Two other sciences in the same way will accurately treat of size: geom — Nicomachus

"To quote the words of Timaeus, in Plato, "What is that which always is, and has no birth, and what is that which is always becoming but never is? The one is apprehended by the mental processes, with reasoning, and is ever the same; the other can be guessed at by opinion in company with unreasoning sense, a thing which becomes and passes away, but never really is." Therefore, if we crave for the goal which is worthy and fitting for man, namely happiness of life—and this is accomplished by philosophy alone and nothing else, and philosophy means... for us desire for wisdom, and wisdom the science of the truth of things... it is reasonable and most necessary to distinguish and systematize the accidental qualities of things."

"And once more is this true in the case of music; not only because the absolute is prior to the relative, as great to greater and rich to richer and man to father, but also because the musical harmonies, diatessaron, diapente, and diapason, are named for numbers; similarly all of their harmonic ratios are arithmetical ones, for the diatessaron [] is the ratio of 4 : 3, the diapente [] that of 3 : 2, and the diapason [perfect ] the double ratio [2 : 1]; and the most perfect, the di-diapason [], is the quadruple ratio [4 : 1]."

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

"Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd."

"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..."

"The ancients, who under the leadership of Pythagoras first made science systematic, defined philosophy as the love of wisdom... [Οἱ παλαιοὶ καὶ πρώτοι μεθοδεύσαντες ἐπιστήμην κατάρξαντος Πυθαγόρου ὡρίζοντο φιλοσοφίαν εἶναι φιλίαν σοφίας...] This wisdom he defined as the knowledge, or science, of the truth in real things, conceiving science to be a steadfast and firm apprehension of the underlying substance. and real things to be those which continue uniformly and the same in the universe and never depart even briefly from their existence; these real things would be things immaterial..."