Proposition IX.21 — If as many even numbers as we please be added together, the …

Proof

Each even number is divisible by 2; the sum is therefore divisible by 2 (Common Notion 2).

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Depends on (2)

2Common notion 2If equals be added to equals, the wholes are equal.
VII.6Definition VII.6An even number is that which is divisible into two equal parts.

Required by (dependents) (2)

IX.22Proposition IX.22If as many odd numbers as we please be added together, and their multitude be even, the whole will be even.
IX.28Proposition IX.28If an odd number by multiplying an even number make some number, the product will be even.

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