A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

DOMNINUS. SIMPLICIUS 539
sophy at Athens, the last members of the school, including
Damascius and Simplicius, migrated to Persia, but returned
about 533 to Athens, where Simplicius continued to teach for
some time though the school remained closed.
Extracts from Eudemus.
To Simplicius we owe two long extracts of capital importance
for the history of mathematics and astronomy. The
first is his account, based upon and to a large extent quoted
textually from Eudemus's History of Geometry, of the attempt
by Antiphon to square the circle and of the quadratures of
lunes by Hippocrates of Chios. It is contained in Simplicius's
commentary on Aristotle's Physics} and has been the subject
of a considerable literature extending from 1870, the date
when Bretschneider first called attention to it, to the latest
critical
edition with translation and notes by Rudio (Teubner,
1907). It has already been discussed (vol. i, pp. 183-99).
The second, and not less important, of the two passages is
that containing the elaborate and detailed account of the
system of concentric spheres, as first
invented by Eudoxus for
explaining the apparent motion of the sun, moon, and planets,
and of the modifications made by Callippus and Aristotle. It
is contained in the commentary on Aristotle's Be caelo * ;
Simplicius quotes largely from Sosigenes the Peripatetic
(second century a.d.) 5
observing that he in his turn drew
from Eudemus, who dealt with the subject in the second
book of his History of Astronomy. It is this passage of
Simplicius which, along with a passage in Aristotle's Metaphysics?
enabled Schiaparelli to reconstruct Eudoxus' s
system
(see vol. i, pp. 329-34). Nor must it be forgotten that it is in
Simplicius's commentary on the Physics^ that the extract
from Geminus's summary of the Meteorologica of Posidonius
occurs which was used by Schiaparelli to support his view
that it was Heraclides of Pontus, not Aristarchus of Samos,
who first propounded the heliocentric hypothesis.
Simplicius also wrote a commentary on Euclid's Elements,
Book I, from which an-Nairizi, the Arabian commentator,
1
2
Simpl. in Phtjs., pp. 54-69, ed. Diels.
Simpl. on Arist. De caelo, p. 488. 18-24 and pp. 493-506, ed. Heiberg.
3
Metaph. A. 8, 1073 b 17-1074 a 14.
4
Simpl. in Phys., pp. 291-2, ed. Diels.
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.