A history of Greek mathematics - Wilbourhall.org

540 COMMENTATORS AND BYZANTINES
made valuable extracts, including the account of the attempt of
'Aganis' to prove the parallel-postulate (see pp. 228
30 above).
Contemporary with Simplicius, or somewhat earlier, was
Eutocius, the commentator on Archimedes and Apollonius.
As he dedicated the commentary on Book I On the Sphere
and Cylinder to Ammonius (a pupil of Proclus and teacher
of Simplicius), who can hardly have been alive after a.d. 510,
Eutocius was probably born about A.D. 480. His date used
to be put some fifty years later because, at the end of the commentaries
on Book II On the Sphere and Cylinder and on
the Measurement of a Circle, there is a note to the effect
'
that
the edition was revised by Isidorus of Miletus, the mechanical
engineer, our teacher '.
But, in view of the relation to Ammonius,
it is impossible that Eutocius can have been a pupil of
Isidorus, who was younger than Anthemius of Tralles, the
architect of Saint Sophia at Constantinople in 532, whose
work was continued by Isidorus after Anthemius's death
about a.d. 534.
Moreover, it was to Anthemius that Eutocius
dedicated, separately, the commentaries on the first four
Books of Apollonius's Conies, addressing Anthemius as my
'
dear friend '. Hence we conclude that Eutocius was an elder
contemporary of Anthemius, and that the reference to Isidorus
is by an editor of Eutocius's commentaries who was a pupil of
Isidorus. For a like reason, the reference in the commentary
on Book II On the Sphere and Cylinder 1 to a SiafirJTrjs
invented by Isidorus our teacher ' ' for drawing a parabola
must be considered to be an interpolation by the same editor.
Eutocius's commentaries on Archimedes apparently extended
only to the three works, On the
Sphere and Cylinder,
Measurement of a Circle and Plane Equilibriums, and those
on the Conies of Apollonius to the first four Books only.
We are indebted to these commentaries for many valuable
historical notes. Those deserving special mention here are
(1) the account of the solutions of the problem of the duplica-
',
tion of the cube, or the finding of two mean proportionals,
'
by Plato Heron, Philon, Apollonius, Diodes, Pappus,
Sporus, Menaechmus, Archytas, Eratosthenes, Nicomedes, (2)
the fragment discovered by Eutocius himself containing the
1
Archimedes, ed. Heiberg, vol. iii, p. 84. 8-11.