Proposition VII.5 — If a number be a part of a number, and another be the same p…

Proof

a = b / n

and

c = d / n

give

a + c = (b + d) / n

by gathering

n

copies of

a + c

together.

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Depends on (2)

2Common notion 2If equals be added to equals, the wholes are equal.
VII.3Definition VII.3A number is a part of a number, the less of the greater, when it measures the greater.

Required by (dependents) (4)

VII.6Proposition VII.6If a number be parts of a number, and another be the same parts of another, the sum will also be the same parts of the…
VII.9Proposition VII.9If a number be a part of a number, and another be the same part of another, alternately, whatever part or parts the…
VII.12Proposition VII.12If there be as many numbers as we please in proportion, then, as one of the antecedents is to one of the consequents,…
VII.16Proposition VII.16If two numbers by multiplying one another make certain numbers, the numbers so produced will be equal to one another.

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