and for gradually conducting him from the level of the subordinate sciences, to the vantage-ground of a higher philosophy. Unwilling as I am to touch on a topic so hopeless as that of Academical Reform, I cannot dismiss this subject, without remarking, as a fact which, at some future period, will figure in literary history, that two hundred years after the date of Bacon's philosophical works, the antiquated routine of study, originally prescribed in times of scholastic barbarism and of popish superstition, should, in so many Universities, be still suffered to stand in the way of improvements, recommended at once by the present state of the sciences, and by the order which nature follows in developing the intellectual faculties. On this subject, however, I forbear to enlarge. Obstacles of which I am not aware may perhaps render any considerable innovations impracticable; and, in the meantime, it would be in vain to speculate on ideal projects, while the prospect of realizing them is so distant and uncertain. NOTES AND ILLUSTRATIONS TO PART SECOND, FIRST DIVISION. NOTE A, p. 32.-Fundamental Laws of Belief. (2 1.) Or the fault in Euclid's arrangement which I have here remarked, some of the ancient editors were plainly aware, as they removed the two Theorems in question from the class of Axioms, and placed them, with at least an equal impropriety, in that of Postulates. "In quibusdam codicibus," says Dr. Gregory, "Axiomata 10 et 11 inter postulata numerantur."-Euclidis quæ supersunt omnia. Ex Recensione Davidis Gregorii. Oxonii, 1703, p. 3. The 8th Axiom too in Euclid's enumeration is evidently out of its proper place. Καὶ τὰ ἐφαρμόζοντα ἐπ ̓ ἄλληλα ἴσα ἄλληλοις ἐστί: thus translated by Dr. Simson ; Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality;-the fundamental principle upon which the comparison of all geometrical magnitudes will be found ultimately to depend. For some of these slight logical defects in the arrangement of Euclid's Definitions and Axioms, an ingenious, and, I think, a solid apology, has been offered by M. Prévost, in his Essais de Philosophie. According to this author, (if I rightly understand his meaning,) Euclid was himself fully aware of the objections to which this part of his work is liable; but found it impossible to obviate them, without incurring the still greater inconvenience of either departing from those modes of proof which he had resolved to employ exclusively in the composition of his Elements; or of revolting the student, at his first outset, by prolix and circuitous demonstrations of manifest and indisputable truths. I shall distinguish by italics, in the following quotation, the clauses to which I wish more particularly to direct the attention of my reader. "C'est donc l'imperfection (peut-être inévitable) de nos conceptions, qui a 1 By introducing, for example, the idea of Motion, which he has studied to avoid, as much VOL. III. as possible, in delivering the Elements of Plane Geometry. 2 A |