The English works of Thomas Hobbes of Malmesbury, Volume 07 (of 11)
Thomas Hobbes · en
Your next objections are to my definition of a point. Which definition
adhereth to the former in these words, “and the body itself is called a
point.” Here again you call for help: “_Quis unquum mortalium, etc._
What mortal man, what sober man, did ever so define a point?” It is
well, and I take it to be an honour to be the first that do so. But what
objection do you bring against it. This: “That a point added to a point,
if it have magnitude, makes it greater.” I say it doth so, but then
presently it loseth the name of a point, which name was given to signify
that it was not the meaning of him that used it in demonstration to add,
subtract, multiply, divide, or any way compute it. Then you come in
with, “perhaps you will say though it have magnitude, that magnitude is
not considered.” You need not say _perhaps_. You know I affirm it; and
therefore your argument might have been left out, but that it gave you
an occasion of a digression into scurvy language.
And whereas you ask why I defined not a point thus: “_Punctum est corpus
quod non consideratur esse corpus, et magnum quod non consideratur esse
magnum_.” I will tell you why. First, because it is not Latin. Secondly,
because when I had defined it by _corpus_, there was no need to define
it again by _magnum_. I understand very well this language, “_punctum
est corpus, quod non consideratur ut corpus_.” A point is a body not
considered as body. But _punctum est corpus, quod non consideratur esse
corpus, vel esse magnum_, is not Latin; nor the version of it, _a point
is a body which is not considered to be a body_, English. My definition
was, that a point is that body whose magnitude is not considered, not
reckoned, not put to account in demonstration. And I exemplified the
same by the body of the earth describing the ecliptic line; because the
magnitude is not there reckoned nor chargeth the ecliptic line with any
breadth. But I perceive you understand not what the word _consideration_
signifieth, but take it for comparison or relation; and say I ought to
define a point simply, and not by relation to a great body; as if to
reckon and to compare were the same thing. “_Omnia mihi_,” saith Cicero,
“_provisa et considerata sunt_.” I have provided and reckoned
everything. There is a great difference between reckoning and relation.
Again, you ask, why _corpus motum_, a body moved? I will tell you;
because the motion was necessary for the generation of a line. And
though after the generation of the line the point should rest, yet it is
not necessary from this definition that it should be no more a point;
nor when Euclid defines a sphere by the circumduction of a semicircle
upon an axis that resteth, doth it follow from thence when the sphere,
axis, centre and all, as that of the earth, is moved from place to
place, that it is no more an axis.