Proposition X.112 — The square on a rational straight line applied to the binomi…

Proof

R^{2} / (a + b) = a^{'} - b^{'}

with

a^{'}

b^{'}

in the same ratio as

a

b

. Verified by direct manipulation of the square-on-binomial identity.

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Depends on (2)

X.91Proposition X.91If an area be contained by a rational straight line and a first apotome, the side of the area is an apotome.
X.97Proposition X.97The square on an apotome straight line applied to a rational straight line produces as breadth a first apotome.

Required by (dependents) (2)

X.113Proposition X.113The square on a rational straight line applied to an apotome produces as breadth a binomial the terms of which are…
X.114Proposition X.114If an area be contained by an apotome and the binomial the terms of which are commensurable with the terms of the…

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