Infinite Divisebiity of Finite Matter. 357 
will draw a line from A —_*?__B, and, if you will move your 
penknife first over half of it from A to B, and then over half 
the remainder, and again over half the remainder, and in the 
same ratio keep moving your knife, as fast as you can, and 
you can never nove it from A to B_ Experience proves that 
one can move his knife from A to Bb; and what experience 
proves is always true: therefore the proposition involves an 
impossibility. The proposition is predicated on the opinion, 
that every finite line contains an infinite number of parts of 
smaller lines, which can be divided ad infinitum But it is im- 
possible that a finite line can contain an infinite number of 
parts, or smaller lines; for any number of equal parts into 
which every finite line caa be divided, will be a definite 
number of parts, of equal lengths; and all the parts being 
equal to the whole, if you keep constantly taking the parts of 
a finite quantity, you will, if you take fast enough, eventually 
take the whole. If you first take half the parts, and then half 
the remainder, and again half of the remainder, and so on, ac- 
cording to this ratio, you will eventually have but one part 
left, out of any definite number of parts whatever. If the 
line be divided into parts as small as they possibly can be, 
so small that no one of them can possibly be any smaller; if 
you have moved the knife to within the least possible part of 
the end of the line, or over all the definite parts of it but the 
very last one; if this last remainder be the least possible part 
of the line, how can it be divided into less remainders? If it 
is now the least possible part, how can it be divided into less 
parts? Suppose you put the point of your knife on the end 
of the line at B, and move it the least possible part of the line 
towards A, is it not clearly perceived by the mind, that the part 
’ moved over is as small as any part possibly can be; that it 
cannot contain parts smaller than itself? for no part can be 
jess than the least possible; therefore the least possible part 
is indivisible. For this reason, when there is but one part of 
the line left, and that the least possible, if you move the knife 
any further, you must move it to the end of the line. It is 
asked, if the least possible part of the line has not a beginning, 
a middle, and anend? Every indivisible part has a begin- 
ning and an end; but there is no absolute distance between 
them, though the beginning and the end together make abso- 
lute distance. ‘The least possible part is so small that it can- 
not be divided into halves, each of which shall have a begin- 
ning, a middle, and an end, and an infinite number of smaller 
