Proposition VII.28 — If two numbers be prime to one another, the sum will also be…

Proof

Any common divisor of

a + b

and

a

would also divide

b

(by Common Notion 3), contradicting

g cd (a, b) = 1

. Converse runs the same way.

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Depends on (2)

3Common notion 3If equals be subtracted from equals, the remainders are equal.
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)

IX.15Proposition IX.15If three numbers in continued proportion be the least of those which have the same ratio with them, any two whatever…

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