X.9 to construct an incommensurable-in-length pair; build the incommensurable-in-square one similarly with a ratio that is neither square nor cube.

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Depends on (2)

VI.13Proposition VI.13To two given straight lines to find a mean proportional.
X.9Proposition X.9The squares on straight lines commensurable in length have to one another the ratio which a square number has to a…

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