Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: II. Continuation of the same Subject. The difference of opinion between Locke and Rfill, of which I took notice in the foregoing part of this Section, appears greater than it really is, in consequence of an ambiguity in the word principle, as employed by the latter. In its proper acceptation, it seems to me to denote an assumption (whether resting on fact or on hypothesis), upon which, as a datum, a train of reasoning proceeds; and for the falsity or incorrectness of which no logical rigour in the subsequent process can compensate. Thus the gravity and the elasticity of the air are principles of reasoning in our speculations about the barometer. The equality of the angles of incidence and reflection; the proportionality of the sines of incidence new ones of his own invention. The first of these is, that" Every " quantity is equal to itself;" to which he adds afterwards, that " a quantity expressed one way is equal to itself expressed any " other way."?See Elements of Mathematical Analysis, by Pro- "fessor Vilant of St Andrew's. We are apt to smile at the formal statement of these propositions; and yet, according to the theory alluded to in the text, it is in truths of this very description that the whole science of mathematies not only begins but ends. " Omnes mathematicorum propositions sunt identic, et " repraesentantur hac formula, a =r a." This sentence, which I quote from a dissertation published at Berlin about fifty years ago, expresses, in a few words, what seems to be now the prevailing opinion (more particularly on the Continent) concerning the nature of mathematical evidence. The remarks which I have to offer upon it I delay till some other questions shall be previously considered. ? and refraction; are principles of reasoning in catoptrics and in diopt...