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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 a square.

Let

A B C D

be the given circle with centre

E

. Draw two diameters

A C

and

B D

at right angles (I.11). Join

A B

B C

C D

D A

. The four right triangles at

E

are congruent by I.4 (two radii and the common right angle), so

A B = B C = C D = D A

. The inscribed angles standing on the diameters are right (III.31), so all four angles of

A B C D

are right. Therefore

A B C D

is a square.

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