Proposition V.9 — Magnitudes which have the same ratio to the same are equal t…

Proof

Contrapositive of V.8: if

a \neq = b

, then

a : c \neq = b : c

. Hence if

a : c = b : c

then

a = b

. Same argument with

c

as antecedent.

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Depends on (1)

V.8Proposition V.8Of unequal magnitudes the greater has to the same a greater ratio than the less has, and the same has to the less a…

Required by (dependents) (1)

VI.26Proposition VI.26If from a parallelogram there be taken away a parallelogram similar and similarly situated to the whole and having a…

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