Submit Spec API

//

··

rrxiv is an open protocol. Specification · API · Pulse · AboutMaintained by the rrxiv working group · Privacy-respecting analytics

Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

Browse/Euclid's Elements, encoded as an rrxiv paper/source

Source — Euclid's Elements, encoded as an rrxiv paper

··Download archive (.tar.gz)

Reader · live HTML Source files · loading…Rendered · PDF

58 files·489.1 KB·

· 58 files

← Claims Full view

IX.34 Proposition IX.34

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

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

).

lines 74–74 in main.tex