Historical background

Apollonius of Perga was a famous Greek geometer (262 BCE – 190 BCE), who studied conics intensively, and invented the terms parabola, ellipse and hyperbola still in common use today. Among other things, he invented the parabolic mirror.

Regarding this “Circle of Apollonius”, Heath1 writes:

“This locus was discussed by Apollonius in his Plane Loci, Book II, as we know from Pappus…

But the construction was not discovered by Apollonius; it belongs to a much earlier date, since it appears in exactly the same form in Aristotle, Meteorologica III. 5, 376 a 3 sqq."

  1. Heath, Thomas L., Euclid: The thirteen books of the elements, 2nd. ed, Cambridge 1926 (reprinted by Dover, 1956), vol. 2, pp. 198–200.