Proposition IX.34 — If an even number be neither one of those which are doubled …

Proof

Such a number has the form

2^{k} m

with

k \geq 2

and

m

odd,

m > 1

: it is even-times even (

2 \cdot 2^{k - 1} m

) and even-times odd (

2^{k} \cdot m

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Depends on (2)

IX.32Proposition IX.32Each of the numbers which are continually doubled beginning from a duad is even-times even only.
IX.33Proposition IX.33If a number have its half odd, it is even-times odd only.

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