100 Infinite Divisibility of Matter. 
en the supposition of the infinite divisibility of the line, the 
absurd inference is drawn, that the body will never arrive at 
B, whereas if the motion be uniform, nothing can be more 
certain, than that it will arrive at B in a time expressed by 
t= *, and that the time can never be infinite unless v=o, or 
v 
there be no motion. 
The fallacy of this statement consists in this. that the same 
time is allowed forthe passage of the body over the least bi- 
partite space, as for the greatest, or the time of passing over 
2 the line, is the same as over 4, 1, or any of the least con- 
ceivable of its divisions, consequently as the number of di- 
visions is supposed 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 
ef the line AB, with a uniform motion, consumes half the 
time of describing the whole line; in moving half the re- 
minder, or from a to 4, the time will be one half of the other 
half, or } of 3=}, &c. The spaces being divid :d by suppo- 
sition according to the series 4,1, 4, ;;, and the times, in 
uniform motion being as the spaces, the times will also be 
divided according to the same geometrical progression ; that 
is the time of the body’s moving from A to B is not what the 
writer of the article asserts infinite, or never to arrive at B, 
but a finite quantity, viz: that which is to the whole time of 
describing AB, as the series 3, 3, 1, ;4, sg, &c of AB=to I 
x AB=AB to AB, that is, the times are equal, consequently 
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 passed 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- 
responding to a point in goemetry, the motion even ofa can- 
non ball is nothing. ‘This shows the absolute necessity of 
taking fame into consideration in all our inquiries concerning 
motion. 
The problem at the end of the article, which proposes to 
divide a line into indivisible parts, proceeds on the unmath- 
ematical and inconsistent assumption, that a point has parts, or 
that it is an indivisible portion of extension.and that a line may 
