On Arithmetic (-1299)

 "[Arithmetic] has a very great and elevating effect, compelling the soul to reason about abstract numbers, and rebelling against the introduction of visible or tangible objects into the argument." (Plato, "The Republic", cca. 375 BC)

"[...] arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up." (Plato, "The Republic", cca. 375 BC)

"[...] the art of calculation (logistika) and arithmetic are both concerned with number; those who have a natural gift for calculating have, generally speaking, a talent for learning of all kinds, and even those who are slow are, by practice in it, made smarter. But the art of calculation is only preparatory to the true science; those who are to govern the city are to get a grasp of logistilca, not in the popular sense with a view to use in trade, but only for the purpose of knowledge, until they are able to con- template the nature of number in itself by thought alone." (Plato, "The Republic", cca. 375 BC)

"[...] those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been [...]" (Plato, "The Republic", cca. 375 BC)

"Can we deny that a warrior should have a knowledge of arithmetic?" (Plato, "The Republic", cca. 375 BC)

"No single instrument of youthful education has such mighty power, both as regards domestic economy and politics, and in the arts, as the study of arithmetic. Above all, arithmetic stirs up him who is by nature sleepy and dull, and makes him quick to learn, retentive, shrewd, and aided by art divine he makes progress quite beyond his natural powers." (Plato, "Laws", cca. 360 BC)

"[...] if arithmetic, mensuration, and weighing be taken away from any art, that which remains will not be much." (Plato, "Philebus", cca. 360 - 347 BC)

"The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantity as such, music the relations between quantities, geometry magnitude at rest, spherics magnitude inherently moving." (Diadochus Proclus)

"Mathematical science […] has these divisions: arithmetic, music, geometry, astronomy. Arithmetic is the discipline of absolute numerable quantity. Music is the discipline which treats of numbers in their relation to those things which are found in sound." (Cassiodorus, cca. 6th century)