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Proposition·Untested·2605.00009

Proposition VII.9

If a number be a part of a number, and another be the same part of another, alternately, whatever part or parts the first is of the third, the same part or the same parts will the second also be of the fourth.

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Proof

The "part of a part" relation is symmetric across the alternation by construction; apply VII.5 / VII.6 on a per-piece basis to confirm.

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Full neighborhood

Depends on (2)

Required by (dependents) (2)

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