Stechers 7-3-42 45902 PREFACE. NorwITHSTAND OTWITHSTANDING the many publications which have appeared on Mathematical subjects, and the great improvements that have been made in every department of the science, a general treatise, on a cheap and accurate plan, seems as yet to be a defi. deratum. Volumes have been wrote, not only upon every branch, but even upon particular parts of every branch. These are more particularly adapted to the learned, and cannot all be purchased but at an extraordinary expence. This inconvenience has no less been felt by those who have undertaken the charge of teaching, than by their pupils. It must be very disagreeable to a teacher, before he can lead a class through a course of Practical Geometry, to make the students purchase a number of volumes on detached parts of the course : It is no b. less less perplexing to a scholar to read them in order to retain what has been taught : Not to mention that the books so purchased may have a very different mode of expressing the same thing, which must still encrease the perplexity. The author has frequently found, from his own experience, as well as from the report of others, that treatises of this nature afford but imperfect materials for the exercise of youth. Hence teachers are under the necessity of inventing what they esteem a proper set of exercises ; and to this circumstance must we chiefly ascribe the absurd custom adopted by some, viz, that of teaching in their own way. With a view to obviate this inconvenience ; to furnith those who incline either to teach or learn practical Geometry, with a system at once full and complete, for every purpose in ordinary life; and to afford them this advantage at an easy rate the following treatise is respectfully submitted to the attention of the Public. And, as the author has had sonie years experience of its utility and convenience in the course of his practice, he thinks he can, with some degree of confidence, recommend it as the only trea tise that has yet appeared proper for being taught at academies and schools, the ingenious Dr Hutton's excepted. But though this work is excellent in its kind, its high price prevents its being generally useful ;-an objection which, it is hoped, the following treatise will entirely remove. The author is conscious that there can now be but few claims to originality; yet he flatters himself that, even in this respect, he will not be found entirely deficient. The arrangement is such as seems best calculated for instruction—beginning with the simple radiments, and, by gradual and easy steps, proceeding to that which is more complex, in such order that what is prior paves the way for what is to follow. The greatest care has been taken to select the moft important articles, and to introduce every necessary information, in so far as regards Mensuration. To some of the problems two or more rules are annexed, and an example wrouglit at large to each, in such a manner as to be intelligible to the most ordinary capacity; and, for exercise, copious fets of unwrought 1 unwrought examples, with their answers, are inserted ; and, in order to render this work still more acceptable, a great variety of miscellaneous questions, with their answers, are proposed, as a general exercise and conclusion to the work. Upon the whole, It is hoped that, by means of the present treatise, the business of teaching and learning the practical part of Mathematics will be attended with less trouble and expence than former ly. CONTENTS. CONTENTS. EFINITIONS, , The Construction of the Line of Cords, Sines, Tangents, Triangles constructed and measured by the Scale, Construction and Use of Logarithms, Mensuration of Heights and Distances, To find the Diameter of the Earth by Trigonometry, 54 To find the Height of an Object by means of one Staff, To measure the Height from the Length of its Shadow, 57 To find the Height of an Object by a plane Mirror, To find the Velocity of the Wind, Heights and Depths estimated by falling Bodies, |