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

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

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VII.35 Proposition VII.35

If two numbers measure any number, the least number measured by them will also measure the same.

Proof

Let

L = lcm (a, b)

and suppose

a, b ∣ n

. Divide

n

by

L

with remainder; the remainder

r

is measured by both

a

and

b

(Common Notion 3 on the equimultiples) and is less than

L

. By minimality of

L

,

r = 0

.

lines 74–74 in main.tex