The Complete Works of Gioseffo Zarlino, Vol. 2

stream; being that without them I could not do a good thing. It is true, however, that I will add a few others, to conduct this my enterprise 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 reason of that, which I am about to tell you, and which will be proposed to me by you. The blamers of those, who have written some things in the sciences, and have taken the principles from those, who have written before; replied Signor Desiderio; have little judgment. Who does not know, that wishing to write, or speak of any Art, or Science, it is necessary to do one of two things; either to find new principles; or else use those, which other professors of that Art, or Science have used? Therefore Plato, Aristotle, and other most excellent Philosophers, have made many things their own; even though they were inventions of others; as is clearly understood in their Writings. But this is perceived more in the writings of Euclid, than in another author; since we are to reason of Demonstration; who put together so many and so many Demonstrations made by others, making them his own, and also the Principles, with the beautiful order, which he gave them, as Proclus recounts, in the Commentaries made upon Book 1 of the Elements of the same Euclid, which to many is of great wonder, that such a man would do it; almost as if the life of a man were enough to find, put together, and give perfection to so many things. But let us leave this on one side and say, that if this is permitted and conceded to so many and such men; nor is any vice attributed to them; for what reason will this same thing not be conceded to you? since I do not see, that they have had from the world a greater privilege than that which you have. This is the duty; said Master Francesco. But let us leave, upon your faith, this on one side, and attend to what matters to us, without losing so much time. Wishing therefore, I added, to have full knowledge of that, which I have to tell you; it is necessary that you know; That being every Science placed in the intellect; all things render themselves intelligible in act, according to how they are in some manner considered distant from matter. Wherefore according to how diversely they have (I will say so) proportion with it, their consideration belongs to diverse Sciences; which cannot be acquired, if not with the help of Demonstration; the means of which, is Definition. Wherefore being Definition that, which makes us come into knowledge of the thing; because it expresses the essential things of it; it is necessary, that just as they are different among themselves, that also the Definitions, or means, that we wish to call them, be different.

*See ch. 7. & 12. lib. 1. Supp. etc.

Wherefore arises the diversity of the Sciences from the variety of things considered in many manners; which can be considered in three ways; For first there are some, which have their being, which depends on Matter, nor can they be defined without it; Secondly there are some, which cannot stand far from this matter, and in their definitions such matter is not placed; Beyond this some others there are, which not only do not depend on such matter according to their being, but not even according to reason or definition; and these are those, which fall under that divine Science, which we call Metaphysics; because those things, which it considers; either are never found to be in matter; as is God blessed, and other separate substances; or because they are not universally in it; as is Substance, Power, and Act, and that also which the philosophers call Being; wherefore in their definition; for not being corporeal things, matter is not placed. But the first, which are natural things, and are considered in natural Science, which they call Physics, and have their being in sensible matter, and are subject to movement, are defined by the named matter; wherefore when we define what Man is, we say, that he is a rational and mortal Animal; and the Animal, without any doubt, is a natural thing, and has its being among the things of nature. The others then are all things belonging to the Mathematical sciences, as are points, lines, surfaces, bodies, and all those things together, which belong to Multitude and to Grandeur; wherefore in their definition sensible matter is not placed; even if they cannot stand without it, being that it is not said, that the Triangle is a figure of wood, or of stone, or of iron, or of whatever