knowledge everything relevant to attain “true reality” (pragmata) and Platonic theology. The
literature upon which Proklos relied included important mathematical works like Euclid’s
Elements, H’s or P’ commentaries thereon, Neo-Pythagorean arithmetic
works, G’ encyclopedia of mathematical science, and astronomical works (especially
Ptolemy’s Almagest and Hypotheseis). (c) Conciliatory, since Proklos also tried to build a harmony
(sumpho ̄nia) between different kinds of reasoning or theories – e.g., Euclid’s proofs and
Aristotle’s theory of demonstration (revised by Syrianus). (d) Agonistic: the interpretation of
texts was discussed in a closed circle, some of them sometimes raising valid objections
(e.g. IE 29 – 30). This, in turn, was consistent with Proklos’ view that teaching should awaken
the souls of his listeners, controlled by, and directed toward, higher levels of cognition.
Main scientific works and influence: IT, Proklos’ favorite work (VP 38), is an ambi-
tious attempt to reconcile Plato’s dialogue with Aristotelian physics and cosmology, which
Proklos substantially criticized and modified. Likewise, his Hupotuposis attempts to criticize
Ptolemy’s cosmology by emphasizing the artificiality of his hypotheses as compared with
the simplicity and the independence from human needs characterizing natural processes,
ideas also explored in IR (2.213–236 Kroll). The 13th dissertation of IR also includes a
long discussion, in which Proklos discusses various issues pertaining to astrology or
Neo-Pythagorean arithmetic. He addresses in particular side and diagonal numbers and
confronts the Neo-Pythagorean procedure with a geometrical proof drawn from Euclid.
Proklos’ IE contains an original theory of mathematical activity and invention, derived from
Syrianus’ own projectionist theories about the activity of the soul (IE 49 – 57). In its first
Prologue, Proklos also developed I’ earlier idea of “general mathematics” (hole ̄
mathe ̄matike ̄) by expressing it according the late Neo-Platonist metaphysics (IE 5 – 10).
Proklos’ Elements of Physics, as well as his Elements of Theology, show his eagerness to adapt the
Euclidean paradigm of demonstration to other subjects, such as Aristotelian physics and
Neo-Platonist theology. Proklos’ immediate influence is seen in the interest that some of
his pupils took in ancient science, particularly Ammo ̄nios and Marinos.
DSB 11.160–162, G.R. Morrow; A.-Ph. Segonds, “Proclus: astronomie et philosophie,” in J. Pepin and
H.D. Saffrey, edd., Proclus, lecteur et interprète des anciens (1987) 319–334; O’Meara (1989) 142–208;
L. Siorvanes, Proclus, Neo-Platonic Philosophy and Science (1996); ECP 452 – 454, D.J. O’Meara;
H.D. Saffrey and A.-Ph. Segonds, Marinus: Proclus ou sur le bonheur (CUF 2001).
Alain Bernard
Prolegomena to Ptolemy’s Suntaxis (ca 450 – 500 CE?)
Some 25 MSS of P’s Suntaxis (early 9th c. and later) have a long introduction
consisting of a preliminary chapter, to which alone the title prolegomena legitimately applies
(ed.: Hultsch 1878: 3.–) and three independent studies, probably not from the
same author: (1) on isoperimetric figures, deriving from an earlier treatment traditionally
ascribed to Z (Knorr 1989: 725 and 738–741; ed.: Hultsch 1878: 3.1138–1165);
(2) on the calculation of the volume of the Earth, perhaps deriving from P with
different, sometimes erroneous, calculations (ed.: Hultsch 1878, 3.–); (3) on various
calculation techniques: multiplication, division, extraction of square roots, division of ratios
( partial ed.: Tannery, Diophantos 3 – 15 and Mémoires Scientifiques II.447–450; Knorr 1989:
185 – 210 and 787–793). This last study explicitly praises S, is close to D’
style, and was plausibly written by a member of the Neo-Platonist circle in Athens around
the middle of the 5th c. (Knorr 1989: 168).
PROLEGOMENA TO PTOLEMY’S SUNTAXIS