First Dialogue

Aristotle makes the world perfect because it has the triple dimension.

...particular demonstrations. Following this same order, I will propose and then freely state my opinion, exposing myself to the criticism of you both, and specifically of Signor Simplicio, who is such a strenuous champion and maintainer of the Aristotelian doctrine Aristotelian doctrine: The system of philosophy and science based on the works of Aristotle, which was the standard academic authority in Galileo's time.. The first step of the Peripatetic Peripatetic: A name for the followers of Aristotle, who often taught while walking about. progress is that passage where Aristotle proves the integrity and perfection of the World by pointing out to us how it is not a simple line, nor a pure surface, but a body adorned with length, width, and depth. Because dimensions do not exceed these three, and because the world has all three, it has them all; and having all, it is perfect. He argues that from simple length is constituted that magnitude called a line; when width is added, a surface is constituted; and when height or depth is added, a body results. After these three dimensions, there is no passage to any other, so that in these three alone, integrity—and, so to speak, totality—is terminated. I would have dearly wished that Aristotle had demonstrated this to me with necessity original: "con necessità" — meaning a logical proof that cannot be otherwise, especially since it could be performed quite clearly and quickly.

Aristotle's demonstrations to prove the dimensions are three, and no more. The number three was famous among the Pythagoreans.

SIMP. There is no lack of most beautiful demonstrations in the second, third, and fourth texts, following the definition of the Continuous Continuous: In geometry, a magnitude where the parts are joined at a common boundary.. Do you not have, first of all, the proof that beyond the three dimensions there is no other, because "three" is everything, and "three" is in every direction? And is this not confirmed by the authority and doctrine of the Pythagoreans Pythagoreans: Followers of the ancient Greek philosopher Pythagoras, who believed numbers were the fundamental reality of the universe., who say that all things are determined by three: beginning, middle, and end, which is the number of the "whole"? And where do you leave the other reason—namely, that almost by natural law this number is used in the sacrifices of the Gods? And that, nature itself dictating thus, we attribute the title of "all" to things that are three, and not fewer? For of two things we say "both," and we do not say "all," but of three we certainly do. You have all this doctrine in Text 2. In Text 3, then, original Latin: "ad pleniorem scientiam" for a fuller understanding, one reads that "everything," "the whole," and "the perfect" are formally the same; and that therefore only the body, among magnitudes, is perfect, because it alone is determined by three, which is the "whole." Being divisible in three ways, it is divisible in all directions. But of the others, some are divisible in one way, and some in two, because they possess division and continuity according to the number that has fallen to them; thus one is continuous in one direction, another in two, but the last—that is, the Body—is continuous in all. Furthermore, in Text 4, after some other doctrines, does he not prove the same with another demonstration—namely, that no passage is made...