Reasoning.

...you will resolve it for us, if you wish.

GIOS. I shall do so, then. But take heed that when I propose anything to you that you have previously heard, read, or encountered in any author, do not accuse me of theft, as some do who are of little judgment and little prudence, accusing this writer or that, nor say that there was no need to commemorate it. For, wishing to demonstrate the things of music to you in order, I cannot avoid discussing things necessary for such reasoning, especially knowing that most of you have not dedicated yourselves to the study of the Arts and do not know what is meant by this term "Demonstration," and those parts that enter into it.

FRAN. This pleases me immensely, because even though it may be that I have heard at times what a Demonstration is from the colloquies of our [men] Maggio and Pigna—great men in letters who often had conversations with our Lord Duke and other distinguished persons—nevertheless, since it is not my profession, I cannot remember it so fully. Therefore, by doing what you have said, it cannot be anything but of great utility to us.

ADRI. You must do it in any case, because I, too, do not remember these things very well, even though I heard them as a young man in the study of Paris when I applied myself to the study of Imperial Laws.

CLAV. I will also take great pleasure in it, because I believe I know little of these things, although I have heard many from the reasoning of those excellent men with whom I am in constant practice. Thus, I will come to remember something and will hold it well in memory.

GIOS. Since you are content with this, I shall do so; thus I will speak now with you, Sig. Desiderio, who I know, from the reasoning had with us a moment ago, to be very well instructed. However, let everyone take heed that in this reasoning I cannot do otherwise than what the majority of those who have written and reasoned about these things before me have also done: that is, that I must take a part of those means that serve me to arrive at the demonstrative act, for without them I could not produce anything good. It is true that I will add some others to them to lead this undertaking of mine to the desired end, since those which have been proposed by others are not enough. And with these and those together, I will come to render a reason for what I am about to tell you and what will be proposed to me by you.

DESI. The detractors of those who have written about the sciences and have taken their principles from those who have written beforehand have little judgment. Who does not know that, wishing to write or speak about any art or science, it is necessary to do one of two things: either find new principles, or use those that other professors of that Art or Science have used? Thus, Plato, Aristotle, and other most excellent Philosophers made many things their own, even though they were the inventions of others, as one clearly understands in their writings. But this is perceived more in the writings of Euclid than in any other author—since we are to reason about the Demonstration—who gathered together so many Demonstrations Lib. 2. ca. 4. made by others, making them his own, as well as the principles, with the beautiful order that he gave them, as Proclus recounts in the Commentaries made by him upon Book 1 of the Elements of this Euclid, which is a great marvel to many that such a man would do so, as if the age of one man were alone sufficient to discover and put together and give perfection to so many things. But let us leave this aside and say that if this is permitted and granted to so many such men, and no vice is attributed to them, for what reason will this same thing not be granted to you, since I do not see that they have had any greater privilege from the world than you have?

FRAN. This is only right. But let us leave this aside, for heaven's sake, and attend to that which concerns us, without losing so much time.

GIOS. Wishing, therefore, to have full knowledge of what I have to tell you, it is necessary that you know: That since every Science is placed in the intellect, all things render themselves intelligible in act according to the way in which they are considered to be removed from matter. Wherefore, according to how differently they have (so to speak) proportion with it, their consideration pertains to different sciences. These, however, cannot be acquired except with the help of the Demonstration, the medium of which is the Definition. Wherefore, since the Definition is that which brings us to the knowledge of a thing—because it expresses the essential things of it—it is necessary that just as they are different among themselves, so too must the Definitions or means that...