The following letter was addressed by the late Professor of Mathematics, &c. in Vermont College, to R. M. Patterson, M. D. Prof. of Math, and Nat. Phil. in the University of Pennsylvania. DEAR SIR, Philad: July 16, 1814. Agreeably to your request, I have cursorily examined Gummere's Treatise on Surveying, and conceive that the author has performed all that his preface promises. The subject is logically distributed and arranged, and the principles correctly and perspicuously displayed. The examples are very properly mul tiplied and ingeniously varied, so as to prepare the student for the most unusual cases. That the Author's success in the publication may equal his high reputation for science, is a wish, which (as far as good wishes go) ought to be as satisfactory to him, as it is sincere on the part of Yours with very high respect and esteem, Extract of a letter from Samuel Knox, esq. principal of the Baltimore College. "I received and submitted to our Mathematical Professor, Gummere's Surveying. We approve of the work. And as often as any of our students want an author on that branch, shall recommend it." I remain very respectfully, your SAMUEL KNOX. I fully concur with the gentlemen who have already given recommendations of Gummere's Treatise on Surveying, in considering the work as well calculated to give youth a correct knowledge of the principles of Surveying, and that it is to be preferred to any treatise on that subject, known in this country. ELIJAH SLACK, Prof. of Math. in Princeton College. J. R. has published Solutions to the Miscellaneous Questions in Gummere's Surveying. By the Author. Price twenty-five cents. Also Mathematical Tables, containing Tables of Latitude and Departure; of Logarithms from one to ten thousand; and artificial Sines, Tangents and Se. cants; the whole carefully revised, and compared with the most correct European editions. Price one dollar and fifty cents, bound. PREFACE. THE following compilation originated in the belief that our schools are in want of a treatise on surveying, adapted to the methods practised in this country, and freed from the defects of the systems now in use. Notwithstanding the importance of the science, and the large number that make it an object of study, it is believed we are not in possession of a treatise on this subject, suited to the wants of the student. The works of Gibson and Jess are the only ones at present in general use; the former, though much the better of the two, is deficient in many respects. It may be sufficent here, merely to advert to its want of examples, which renders it entirely unsuitable for a school book. From the latter, the student would in vain expect to become acquainted with the principles of the science, or the rationale of any of the rules, necessary in performing the various calculations.* 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 Each of these works has lately gone through a new edition, in which considerable additions are stated to have been made. On examination, however, it does not appear, that those additions are such as to supply the deficiencies. The additions made to Gibson, consist principally of some nautical problems, quite foreign to a treatise on Surveying. Those made to Jess, consist of a few extracts from Gibson, in one of which the Pennsylvania method of calculation is introduced, as being quite different from that given by Jess; whereas it is well known to be the method given by that author, and used, as well in the preceding, as in the subsequent part of his work. t 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 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 prac tice. 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 NewGarden; and that several of the demonstrations were furnished by him. West-town Boarding School, J. GUMMERE. SECT. I. Containing rules for finding the areas of trian- gles, quadrilaterals, circles, and ellipses; also the me- thod 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 bear- ings and distances of the boundaries are given |