Discussion.

...you will resolve it for us, if you wish. GIOS. I will do so then. But take note, that when at times I propose something to you that you have previously heard, read, or known from some author: do not accuse me of theft—as some do who have little judgment and little prudence, accusing this or that writer—nor even say that it was not necessary to mention it. Because wanting to show you the matters of Music in their proper order, I cannot help but run through some things necessary for such discussions; especially knowing that the majority of you have not applied yourselves to the study of the [Liberal] Arts, and do not know what this name DemonstrationIn the Renaissance, a "demonstration" was a formal logical or mathematical proof that moved from known principles to a necessary conclusion. implies, nor the parts that go into it. FRAN. This pleases me exceedingly. For although I may have heard at times what a Demonstration is—from the conversations of our friends Maggio and PignaVincenzo Maggi and Giovan Battista Pigna were prominent humanists and scholars in the court of Ferrara., great men of letters, held often with our Lord DukeLikely Alfonso II d'Este, Duke of Ferrara, a major patron of the arts and sciences. and with other distinguished persons—nonetheless, since it is not my profession, I cannot remember it fully. Therefore, by doing what you have said, it can only be of great utility to us. ADRI. You must do it by all means; because I too do not remember these things very well, even though as a youth I heard them in the University of Paris when I devoted myself to the study of the Imperial LawsThe "Imperial Laws" refers to Roman Civil Law, a standard part of the university curriculum in Paris.. CLAV. I too will take great pleasure in it; for I believe I know few of these things, although I have heard much from the discussions of those excellent men with whom I associate continually. Thus I shall come to remember something and will keep it well in my memory. GIOS. Since you are so satisfied, I will do so. Therefore, I will speak now with you, Lord Desiderio, whom I know—from the discussion we had just a little while ago—to be very well-instructed. However, let everyone take note that in this discussion I cannot help but do what the majority of those who have written and spoken of these things before me have done: that is, I must take up a portion of those means that serve me to reach the act of demonstration, since without them I could not produce anything of value. It is true, however, that I will add several others to them to lead this enterprise of mine to the desired end; for those which have been proposed by others are not sufficient. With these old and new principles together, I will come to give an account of what I am about to tell you and what you will propose to me. DESI. Those who blame writers for taking principles from those who have written before have little judgment. Who does not know that when wanting to write or speak of any art or science, one must do one of two things: either find entirely new principles, or else use those which 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 inventions of others, as is clearly understood from their writings. But this is seen more in the writings of Euclid than in any other author (since we are discussing Demonstration), who put together so many and so many demonstrations Book 2, chapter 4. made by others, making them his own—including the principles—through the beautiful order that he gave them. This is recounted by ProclusProclus (412–485 AD) was a Greek Neoplatonist philosopher who wrote an influential commentary on Euclid's "Elements." in the commentaries he made on Book 1 of the Elements of that same Euclid. It is a great marvel to many that such a great man did this, as if the lifespan of one man were enough alone to discover, put together, and give perfection to so many things. But let us leave this aside and say: if this is permitted and granted to so many such men, and no vice is attributed to them, for what reason should this same thing not be granted to you as well? For 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 goodness' sake, and attend to what matters to us without losing any more time. GIOS. Wanting then to have full knowledge of what I have to tell you, it is necessary that you know: That every Science being situated in the intellect, all things are rendered intelligible in action according to how they are considered to be distant from matter. Therefore, according to how they have (so to speak) different proportions with matter, their study belongs to different sciences. These, however, cannot be acquired except with the help of Demonstration, the means of which is the Definition. Since the Definition is that which brings us to the knowledge of a thing—because it expresses the essential qualities of it—it is necessary that just as things are different from one another, the Definitions (or means) must also be different...