A TREATISE ON SURVEYING, CONTAINING THE THEORY AND PRACTICE: TO WHICH IS PREFIXED A PERSPICUOUS SYSTEM OF PLANE TRIGONOMETRY THE WHOLE CLEARLY DEMONSTRATED AND ILLUSTRATED BY A DERGE NUMBER PARTICULARLY ADAPTED TO THE USE OF SCHOOLS. BY JOHN GUMMERE, A. M. FELLOW OF THE AMERICAN PHILOSOPHICAL SOCIETY, AND CORRESPONDING MEMBER EIGHTH EDITION, IMPROVED. PHILADELPHIA: KIMBER & SHARPLESS, No. 8 S. FOURTH STREET. 1833. Entered according to the Act of Congress, in the year 1832, by Kimber & Sharpless, in the Clerk's Office of the District Court of the Eastern District of Pennsylvania. RECOMMENDATIONS. I am much pleased with the Treatise on Surveying, compiled by John Gummere, and hope to see it speedily introduced into general use. With those who appreciate its merits, I apprehend it will supersede every other tract on the subject with which I am acquainted. ENOCH LEWIS. We have no hesitation in giving it as our judgment, that Gummere's Treatise on Surveying is the best publication on the subject with which we are acquainted, and we, accordingly, take great pleasure in recommending it to the public patronage. R. PATTERSON, Vice president of the American Philosophical Society. R. M. PATTERSON, M. D. Prof. of Math, and Nat. Phil. in the Univer. of Pennsylvania. The Treatise on Surveying by John Gummere, is, in our estimation, a very judicious performance. Several things are omitted which only serve to encumber other works on this subject, and a variety of new rules and illustrations are introduced, particularly under the heads of laying out, measuring, and dividing land, which, in connection with its general arrangement, render this Treatise on Surveying, in our opinion, decidedly preferable to any other which has met the public eye. ROBERT ADRAIN, Prof. of Math. and Nat. Phil. Columbia College, New York. Teacher of Math. Prof. of Chem. Colum. Col. New York. Having carefully examined a Treatise on Surveying, by John Gummere, I feel myself perfectly justifiable in pronouncing it to be the best practical work on the subject extant. DAVID M'CLURE, Principal of the Naut. and Math. Acad. Philadelphia. 3 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, 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 multiplied 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, JAMES DEAN. Extract from 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, we shall recommend it." I remain very respectfully, your obedient, humble servant, &c. 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. For sale by the publishers: Solutions to the Miscellaneous Questions in Gummere's Surveying. By the Author. Price twenty-five cents. Also, a Stereotype edition of Mathematical Tables, containing Tables of Latitude and Departures, of Logarithms from one to ten thousand; and artificial Sines, Tangents and Secants; the whole carefully revised and compared with the most correct European editions. 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 sufficient 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 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 * 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. 5 |