Proposition X.42 — A binomial straight line is divided into its terms at one po…

Proof

Suppose two decompositions

a_{1} + b_{1} = a_{2} + b_{2}

of the same binomial. Comparing rationals and medials in the squares forces

a_{1} = a_{2}

and

b_{1} = b_{2}

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Depends on (1)

X.36Proposition X.36If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be…

Required by (dependents) (2)

X.43Proposition X.43A first bimedial straight line is divided at one and the same point only.
X.79Proposition X.79Only one rational straight line can be annexed to an apotome which is commensurable with the whole in square only.

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