100 Infinite Divisibility of’ Matier. 
onthe supposition of the infinite divisibility of the line, the 
absurd inference is drawn, that the body will never arrive at 
B, wiiereas ifthe motion be uniform, nothing can be more 
certain, ‘hai that it will arrive at Bin a time expressed by 
i= * and that the time can never be infinite unless v=0, Or 
v 
there be no motion. 
The fallacy of this statement consists in this, that the same 
time is allowed for the passage of the body over the least bi- © 
parfite space, as for the prenters, or the time of passing over 
4 the line, is the same as over }, 1, or any of the least con- 
ceivable of its divisions, consequently as the number of. di- 
visions is 2 1S tery infinite, the time of passing over them. 
must be infinite. But let us view this subject mathematically. 
The body in passing from A to B, while it describes one half 
of the line AB, with a uniform: motion, consumes half the 
time of describing the whole line; in moving half the re- 
mndindayy or from a to b, the time will be onehalf of the other 
half, or 4 of =}, &c. The apaces: being —— by ae 
; ti 
sition according to the series $, }, $, rss 
uniform motion being as the spaces, the times ‘will also. be 
i to the same geometrical that 
divided according to progression 
is the time of the body’s moving from A to Bis not Fest the 
writer of the article asserts infinite, or never to arrive at B, 
but a finite quantity, viz: that. whet is to oe ar time of 
describing AB, as the series 3, 3,4, 5, 3's B=to 1 
Xx AB=AB to AB, that is, the times are qa, ciiognqiien tty 
the infinite divisibility of the line does not involve the ab- 
surdity of a body in motion requiring an infinite time to de- 
scribe a finite space. as, however, the space parse over by 
a uniform motion, and the time are reciprocally the mea- 
sures of each other, and if one be infinitely little, the other 
will be so also, it follows that if the time be nothing, the space. 
passed over will be nothing, so that in an instant of time cor- 
nding toa point in goemetry, the motion even of a can- 
non ball is nothing. ‘This shows the absolute nécessity of 
rs time into consideration in all our inquiries concerming: 
the ‘problem at the end of the article, which proposes ‘ee 
divide a line into indivisible parts, proceeds on the unmath- 
ematical and inconsistent assumption, thata point has parts, or 
that it i isan nindivisible = of extension,and that a line may 
a Sa a ei 
