The head is borne towards the heavens and has two lights, as it were the sun and moon. - Robert Grosseteste

Ostensive demonstration is that which concludes directly to that which is in question. Reduction ad impossibile is that which, when something the opposite of that which is in question has been assumed, concludes with some other proposition directly to a known and manifest impossibility, from the opposite of which the investigator is led back to the original proposition in question. But there is a difference between ostensive demonstration and reduction ad impossibile, because the former proves from things prior in the order of nature but the latter from things posterior in the order of nature. When things prior in nature are better known in the intellect of the person making the demonstration the process is carried out ostensively; but when posterior things are better known to his intellect then the demonstration is carried out per impossibile... in demonstration carried out per impossibile the showing of the original thing in question is carried out by means of things posterior to it in the order of nature... And there is in the contrary, falsely supposed in predicate of subject, a connecting term by which something is implied to be which impossible in the nature of things.

Because the purity of the eye of the soul is obscured and weighed down by the corrupt body, all the powers of this rational soul born in man are laid hold of by the mass of the body and cannot act and so in a way are asleep. Accordingly, when in the process of time the senses act through many interactions of sense with sensible things, the reasoning is awakened mixed with these very sensible things and is borne along in the senses to the sensible things as in a ship. But the functioning reason begins to divide and separately consider what in sense were confused. ...But the reasoning does not know this to be actually universal except after it has made this abstraction from many singulars, and has reached one and the same universal by its judgement taken from many singulars.

And since the proportions of the human voice and the gesticulations of the human body are regulated by the same modulation as that by which sound and the motion of other bodies are, musical thought is subalternated not only to the harmony of human voice and gesticulation, but also of instruments and of those whose delectation consist in motion or sound and with these the harmony of the celestial and non-celestial. And since the concordance of times and the composition and harmony of the lower world and of all things composed of four elements come from celestial motions, and, moreover, since it is necessary to find the harmony of causes in their effects, the study of music also extends to knowing the proportions of times and the constitution of the elements of the lower world, and even the composition of all the elements.