On Numbers (-1599)

"Why do we believe that in all matters the odd numbers are more powerful […]?" (Pliny the Elder, "Natural History", cca. 77-79 AD)

"[…] in the science of numbers ought to be preferred as an acquisition before all others, because of its necessity and because of the great secrets and other mysteries which there are in the properties of numbers. All sciences partake of it, and it has need of none." (Boethius, cca. 6th century)

"Number is divided into even and odd. Even number is divided into the following: evenly even, evenly uneven, and unevenly uneven. Odd number is divided into the following: prime and incomposite, composite, and a third intermediate class (mediocris) which in a certain way is prime and incomposite but in another way secondary and composite." (Isidore of Seville, Etymologies, Book III, cca. 600)

"Music is fashioned wholly in the likeness of numbers. […] Whatever is delightful in song is brought about by number. Sounds pass quickly away, but numbers, which are obscured by the corporeal element in sounds and movements, remain." (Anon, "Scholia Enchiriadis", cca. 900)

"Every number arises from One, and this in turn from the Zero. In this lies a great and sacred mystery - in hoc magnum latet sacramentum: HE is symbolized by that which has neither beginning nor end; and just as the zero neither increases nor diminishes another number to which it is added or from which it is subtracted so does HE neither wax nor wane. And as the zero multiplies by ten the number behind which it is placed so does HE increase not tenfold, but a thousand fold - nay, to speak more correctly, HE creates all out of nothing, preserves and rules it  - omnia ex nichillo creat, conservat atque gubernat." ("Salem Codex", 12th century)

"The existence of an actual infinite multitude is impossible. For any set of things one considers must be a specific set. And sets of things are specified by the number of things in them. Now no number is infinite, for number results from counting through a set of units. So no set of things can actually be inherently unlimited, nor can it happen to be unlimited." (St. Thomas Aquinas, "Summa Theologica", cca. 1266-1273)

"Sound is generated by motion, since it belongs to the class of successive things. For this reason, while it exists when it is made, it no longer exists once it has been made. […] All music, especially mensurable music, is founded in perfection, combining in itself number and sound." (Jean de Muris, "Ars novae musicae", 1319)

"Every measurable thing, except numbers, is imagined in the manner of continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines and surfaces, or their properties be imagined. For in them, as the Philosopher has it, measure or ratio is initially found, while in other things it is recognized by similarity as they are being referred to by the intellect to the geometrical entities." (Nicole Oresme, "The Latitude of Forms", cca. 1348-1362)

"There are certain pleasures which only fill the outward senses, and there are others also which pertain only to the mind or reason; but music is a delectation so put in the midst that both by the sweetness of the sounds it moveth the senses, and by the artificiousness of the number and proportions it delighteth reason itself." (John Northbrooke , "Against Dicing", 1577)