indeed are of any real utility. Those which most frequently occur in Mechanics, Optics, and in "Newton's Principia," have been given at length, retaining the very letters used in the Works referred to. Hence the Student who shall read this Work along with "Euclid's Elements," will have become already familiarised with the principal Geometrical difficulties of those profounder Works. To these Deductions succeed a number of others of inferior importance certainly, but yet not altogether destitute of interest. Some have a value from their properties being very curious; others as affording examples for the methods of investigation. These are proposed for the exercise of the Student's own ingenuity, accompanied, however, with occasional helps and directions. Many of the Tutors and Lecturers complain against the Works already extant upon Deductions and Geometrical Problems, as calculated to promote a taste in the University for Geometrical quibbling. Impressed with the same sentiments, the Author refrains from pandering to so false an appetite, by supplying his readers with these Mathematical varieties. In reference to similar quirks and conundrums (for they deserve no better name), Simpson has expressed his indignation in no very measured terms, observing, "there is enough of the useful and practical in Science to exercise the utmost labour and ingenuity of which mankind are capable." These remarks are not only applicable to the Geometry which has crept into our system, but also to all other branches in which this trifling has insinuated itself. In short, instead of spending so many months, if not years, in these unprofitable and therefore insipid speculations, wasting so much valuable time in working the endless combinations of Straight-lines or Circles, or the inexhaustible varieties of Equations or Trigonometrical functions, the Student should dwell upon such questions only as have an intimate connection with the grand and sublime Problems of Nature. With this view all Elementary Works should be composed. All, without exception, should be made preparatory to the great standard and immortal labours of Newton, Lagrange, and Laplace. Were Works thus constructed, Students who are now poring over the diversities of Deductions, or long-winded Algebraical Problems, would be taking up as Class Books the "Mecanique Analytique," or even the "Mecanique Celeste." These observations are corroborated by the opinions and expressions of several of the most distinguished Tutors of the University, of whom one of the most influential has declared, "that he who shall contribute to the easier comprehension of Laplace, will confer a benefit upon the University at large.” In this spirit is composed the following Work. Its intention is to render Euclid easy, and to supply an Introduction to the more comprehensive and powerful Science of ANALYTICAL GEOMETRY. The Author has availed himself, of course, of the labours of his Predecessors. He has had constantly before him, "Simson's Euclid," "Playfair's, Barrow's, Tacquet's, De Chales, Elrington's Six Books, Barrow's Geometrical Lectures," "Leslie's Geometry and Geometrical Analysis," &c., &c.; but, although many hints are borrowed from these, especially from the judicious and acute remarks of Elrington, yet the bulk of his labours is drawn from the suggestions of his own experience. Gothic Cottage, Cambridge. J. M. F. WRIGHT. |