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

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Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.

Let

A B C

be the given circle and

D

the given segment, not greater than the diameter

B C

of the circle. Apply I.3 to cut off from

B C

a segment

B E

equal to

D

. With centre

B

and radius

B E

describe a circle

E A F

(Postulate 3); join

B A

where

E A F

meets the given circle. Then

B A = B E = D

by Definition I.15, so

B A

is the required chord.