length, without breadth, or without depth?

Two different answers, I find, have been made to this argument; neither
of which is in my opinion satisfactory. The first is, that the objects of
geometry, those surfaces, lines and points, whose proportions and
positions it examines, are mere ideas in the mind; I and not only never
did, but never can exist in nature. They never did exist; for no one will
pretend to draw a line or make a surface entirely conformable to the
definition: They never can exist; for we may produce demonstrations from
these very ideas to prove, that they are impossible.

But can anything be imagined more absurd and contradictory than this
reasoning? Whatever can be conceived by a clear and distinct idea
necessarily implies the possibility of existence; and he who pretends to
prove the impossibility of its existence by any argument derived from the
clear idea, in reality asserts, that we have no clear idea of it, because
we have a clear idea. It is in vain to search for a contradiction in any
thing that is distinctly conceived by the mind. Did it imply any
contradiction, it is impossible it coued ever be conceived.

There is therefore no medium betwixt allowing at least the possibility of
indivisible points, and denying their idea; and it is on this latter
principle, that the second answer to the foregoing argument is founded.
It has been pretended [L'Art de penser.], that though it be impossible to
conceive a length without any breadth, yet by an abstraction without a
separation, we can consider the one without regarding the other; in the
same manner as we may think of the length of the way betwixt two towns,
and overlook its breadth. The length is inseparable from the breadth both
in nature and in our minds; but this excludes not a partial consideration,
and a distinction of reason, after the manner above explained.