Proposition IX.23 — If as many odd numbers as we please be added together, and t…

Proof

Group all but one of the summands by pairs (sum of those is even, IX.22); add the remaining odd number; the result is even + odd = odd by Common Notion 2 and Definition VII.7.

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Depends on (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.
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.29Proposition IX.29If an odd number by multiplying an odd number make some number, the product will be odd.

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