78
PYTHAGOREAN ARITHMETIC
(y) History of the term ‘ gnomon ’.
It will be noticed that the gnomons shown in the above
figure correspond in shape to the geometrical gnomons with
which Euclid, Book II, has made us familiar. The history of
the word ‘gnomon’ is interesting. (1) It was originally an
astronomical instrument for the measuring of time, and con
sisted of an upright stick which cast shadows on a plane or
hemispherical surface. This instrument is said to have been
introduced into Greece by Anaximander * 1 and to have come
from Babylon. 2 Following on this application of the word
‘ gnomon ’ (a ‘ marker ’ or ‘ pointer a means of reading off and
knowing something), we find Oenopides calling a perpendicular
let fall on a straight line from an external point a straight line
drawn ‘ gnomon-iuise ’ (Kara yvdfiova). 3 Next (2) we find the
term used of an instrument for drawing right angles, which
took the form shown in the annexed figure. This seems to
be the meaning in Theognis 805, where it is said
that the envoy'sent to consult the oracle at Delphi
should be ‘ straighter than the roproy (an instru-
■j ment with a stretched string for drawing a circle),
~ the ardOyr] (a plumb-line), and the gnomon’.
It was natural that, owing to its shape, the gnomon should
then be used to describe (3) the figure which remained of
a square when a smaller square was cut out of it (or the figure
which, as Aristotle says, when added to a square, preserves
the shape and makes up a larger square). The term is used
in a fragment of Philolaus where he says that ‘ number makes
all things knowable and mutually agreeing in the way charac
teristic of the gnomon’. 4 Presumably, as Boeckh says, the
connexion between the gnomon and the square to which it is
added was regarded as symbolical of union and agreement,
and Philolaus used the idea to explain the knowledge of
things, making the knowing embrace the knovm as the
gnomon does the square. 5 (4) In Euclid the geometrical
meaning of the word is further extended (II. Def. 2) to cover
1 Suidas, s. v. . 2 Herodotus, ii. 109.
3 Proclus on Eucl. I, p. 283. 9.
4 Boeckh, Philolaos des Pythagoreers Lehren, p. 141 ; ib., p. 144 ; Vors. i 3 ,
p. 313. 15.
5 Cf. Scholium No. 11 to Book II in Euclid, ed. Heib., vol. v, p. 225.