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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

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Source — Euclid's Elements, encoded as an rrxiv paper

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X.42 Proposition X.42

A binomial straight line is divided into its terms at one point only.

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}

.

lines 74–74 in main.tex