176 THE ELEMENTS DOWN TO PLATO’S TIME
lay down the restriction of the means permissible in construc
tions to the ruler and compasses which became a canon of
Greek geometry for all ‘ plane ’ constructions, i.e. for all
problems involving the equivalent of the solution of algebraical
equations of degree not higher than the second.
Democritus, as mathematician, may be said to have at last
come into his own. In the Method of Archimedes, happily
discovered in 1906, we are told that Democritus w T as the first
to state the important propositions that the volume of a cone
is one third of that of a cylinder having the same base and
equal height, and that the volume of a pyramid is one third of
that of a prism having the same base and equal height; that is
to say, Democritus enunciated these propositions some fifty
years or more before they were first scientifically proved by
Eudoxus.
Democritus came from Abdera, and, according to his own
account, w T as young w r hen Anaxagoras was old. Apollodorus
placed his birth in 01. 80 (■= 460-457 B.C.), while according
to Thrasyllus he was born in 01. 77. 3 (= 470/69 B.C.), being
one year older than Socrates. He lived to a great age, 90
according to Diodorus, 104, 108, 109 according to other
authorities. He was indeed, as Thrasyllus called him,
irevTaOXos in philosophy 1 ; there was no subject to which he
did not notably contribute, from mathematics and physics on
the one hand to ethics and poetics on the other; he even went
by the name of ‘ Wisdom ’ {Zocpia). 2 Plato, of course, ignores
him throughout his dialogues, and is said to have wished to
burn all his works; Aristotle, on the other hand, pays
handsome tribute to his genius, observing, e.g., that on the
subject of change and growth no one save Democritus had
observed anything except superficially; whereas Democritus
seemed to have thought of everything. 3 He could say
of himself (the fragment is, it is true, considered by Diels
to be spurious, while Gomperz held it to be genuine), ‘ Of
all my contemporaries I have covered the most ground in
my travels, making the most exhaustive inquiries the while ;
I have seen the most climates and countries and listened to
1 Diog. L. ix. 37 (Vors. ii 3 , p. 11. 24-30).
2 Clem. Strom, vi. 32 (Vor<. ii 3 , p. 16. 28).
3 Arist. De yen. et corr. i. 2, 315 a 35.