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

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

In a given circle to inscribe an equilateral and equiangular hexagon.

Let

G

be the centre and

A D

a diameter of the given circle. With centre

D

and radius

D G

describe a circle meeting the given circle at

C

and

E

(Postulate 3). Join

GC

GE

. The triangle

G D C

has

G D = D C = C G

(radii of equal circles), so it is equilateral, and

∠ D GC = 6 0^{\circ}

(I.32). Stepping this

6 0^{\circ}

chord around the circle six times produces the regular hexagon.

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