The English works of Thomas Hobbes of Malmesbury, Volume 07 (of 11) — Thomas Hobbes — John Shaqi
The English works of Thomas Hobbes of Malmesbury, Volume 07 (of 11)
Thomas Hobbes · en
The nineteenth article of mine in this fourteenth chapter, is this:
“_All respect or variety of position of two lines, seemeth to be
comprehended in four kinds_. For they are either _parallel_, or (_being
if need be produced_) _make an angle_; or, (if drawn out far enough)
_touch_; or, lastly, they are _asymptotes_”; in which you are first
offended with the word _It seems_. But I allow you, that never err, to
be more peremptory than I am. For to me it seemed (I say again seemed)
that such a phrase, in case I should leave out something in the
enumeration of the several kinds of position, would save me from being
censured for untruth; and yet your instance of two straight lines in
divers planes, does not make my enumeration insufficient. For those
lines, though not parallels, nor cutting both the planes, yet being
moved parallelly from one plane to another, will fall into one or other
of the kinds of position by me enumerated; and consequently, are as much
that position, as two straight lines in the same plane, not parallel,
make the same angle, though not produced till they meet, which they
would make if they were so produced: for you have nowhere proved, nor
can prove, that two such lines do not make an angle. It is not the
actual concurrence of the lines, but the arch of a circle, drawn upon
that point for centre, in which they would meet if they were produced,
and intercepted between them, that constitutes the angle.
Also your objection concerning asymptotes _in general_ is absurd. You
would have me add, that _their distance shall at last be less than any
distance that can be assigned_; and so make the definition of the
_genus_ the same with that of the _species_. But because you are not
professors of logic, it is not necessary for me to follow your counsel.
In like manner, if we understand one line to be moved towards another
always parallelly to itself, which is, though not actually, yet
potentially the same position, all the rest of your instances will come
to nothing.
At the two-and-twentieth article you object to me the use of the word
_figure_, before I had defined it: wherein also you do absurdly; for I
have nowhere before made such use of the word _figure_, as to argue
anything from it; and therefore your objection is just as wise as if you
had found fault with putting the word figure in the titles of the
chapters placed before the book. If you had known the nature of
demonstration, you had not objected this.