In geometry, Pappos relies on a considerable number of works, many known only
through his allusions in MC 7 (also MC 3, 4 and 5), several from Euclid and Apollo ̄nios.
Pappos includes them in the “field of analysis” described as “useful material” for the
invention of geometrical problems ( Jones 66–70).
Key Interests and Contribution to Ancient Science: In modern commentaries,
Pappos is sometimes characterized as only interested in geometry (e.g. Heath 2.358). But in
late antiquity, Pappos was mainly known for IA (to which MC also refers) and anthologies
of geometrical and mechanical problems, well reflecting the content and structure of many
of his works (mainly MC 3, 4, 7 and 8). His exposition is often structured by problems or
series of problems, for which he provides various approaches: fully articulated demonstrations,
analyses that open to new problems, mechanical devices, missing lemmas, or calculations.
In some cases unsolved problems or questions are presented with a variety of solutions
(e.g. the treatment of the “squaring” curve in MC 4). In one famous case, the generalization
of Euclid’s problem of three and four lines, Pappos proposes a generalization of the prob-
lem itself (MC 7, pp. 120–123 Jones). This taste for the variety of problems or solutions
is related to Pappos’ interest in problem-solving and mathematical heuristic and to his
endeavor to provide his students treasuries of solutions as a resource for their own efforts as well
as guidance through the use of these works.
This core feature of Pappos’ work is related to his other characteristics: his emphasis on
the dichotomy between invention and demonstration (MC 3.30 Hultsch and 7.1, p. 83
Jones); his tendency to classify and generalize problems according to kinship, either formally
or according to the solutions used; his mixture of mechanics and geometry (MC 8);
his mixture of calculation and geometrical reasoning, akin to the techniques used in the
Almagest; his complex use of the tradition, simultaneously reverential and critical (Cuomo
186 – 199).
Heath (1921); RE 18 (1949) 1084–1106, K. Ziegler; Jones (1986); Cuomo (2000); Decorps-Foulquier
(2000); Alain Bernard, “Sophistic aspects of Pappus’s Collection,” AHES 57 (2003) 93–150.
Alain Bernard
Pappos (II) (600 – 800 CE)
The early table in MS Marcianus gr. 299 mentions a treatise entitled By Pappos the Philosopher,
On the Divine Art; in the same MS is found a short treatise By Pappos the Philosopher (CAAG
2.27–28), which begins with a sermon steeped in Christian metaphysics and consisting in
an enigmatic description of the alchemical task. The author’s abridgment of a recipe of
S provides the terminus post.
Ed.: CAAG 2.27–28.
Letrouit (1995) 61.
Cristina Viano
Papyri (Overview)
Numerous papyri survive, mostly in small pieces, containing scientific texts. They are pri-
marily texts of practical science, with alchemy, astrology, pharmacy, and medicine being
the most heavily represented; mathematical, astronomical, and other scientific texts are
also found. Papyri constitute a kind of snapshot of what was in circulation and used – for
example, there are more papyri of H than of any other author or text. We have
PAPPOS (II)