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

58 files·489.1 KB·

· 58 files

To bisect a given arc.

Let

A D B

be the given arc with chord

A B

. Bisect

A B

at

C

(I.10). At

C

erect

C D ⊥ A B

(I.11), meeting the arc at

D

. Join

A D

,

B D

. In right triangles

△ A C D

and

△ B C D

:

A C = C B

(construction),

C D

common, right angles at

C

. By I.4, the triangles are congruent and

A D = B D

. By III.28, equal chords cut off equal arcs (in the same circle), so arc

A D

equals arc

B D

.