428 
PAPPUS OF ALEXANDRIA 
Historical preface. 
It begins wit!} 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 
lamblichus 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 prj^aviKos) 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 (ttoow), since it 
represents a sort of ‘ distance ’ between the two lines forming 
it, this distance being ‘extended one way’ (k(f> eu Sieo-Tcos) 
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 ; Qarpus seems in reality to have 
been anticipating the modern view of an angle as representing 
divergence rather than distance, and to have meant by e0’ iv 
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 
(\tLpovpyu<6v), the former being made up of geometry, arith 
metic, 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 diffi 
cult or impossible for the same person to do both the necessary 
1 Simplicius on Arist. Categ., p. 192, Kalbfleisch. 
2 Proclus on Eucl. I, pp. 241-3. 3 lbpp. 125. 25-126. 6.