Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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ſpread amongſt the vulgar; and this with a diſcretion and ſubtlety
reſembling that of the prudent young man, that to be freed
from the importunity of his inquiſitive Mother or Wife, I know
not whether, who preſſed him to impart the ſecrets of the Senate,
contrived that ſtory, which afterwards brought her and many o
ther women to be derided and laught at by the ſame Senate.

Plato held that
humane under
ſtanding partook
of divinity, becauſe
it understood num
bers.

The Myſtery of
Pythagorick num
bers fabulous.

De Papyrio præ
textato, Gellius I:
2. 3.

SIMPL. I will not be of the number of thoſe who are over curi
ous about the Pythagorick myſteries; but adhering to the point
in hand; I reply, that the reaſons produced by Ariſtotle to prove
the dimenſions to be no more than three, ſeem to me conclu
dent, and I believe, That had there been any more evident demon
ſtrations thereof, Ariſtotle would not have omitted them.

SAGR. Put in at leaſt, if he had known, or remembred any more.
But you Salviatus would do me a great pleaſure to alledge unto
me ſome arguments that may be evident, and clear enough for me
to comprehend.

SALV. I will; and they ſhall be ſuch as are not onely to be ap
prehended by you, but even by Simplicius himſelf: nor onely
to be comprehended, but are alſo already known, although hap
ly unobſerved; and for the more eaſie underſtanding thereof,
we will take this Pen and Ink, which I ſee already prepared for

ſuch occaſions, and deſcribe a few figures. And firſt we will note
[Fig. 1. at the end of this Dialog.] theſe two points AB, and draw
from the one to the other the curved lines, ACB, and ADB, and the
right line A B, I demand of you which of them, in your mind, is
that which determines the diſtance between the terms AB, & why?

A Geometrical de
monſtration of the
triple dimenſion.

SAGR. I ſhould ſay the right line, and not the crooked, as well
becauſe the right is ſhorter, as becauſe it is one, ſole, and deter
minate, whereas the others are infinit, unequal, and longer; and my
determination is grounded upon that, That it is one, and certain.

SALV. We have then the right line to determine the length be
tween the two terms; let us add another right line and parallel to
AB, which let be CD, [Fig. 2.] ſo that there is put between them a
ſuperficies, of which I deſire you to aſſign me the breadth, therefore
departing from the point A, tell me how, and which way you will
go, to end in the line C D, and ſo to point me out the breadth com
prehended between thoſe lines; let me know whether you will
terminate it according to the quantity of the curved line A E, or
the right line A F, or any other.

SIMPL. According to the right A F, and not according to the
crooked, that being already excluded from ſuch an uſe.

SAGR. But I would take neither of them, ſeeing the right line
A F runs obliquely; But would draw a line, perpendicular to C
D, for this ſhould ſeem to me the ſhorteſt, and the propereſt of
infinite that are greater, and unequal to one another, which may be

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