Proposition IX.29 — If an odd number by multiplying an odd number make some numb…

Proof

(2 k + 1) (2 m + 1) = 4 k m + 2 k + 2 m + 1

, which is odd (one more than even).

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Depends on (2)

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.
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.

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