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 other women to be derided and laught at by the same Senate.
Simpl.I will not be of the number of those who are over curious 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 concludent, and I believe, That had there been any more evident demonstrations 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 apprehended by you, but even by Simplicius himself: nor onely to be comprehended, but are also already known, although haply unobserved; and for the more easie understanding thereof, we will take this Pen and Ink, which I see already prepared for such occasions,A Geometrical demonstration of the triple dimension. and describe a few figures. And first we will note [Fig. 1. at the end of this Dialog.] these two points A B, and draw from the one to the other the curved lines, A C B, and A D B, 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 A B, & why?
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 determinate, 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 between the two terms; let us add another right line and parallel to A B, which let be C D, [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 comprehended 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 bepro-
