Proposition X.114 — If an area be contained by an apotome and the binomial the t…

Proof

The rectangle on

(a - b)

and

(a^{'} + b^{'})

with

a^{'} = k a

b^{'} = k b

equals

k (a^{2} - b^{2})

, which is rational.

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Depends on (2)

X.112Proposition X.112The square on a rational straight line applied to the binomial straight line produces as breadth an apotome the terms…
X.113Proposition X.113The square on a rational straight line applied to an apotome produces as breadth a binomial the terms of which are…

Required by (dependents) (1)

X.115Proposition X.115From a medial straight line there arise irrational straight lines infinite in number, and none of them is the same with…

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