there may not be above an inch in it. After this manner, the properties
of the lines signified are (by a very usual figure) transferred to the
sign, and thence, through mistake, though to appertain to it considered
in its own nature.

127. Because there is no number of parts so great but it is possible
there may be a line containing more, the inch-line is said to contain
parts more than any assignable number; which is true, not of the inch
taken absolutely, but only for the things signified by it. But men, not
retaining that distinction in their thoughts, slide into a belief that
the small particular line described on paper contains in itself parts
innumerable. There is no such thing as the ten--thousandth part of an
inch; but there is of a mile or diameter of the earth, which may be
signified by that inch. When therefore I delineate a triangle on paper,
and take one side not above an inch, for example, in length to be the
radius, this I consider as divided into 10,000 or 100,000 parts or more;
for, though the ten-thousandth part of that line considered in itself is
nothing at all, and consequently may be neglected without an error or
inconveniency, yet these described lines, being only marks standing for
greater quantities, whereof it may be the ten--thousandth part is very
considerable, it follows that, to prevent notable errors in practice, the
radius must be taken of 10,000 parts or more.

128. LINES WHICH ARE INFINITELY DIVISIBLE.--From what has been said
the reason is plain why, to the end any theorem become universal in
its use, it is necessary we speak of the lines described on paper
as though they contained parts which really they do not. In doing
of which, if we examine the matter thoroughly, we shall perhaps
discover that we cannot conceive an inch itself as consisting of,
or being divisible into, a thousand parts, but only some other line which