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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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IV.8 Proposition IV.8

In a given square to inscribe a circle.

Proof

Let

A B C D

be the given square. Bisect the sides at

F H

,

F

,

G

,

H

(I.10). Join

E G

and

F H

, meeting at

K

. By I.34 and the construction,

K E = K F = K G = K H

. Drop perpendiculars from

K

to each side; each is equal to

K E

. Thus the circle with centre

K

and radius

K E

touches each side at its midpoint (III.16).

lines 74–74 in main.tex