Proposition VII.33 — Given as many numbers as we please, to find the least of tho…

Proof

Divide each given number by their common gcd (VII.3); the quotients are pairwise coprime (VII.22) and least in the original ratio.

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Depends on (2)

VII.3Proposition VII.3Given three numbers not prime to one another, to find their greatest common measure.
VII.22Proposition VII.22The least numbers of those which have the same ratio with them are prime to one another.

Required by (dependents) (1)

VIII.4Proposition VIII.4Given as many ratios as we please in least numbers, to find numbers in continued proportion which are the least in the…

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