Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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Moreover in the fourth Text; doth he not after ſome other Do
ctrines, prove it by another demonſtration? Scilicet, That no tran
ſition is made but according to ſome defectus (and ſo there is a tran
ſition or paſſing from the line to the ſuperficies, becauſe the line is
defective in breadth) and that it is impoſſible for the perfect to
want any thing, it being every way ſo; therefore there is no tran
ſition from the Solid or Body to any other magnitude. Now
think you not that by all theſe places he hath ſufficiently proved,
how that there's no going beyond the three dimenſions, Length,
Breadth, and Thickneſs, and that therefore the body or ſolid,
which hath them all, is perfect?

Ariſtotles demon
ſtrations to prove
the dimenſions to be
three and no more.

The number three
celebrated among ſt
the Pythagorians

Omne, Totum &
Perfectum.

SALV. To tell you true, I think not my ſelf bound by all theſe
reaſons to grant any more but onely this, That that which hath
beginning, middle, and end, may, and ought to be called perfect: But
that then, becauſe beginning, middle, and end, are Three, the num
ber Three is a perfect number, and hath a faculty of conferring
Perfection on thoſe things that have the ſame, I find no inducement
to grant; neither do I underſtand, nor believe that, for example,
of feet, the number three is more perfect then four or two, nor do
I conceive the number four to be any imperfection to the Ele
ments: and that they would be more perfect if they were three.
Better therefore it had been to have left theſe ſubtleties to the
Rhetoricians, and to have proved his intent, by neceſſary demonſtra
tion; for ſo it behoves to do in demonſtrative ſciences.

SIMPL. You ſeem to ſcorn theſe reaſons, and yet it is all the
Doctrine of the Pythagorians, who attribute ſo much to numbers;
and you that be a Mathematician, and believe many opinions in
the Pythagorick Philoſophy, ſeem now to contemn their My
ſteries.

SALV. That the Pythagorians had the ſcience of numbers in
high eſteem, and that Plato himſelf admired humane underſtand
ing, and thought that it pertook of Divinity, for that it under

ſtood the nature of numbers, I know very well, nor ſhould I be
far from being of the ſame opinion: But that the Myſteries for
which Pythagoras and his ſect, had the Science of numbers in ſuch
veneration, are the follies that abound in the mouths and writings

of the vulgar, I no waies credit: but rather becauſe I know that they,
to the end admirable things might not be expoſed to the con
tempt, and ſcorne of the vulgar, cenſured as ſacrilegious, the pub

liſhing of the abſtruce properties of Numbers, and incommen
ſurable and irrational quantities, by them inveſtigated; and di
vulged, that he who diſcovered them, was tormented in the other
World: I believe that ſome one of them to deter the common
ſort, and free himſelf from their inquiſitiveneſs, told them that the
myſteries of numbers were thoſe trifles, which afterwards did ſo

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