Proposition VII.6 — If a number be parts of a number, and another be the same pa…

Proof

Same argument as VII.5 with

p / q

fractions; each fractional piece sums separately by VII.5 and then by VII.5 again on the multiples.

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Depends on (1)

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…

Required by (dependents) (3)

VII.8Proposition VII.8If a number be the same parts of a number that a subtracted number is of a subtracted number, the remainder will also…
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,…

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