A history of Greek mathematics - Wilbourhall.org

428 PAPPUS OF ALEXANDRIA
Historical 'preface.
It begins with an interesting preface on the claim of
theoretical mechanics, as distinct from the merely practical
or industrial, to be regarded as a mathematical subject.
Archimedes, Philon, Heron of Alexandria are referred to as
the principal exponents of the science, while Carpus of Antioch
is also mentioned as having applied geometry to ' certain
(practical) arts'.
The date of Carpus is uncertain, though it is probable that
he came after Geminus; the most likely date seems to be the
first or second century A. D.
Simplicius gives the authority of
Iamblichus for the statement that Carpus squared the circle
by means of a certain curve, which he simply called a curve
generated by a double motion. 1 '
Proclus calls him Carpus the
writer on mechanics (o firjxaviKos) and quotes from ',
a work of
his on Astronomy some remarks about the relation between
problems and theorems and the 'priority in order' of the
former. 2 Proclus also mentions him as having held that an
angle belongs to the category of quantity (ttoo-ou), since it
represents a sort of ' distance ' between the two lines forming
it, this distance being ' extended one way '
{k %v SiecrTcos)
though in a different sense from that in which a line represents
extension one way, so that Carpus's view appeared to be the
'
greatest possible paradox ' 3
;
Carpus seems in reality to have
been anticipating the modern view of an angle as representing
divergence rather than distance, and to have meant by eft ef
in one sense (rotationally), as distinct from one way or in one
dimension (linearly).
Pappus tells us that Heron distinguished the logical, i.e.
theoretical, part of mechanics from the practical or manual
(xtLpovpyiKov), the former being made up of geometry, arithmetic,
astronomy and physics, the latter of work in metal,
architecture, carpentering and painting ; the man who had
been trained from his youth up in the sciences aforesaid as well
as practised in
the said arts would naturally prove the best
architect and inventor of mechanical devices, but, as it is
difficult
or impossible for the same person to do both the necessary
1
Simplicius on Arist. Categ., p. 192, Kalbfleisch.
2
y
Proclus on Eucl. I, pp. 241-3. lb., pp. 125. 25-126. 6.