elements of that science. The references are adapted to Playfair's Geometry, but ley 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 through a course of Geometry, the author has adapted his 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 is 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 recommended to every one, who has the opportunity, 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, Application of Plane Trigonometry to the Mensuration of Preliminary Definitions, Observations, &c. Sect. I. Containing rules for finding the areas of triangles, quadrilaterals, circles, and' ellipses; also the method of protracting a survey, and finding its area by dividing it into triangles and trapeziums, Sect. II. Containing three different rules for finding the areas of right-lined figures generally, when the bearings and distances of the boundaries are given, EXPLANATION OF THE CHARACTERS USED IN THIS WORK. + signifies plus, or addition. minus, or subtraction. is not known which is the greater. OF LOGARITHMS. LOGARITHMS are a series of numbers so contrived, that by them the work of multiplication is performed by addition, and that of division by subtraction. If a series of numbers in arithmetical progression be placed as indices, or exponents, to a series of numbers in geometrical progression, the sum or difference of any two of the fornier, will answer to the product or quotient of the two corresponding terms of the latter. Thus, 0. 1. 2. 3. 3 4. 5. 6. 7. &c. arith. series, or indices. 1. 2. 4. 8. 16. 32. 64. 128. &c. geom. series. Now 2 + 3 = 5. also 7-3=4. Therefore the arithmetical series, or indices, have the same properties as logarithms; and these properties hold true, whatever may be the ratio of the geometrical series. There may, therefore, be as many different systems of logarithms, as there can be taken different geometrical series, having unity for the first term. But the most con B part of the logarithm. The index must be placed before it agreeably to the above observation. Thus the log. of 421 is 2.62428, the log. of 4.21 is 0.62428, and the log. of .0421 is 2.62428. If the given number consist of four figures, find the three left hand figures in the column marked No. as before, and the remaining or right hand figure at the top of the table; in the column under this figure, and against the other three, is the decimal part of the logarithm. Thus the log. of 5163 is 3.71290, and the log. of .6387 is -1.80530. If the given number consist of five or six figures, find the logarithm of the four left hand figures as before; then take the difference between this logarithm and the next greater in the table. Multiply this difference by the remaining figure or figures of the given number, and cut off one or two figures to the right hand of the product, according as the multiplier consists of one or two figures; then add the remaining figure or figures of the product to the logarithm first taken out of the table, and the sum will be the logarithm required. Thus, let it be required to find the logarithm of 59686; then, |