Proposition VII.12 — If there be as many numbers as we please in proportion, then…

Proof

Discrete analogue of V.12: each pair contributes the same multiple or part, so the sum does too.

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Depends on (2)

VII.5Proposition VII.5If a number be a part of a number, and another be the same part of another, the sum will also be the same part of the…
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…

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