Proposition VII.23 — If two numbers be prime to one another, the number which mea…

Proof

a

b

are coprime and

d ∣ a

, any common divisor of

d

and

b

would divide both

a

and

b

, contradicting coprimality.

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Depends on (2)

VII.2Proposition VII.2Given two numbers not prime to one another, to find their greatest common measure.
VII.12Definition VII.12Numbers prime to one another are those which are measured by a unit alone as a common measure.

Required by (dependents) (1)

VII.24Proposition VII.24If two numbers be prime to any number, their product also will be prime to the same.

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