Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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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.

In phyfical proofs
geometrical exact
neſs is not neceſſa
ry.

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

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