Nicomachus

"All that has by nature, with systematic method, been arranged in the universe, seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and t…"

"The even is that which can be divided into two equal parts without a unit intervening in the middle; and the odd is that which cannot..."

"In Plato's Republic, when the interlocutor of Socrates appears to bring certain plausible reasons to bear upon the mathematical sciences, to show that they are useful to human life, arithmetic for rec…"

"Bodily, material things are... continuously involved in continuous flow and change—in imitation of the nature and peculiar quality of that eternal matter and substance which has been from the beginnin…"

"Some... agreeing with, believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that 'geometric harmony' is the cube because it is harmonized in all t…"

"Scientific number, being set over such things as these, should be harmoniously constituted, in accordance with itself; not by any other but by itself."

"Nicomachus of Gerusa: Introduction to Arithmetic . Tr. Martin Luther D'Ooge with studies in Greek arithmetic by Frank Egleston Robbins and."

"Without the aid of these, then, it is not possible to deal accurately with the forms of being nor to discover the truth in things, knowledge of which is wisdom, and evidently not even to philosophize …"