Dialogue Concerning the Two Chief World Systems

...spread among the common people; and this with cunning and cleverness similar to that of the sagacious young man Salviati refers to the legend of Papirius Praetextatus, a Roman youth who, when pressured by his mother to reveal the secrets of the Senate, lied and said the Senate was debating whether it was better for one man to have two wives or one wife to have two husbands., who, to rid himself of the importunity of—I know not if it were his Mother or his curious Wife—who besieged him to share the secrets of the Senate, composed that fable, whereby she and many other women were later mocked, to the great laughter of the same Senate.

SIMP. I do not wish to be numbered among those too curious about the mysteries of the Pythagoreans Pythagoreans: Followers of Pythagoras who believed that numbers held mystical and physical power over the universe., but staying with our purpose, I repeat that the reasons produced by Aristotle to prove that dimensions dimensions: The measurable extents of an object—length, width, and height. are not, and cannot be, more than three, seem conclusive to me; and I believe that if there had been a more necessary demonstration, Aristotle would not have left it out.

SAGR. Add at least "if he had known it," or "if it had occurred to him." But you, Mr. Salviati, would do me a great favor by providing me with some evident reason, if you have any so clear that it can be understood by me.

Geometric demonstration of the triple dimension.

SALV. Indeed, it shall be understood by you, and by Mr. Simplicio as well; and not only understood, but already known, though perhaps not noticed. And for easier understanding, we will take paper and pen, which I see are already prepared here for such occurrences, and we will make a little figure. First, we will mark these two points, A and B, and drawing from one to the other the curved lines A. C. B. and A. D. B. and the straight line A. B., I ask you which of them in your mind is the one that determines the distance between the endpoints A and B, and why.

A geometric diagram showing two points, A and B, connected by a horizontal straight line. Two curved arcs also connect A and B: one passing through point C above the straight line, and another passing through point D below it.

SAGR. I would say the straight line, and not the curves; both because the straight line is the shortest, and because it is unique, alone, and determined, whereas the others are infinite, unequal, and longer; and it seems to me that the determination must be taken from that which is single and certain.

SALV. We have, then, the straight line as the determinant of the length between two endpoints; let us now add another straight line, parallel to A. B., which shall be C. D., so that between them a surface remains interposed, of which I would like you to assign me—

A geometric diagram showing two parallel horizontal lines. The top line is marked with points A and B. The bottom line is marked with points C, F, E, and D. A straight vertical line connects A and C. A curved line connects A and F. A longer, more pronounced curved line connects A and E.