Return to Vignettes of Ancient Mathematics Definition of faster
(Physics Z 2.232a23-7) Since every magnitude is divisible into
magnitudes (for it was proved that it is impossible for a
continuous magnitude to be from indivisible ones, but every
magnitude is continuoous), then it is necessary that (a) the
faster traverse a greater distance in the equal time and (b) an
equal distance in the lesser time and (c) more distance in the
lesser time, just as some define the faster. Argument for a
(Physics Z 2.232a27-31): (figure 1: moving) or (figure 2: still)
For let A be faster than B. Then since that which changes first
is faster, in the time in which A has changed from to , e.g. ZH,
B will not yet be at , but it will fall short, so that in the
equal time the faster will traverse more in an equal time.
Argument for c (Physics Z 2.232a31-b5): 1) In fact, it will also
move more in less time. For in the time in which A has come to
be at , let B be at E, since it is the slower. (figure 2)
Accordingly since A has come t