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

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

Given a segment of a circle, to describe the complete circle of which it is a segment.

Let

A B C

be the given segment with chord

A C

and arc through

B

. Pick

B

on the arc; join

A B

B C

. Bisect

A B

D

and

B C

E

(I.10). At

D

and

E

erect perpendiculars to

A B

and

B C

respectively (I.11). By III.3 / III.9 these perpendiculars both pass through the centre, so their intersection

F

is the centre. With centre

F

and radius

F A

describe the full circle.

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