Galilei, Galileo Dialogues on two world systems 1661, tr. Salusbury, Thomas
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4
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