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.