Book I, 715b.15
Generation of Animals
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 175
“Infinite product spaces are the natural habitat of probability theory.”
Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter V, Conditional Probability, Stochastic Independence, p. 130
“Man, limited by his nature, is infinite in his desires.”
“The world's nature is a harmonious compound of infinite and finite elements”
The Life of Pythagoras (1919)
Context: Fragment 1. (Stob.21.7; Diog.#.8.85) The world's nature is a harmonious compound of infinite and finite elements; similar is the totality of the world in itself, and of all it contains.
b. All beings are necessarily finite or infinite, or simultaneously finite and infinite; but they could not all be infinite only.
“Nature is an infinite sphere whose center is everywhere and whose circumference is nowhere.”
“Since, however, all multitude and magnitude are by their own nature of necessity infinite”
Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Context: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184
Book III, Ch. V, p. 156.
Physics
Book III, Ch. IV, pp. 152-155.
Physics
