Nicomachus quotes

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 reckoning, distributions, contributions, exchanges, and partnerships, geometry for sieges, the founding of cities and sanctuaries, and the partition of land, music for festivals, entertainment, and the worship of the gods, and the doctrine of the spheres, or astronomy, for farming, navigation and other undertakings, revealing beforehand the proper procedure and suitable season, Socrates, reproaching him says: "You amuse me, because you seem to fear that these are useless studies that I recommend; but that is very difficult, nay, impossible. For the eye of the soul, blinded and buried by other pursuits, is rekindled and aroused again by these and these alone, and it is better that this be saved than thousands of bodily eyes, for by it alone is the truth of the universe beheld." (Nicomachus)
Some... agreeing with Philolaus, 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 three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion... View quote
Nicomachus
Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves. View quote
Nicomachus
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... View quote
Nicomachus
If geometry exists, arithmetic must also needs be implied. View quote
Nicomachus
Since, however, all multitude and magnitude are by their own nature of necessity infinite. View quote
Nicomachus
Things... are some of them continuous. View quote
Nicomachus
Now it is with such things that 'wisdom' is particularly concerned, but accidentally also with. View quote
Nicomachus
All that has by nature, with systematic method, been arranged in the universe, seems. View quote
Nicomachus
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. View quote
Nicomachus
A science, however, would arise to deal with something separated from each of them. (Nicomachus)
Bodily, material things are... continuously involved in continuous flow and change. View quote
Nicomachus
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. View quote
Nicomachus
And once more is this true in the case of music. View quote
Nicomachus
Since of quantity, one kind is viewed by itself, having no relation to anything else. View quote
Nicomachus
Every number is at once half the sum of the two on either side of itself... View quote
Nicomachus
Everything that is harmoniously constituted is knit together out of opposites... View quote
Nicomachus
Scientific number, being set over such things as these, should be harmoniously constituted, in accordance with itself; not by any other but by itself. View quote
Nicomachus
More evidently still astronomy attains through arithmetic the investigations that pertain to it, not alone because it is later than geometry in origin-for motion naturally comes after rest-nor because the motions of the stars have a perfectly melodious harmony, but also because risings, settings, progressions, retrogressions, increases, and all sorts of phases are governed by numerical cycles and quantities. So then we have rightly undertaken first the systematic treatment of this, as the science naturally prior, more honorable, and more venerable, and, as it were, mother and nurse of the rest; and here we will take our start for the sake of clearness. View quote
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. View quote
Nicomachus