Archimedes Texts

SIMPL. And who saith that I cannot draw other lines? why
may not I protract another line underneath, unto the point A,
that may be perpendicular to the rest?

SALV. You can doubtless, at one and the same point, make no
more than three right lines concurre, that constitute right angles
between themselves.

SAGR. I see what Simplicius means, namely, that should the
said D A be prolonged downward, then by that means there might
be drawn two others, but they would be the same with the first
three, differing onely in this, that whereas now they onely touch,
then they would intersect, but not produce new dimensions.

SIMPL. I will not say that this your argument may not be con
cludent; but yet this I say with Aristotle, that in things natural
it is not alwaies necessary, to bring Mathematical demonstrations.

SAGR. Grant that it were so where such proofs cannot be had,
yet if this case admit of them, why do not you use them? But it
would be good we spent no more words on this particular, for I
think that Salviatus will yield, both to Aristotle, and you, with
out farther demonstration, that the World is a body, and perfect,
yea most perfect, as being the greatest work of God.

SALV. So really it is, therefore leaving the general contempla

tion of the whole, let us descend to the consideration of its parts,
which Aristotle, in his first division, makes two, and they very diffe
rent and almost contrary to one another; namely the Cœlestial,
and Elementary: that ingenerable, incorruptible, unalterable, un
passible, &c. and this exposed to a continual alteration, mutati
on, &c. Which difference, as from its original principle, he de
rives from the diversity of local motions, and in this method he
proceeds.

Parts of the world
are two, according
to Aristotle, Cœle
stial and Elemen
tary contrary to
one another.

Leaving the sensible, if I may so speak, and retiring into the
Ideal world, he begins Architectonically to consider that nature
being the principle of motion, it followeth that natural bodies be

indued with local motion. Next he declares local motion to be
of three kinds, namely, circular, right, and mixt of right and cir
cular: and the two first he calleth simple, for that of all lines the

circular, and right are onely simple; and here somewhat re
straining himself, he defineth anew, of simple motions, one to be
circular, namely that which is made about the medium, and the
other namely the right, upwards, and downwards; upwards, that
which moveth from the medium; downwards, that which goeth to
wards the medium. And from hence he infers, as he may by and ne

cessary consequence, that all simple motions are confined to these
three kinds, namely, to the medium, from the medium, and about
the medium; the which corresponds saith he, with what hath been
said before of a body, that it also is perfected by three things, and so