ZENO’S ARGUMENTS ABOUT MOTION 277 
letters A, B, C the exact interpretation of which is a matter 
of some doubt 1 ; the essence of it, however, is clear. The first 
diagram below shows the original positions of the rows of 
A, 
A 4 
AbK 
Ar 
¡0 
b 8 
hi 
B 5 
B 4 
B 2 
B, ► 
Hi 
E 
bodies (say eight in number). The is represent a row which 
is stationary, the B’s and Us are rows which move with equal 
velocity alongside the A’s and one another, in the directions 
shown by the arrows. Then clearly there will be (1) a moment 
Ai 
> 
IO 
& 
A^Ag 
A ef Ariosi 
B 8 
B y Bg 
Bs 
B 4 B.tj 
B 2 B 1 
Çs 
c rl c el 
when the B’s and O’ s will be exactly under the respective is, 
as in the second diagram, and after that (2) a moment when 
the B’s and C’s will have exactly reversed their positions 
relatively to the M’s, as in the third figure. 
The observation has been made 2 that the four arguments 
form a system curiously symmetrical. The first and fourth 
consider the continuous and movement within given limits, 
the second and third the continuous and movement over 
1 The interpretation of the passage 240 a 4-18 is elaborately discussed 
by R. K. Gaye in the Journal of Philology, xxxi, 1910, pp. 95-116. It is 
a question whether in the above quotation Aristotle means that Zeno 
argued that half the given time would be equal to double the half, i. e. 
the whole time simply, or to double the whole, i. e. four times the half. 
Gaye contends (unconvincingly, I think) for the latter. 
2 Brochard, loc. cit., pp. 4, 5,