12. And seeing teaching is nothing but leading the mind of him we teach, to the knowledge of our inventions, in that track by which we attained the same with our own mind; therefore, the same method that served for our invention, will serve also for demonstration to others, saving that we omit the first part of method which proceeded from the sense of things to universal principles, which, because they are principles, cannot be demonstrated; and seeing they are known by nature, (as was said above in the 5th article) they need no demonstration, though they need explication. The whole method, therefore, of demonstration, is _synthetical_, consisting of that order of speech which begins from primary or most universal propositions, which are manifest of themselves, and proceeds by a perpetual composition of propositions into syllogisms, till at last the learner understand the truth of the conclusion sought after. [Sidenote: Definitions only are primary, & universal propositions.] 13. Now, such principles are nothing but definitions, whereof there are two sorts; one of names, that signify such things as have some conceivable cause, and another of such names as signify things of which we can conceive no cause at all. Names of the former kind are, _body_, or _matter_, _quantity_, or _extension_, _motion_, and whatsoever is common to all matter. Of the second kind, are _such a body_, _such and so great motion_, _so great magnitude_, _such figure_, and whatsoever we can distinguish one body from another by. And names of the former kind are well enough defined, when, by speech as short as may be, we raise in the mind of the hearer perfect and clear ideas or conceptions of the things named, as when we define motion to be _the leaving of one place, and the acquiring of another continually_; for though no thing moved, nor any cause of motion be in that definition, yet, at the hearing of that speech, there will come into the mind of the hearer an _idea_ of motion clear enough. But definitions of things, which may be understood to have some cause, must consist of such names as express the cause or manner of their generation, as when we define a circle to be a figure made by the circumduction of a straight line in a plane, &c. Besides definitions, there is no other proposition that ought to be called primary, or (according to severe truth) be received into the number of principles. For those _axioms of Euclid_, seeing they may be demonstrated, are no principles of demonstration, though they have by the consent of all men gotten the authority of principles, because they need not be demonstrated. Also, those _petitions_, or _postulata_, (as they call them) though they be principles, yet they are not principles of demonstration, but of construction only; that is, not of science, but of power; or (which is all one) not of _theorems_, which are speculations, but of _problems_, which belong to practice, or the doing of something.