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

THE COLLECTION 359
sizes and distances of the sun and moon), Autolycus (On the
moving sphere), Carpus of Antioch (who is quoted as having
said that Archimedes wrote only one mechanical book, that
on sphere-making, since he held the mechanical appliances
which made him famous to be nevertheless unworthy of
written description : Carpus himself, who was known as
mechanicus, applied geometry to other arts of this practical
kind), Charmandrus (who added three simple and obvious loci
to those which formed the beginning of the Plane Loci of
Apollonius), Conon of Samos, the friend of Archimedes (cited
as the propounder of a theorem about the spiral in a plane
which Archimedes proved : this would, however, seem to be
a mistake, as Archimedes says at the beginning of his treatise
that he sent certain theorems, without proofs, to Conon, who
would certainly have proved them had he lived), Demetrius of
Alexandria (mentioned as the author of a work called ' Linear
considerations', ypa/ifxtKal emo-Tcco-eL?, i.e. considerations on
curves, as to which nothing more is known), Dinostratus,
the brother of Menaechmus (cited, with Nicomedes, as having
used the curve of Hippias, to which they gave the name of
quadratrix, TeTpayoovigovo-a, for the squaring of the circle),
Diodorus (mentioned as the author of an Ancdemma), Eratosthenes
(whose mean-finder, an appliance for finding two or
any number of geometric means, is described, and who is
'
further mentioned as the author of two Books On means
and of a work entitled 'Loci wiih reference to means'),
Erycinus (from whose Paradoxa are quoted various problems
seeming at first sight to be inconsistent with Eucl. I. 21, it
being shown that straight lines can be drawn from two points
on the base of a triangle to a point within the triangle which
are together greater than the other two sides, provided that the
points in the base may be points other than the extremities),
Euclid, Geminus the mathematician (from whom is cited a
remark on Archimedes contained in his book ' On the classification
of the mathematical sciences ', see above, p. 223), Heraclitus
(from whom Pappus quotes an elegant solution of a vevcris
with reference to a square), Hermodorus (Pappus's son, to
whom he dedicated Books VII, VIII of his Collection), Heron
of Alexandria (whose mechanical works are extensively quoted
from), Hierius the philosopher (a contemporary of Pappus,
360 PAPPUS OF ALEXANDRIA
who is mentioned as having asked Pappus's opinion on the
attempted solution by ' plane ' methods of the problem of the two
means, which actually gives a method of approximating to
a solution 1 ), Hipparchus (quoted as practically adopting three
of the hypotheses of Aristarchus of Samos), Megethion (to
whom Pappus dedicated Book V of
his Collection), Menelaus
of Alexandria (quoted as the author of Sphaerica and as having
applied the name 7rapd8o£os to a certain curve), Nicomachus
(on three means additional to the first three), Nicomedes,
Pandrosion (to whom Book III of the Collection is dedicated),
Pericles (editor of Euclid's Data), Philon of Byzantium (mentioned
along with Heron), Philon of Tyana (mentioned as the
discoverer of certain complicated curves derived from the interweaving
of plectoid and other surfaces), Plato (with reference
to the five regular solids), Ptolemy, Theodosius (author of the
Sphaerica and On Bays and Nights).
(y)
Translations and editions.
The first published edition of the Collection was the Latin
translation by Commandinus (Venice 1589, but dated at the
end * Pisauri apud Hieronymum Concordiam 1588'; reissued
with only the
'
title-page changed Pisauri ... 1602 '). Up to
1876 portions only of the Greek text had appeared, namely
Books VII, VIII in Greek and German, by C. J. Gerhardt, 1871,
chaps. 33-105 of Book V, by Eisenmann, Paris 1824, chaps.
45-52 of Book IV in losephi Torelli Veronensis Geometrica,
1769, the remains of Book II, by John Wallis (in Opera
mathematica, III, Oxford 1699); in addition, the restorers
of works of Euclid and Apollonius from the indications
furnished by Pappus give extracts from the Greek text
relating to the particular works. Breton le Champ on Euclid's
Porisms, Halley in his edition of the Conies of Apollonius
(1710) and in his translation from the Arabic and restoration
respectively of the Be sectione rationis and Be, sectione spatii
of Apollonius (1706), Camerer on Apollonius's Tactiones (1795),
Simson and Horsley in their restorations of Apollonius's Plane
Loci and IncUnationes published in the years 1749 and 1770
respectively. In the years 1876-8 appeared the only com-
- 1 See vol. i, pp. 268-70.