Proposition X.29 — To find two rational straight lines commensurable in square …

Proof

Take a rational line

a

and apply X.17 with a deficient square; the construction gives the required pair.

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Depends on (1)

X.17Proposition X.17If there be two unequal straight lines, and to the greater there be applied a parallelogram equal to the fourth part of…

Required by (dependents) (3)

X.31Proposition X.31To find two medial straight lines commensurable in square only, containing a rational rectangle, such that the square…
X.48Proposition X.48To find the first binomial straight line.
X.50Proposition X.50To find the third binomial straight line.

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