Proof: By Euclid
(related to Corollary: Every Equilateral Triangle Is Equiangular.)
 If a triangle $ABC$ is equilateral, then the sides $AB$ and $BC$ have equal lengths.
 From Prop 1.05 it follows that the angles $\angle{ABC}$ and $\angle{BCA}$ are equal.
 The same follows for the angles $\angle{ABC}$ and $\angle{CAB}$, since the sides $AB$ and $AC$ are equal.
 Thus, the triangle is equiangular.
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"