Proposition IX.33 — If a number have its half odd, it is even-times odd only.

Proof

n = 2 k

with

k

odd is even-times-odd; it cannot be even-times-even because then its half would be even.

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Depends on (2)

VII.6Definition VII.6An even number is that which is divisible into two equal parts.
VII.9Definition VII.9An even-times odd number is that which is measured by an even number according to an odd number.

Required by (dependents) (1)

IX.34Proposition IX.34If an even number be neither one of those which are doubled from a duad, nor have its half odd, it is both even-times…

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