Besides this knowledge of what is quantity and measure, and their several sorts, it behoveth a geometrician to know why, and of what, they are called principles. For not every proposition that is evident is therefore a principle. A principle is the beginning of something. And because definitions are the beginnings or first propositions of demonstration, they are therefore called principles, principles, I say, of demonstration. But there be also necessary to the teaching of geometry other principles, which are not the beginnings of demonstration, but of construction, commonly called petitions; as that it may be granted _that a man can draw a straight line, and produce it; and with any radius, on any centre describe a circle_, and the like. For that a man may be able to describe a square, he must first be able to draw a straight line; and before he can describe an equilateral triangle, he must be able first to describe a circle. And these petitions are therefore properly called principles, not of demonstration, but of operation. As for the commonly received third sort of principles, called _common notions_, they are principles, only by permission of him that is the disciple; who being ingenuous, and coming not to cavil but to learn, is content to receive them, though demonstrable, without their demonstrations. And though definitions be the only principles of demonstration, yet it is not true that every definition is a principle. For a man may so precisely determine the signification of a word as not to be mistaken, yet may his definition be such as shall never serve for proof of any theorem, nor ever enter into any demonstration, such as are some of the definitions of Euclid, and consequently can be no beginnings of demonstration, that is to say, no principles. All that hitherto hath been said, is so plain and easy to be understood, that you cannot, most egregious professors, without discovering your ignorance to all men of reason, though no geometricians, deny it. And the same (saving that the words are all to be found in dictionaries) new; also to him that means to learn, not only the practice, but also the science of geometry necessary, and, though it grieve you, mine. And now I come to the definitions of Euclid.