In order to understand the principles of surveying, a previous knowledge of Geometry is absolutely necessary; and this knowledge will be best acquired from a regular treatise on the subject. In the demonstrations, therefore, throughout this work, the student is supposed to be acquainted with the elements of that science. The references are adapted to Playfair's Geometry, but they will in general apply equally well to Simson's translation of Euclid's Elements. As there are many who wish to obtain a practical knowledge of Surveying, whose leisure may be too limited to admit of their going throụgh a course of Geometry, the author has adapted bis work to this class, by introducing the necessary geometrical definitions and problems, and by giving plain and concise rules, entirely detached from the demonstrations; the latter being placed in the form of notes at the bottom of the page. Each rule is exemplified by one wrought example; and the most of them by several unwrought examples, with the answers annexed. In the laying out and dividing of land, which forms the most difficult part of surveying, a variety of problems are introduced, adapted to the cases most likely to occur in practice. This part of the subject, however, presents such a great variety of cases, that we should in vain attempt to give rules that would apply to all of them. It cannot therefore be too strongly to make himself well acquainted with Geometry, and also with Algebra, previous to entering on the study of Surveying. Furnished with these useful auxiliaries, and acquainted with the principles of the science, the practitioner will be able to perform with ease, any thing likely to occur in his practice. The compiler thinks proper to acknowledge, that in the arrangement of the work, he availed himself of the advice of his learned preceptor and friend E. Lewis, of New-Garden; and that several of the demonstrations were furnished by him. J. GUMMERE. West-town Boarding School, First Month, 31st, 1814. CONTENTS. Application of Plane Trigonometry to the Men- suration of Distances and Heights Preliminary Definitions, Observations, &c. ib. Sect. I. Containing rules for finding the areas of triangles, quadrilaterals, circles, and ellipes; also, the method of protracting a survey, and finding its area by dividing it into triangles Sect. II. Containing three different rules for finding the areas of right lined figures gene- rally, when the bearings and distances of the |