Proposition IX.22 — If as many odd numbers as we please be added together, and t…

Proof

Pair the odd summands: each pair has even sum (since odd + odd = even, by the definitions); the total of even-many pairs is even by IX.21.

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Depends on (2)

IX.21Proposition IX.21If as many even numbers as we please be added together, the whole is even.
VII.7Definition VII.7An odd number is that which is not divisible into two equal parts, or that which differs by a unit from an even number.

Required by (dependents) (1)

IX.23Proposition IX.23If as many odd numbers as we please be added together, and their multitude be odd, the whole will also be odd.

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