358 Infinite Divisibility of Finite Matter. 
hg 3 which is proved by the fact that we can move over it. 
hereas, if the least possible part of any line did contain, and 
could be divided into, an infinite number of infinitely divisible 
parts, and we were to move, as we necessarily must, first over 
half these parts, then over half the remainder, and so on in this 
ratio, we could never. to all eternity, move over all the parts 
of the least possible part; for there would always be half of a 
remainder left. But the fact is, there is no absolute distance 
between the beginning and the end of the least possible part, 
for such a part itself is as indivisible as the centre of a circle. 
The impossibility involved in the proposition is, that the last 
remaining part cannot be divided into halves. Therefore, 
when in moving over any finite line, we have moved over all 
the least possible parts of it but one, if we move any further, 
we must move over that one, which brings us to the end of 
the line. 
'N. B. The reason why the lines of the Asymtotes will 
never come in contact, is because they approach each other 
. 80 slowly. According to the nature of their approaching, it 
must take to all eternity for them to touch each other. 
pose that one should move so slowly that it would take to all 
eternity to go from his house to his office, how long would he 
be in going half the distance? Would he be as long as he 
would be in going the whole distance ? 
How to divide a Finite Material Line into indivisible parts. 
First describe a circle, and make its diameter the line to be 
divided. The centre of a circle is indivisible, and so is the 
line of its periphery, taken lengthwise; the diameter, or line 
to be divided, therefore, has three indivisible points: its cen- 
tre, which is the centre of its circle, and its points of union, 
with its periphery. Each of the semi-diameters will be di- 
vided into as many parts as you describe circles within its own 
circle. Now if you describe its own circle perfectly full of 
lesser circles, that is, if you make the indivisible periphery 
of the first inner circle to come into actual contact with the 
= indivisible periphery of its own circle,* and the indivisible 
periphery of the second inner circle into actual contact with 
*® Viz. of the circle of which the given line is the diameter. 
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