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GEOMETRY AND TRIGONOMETRY,
COMPRISING VARIOUS METHODS OF TAKING THE SURVEY OF A
AND FINDING AREAS;
IN WHICH, ALSO, THE PRINCIPLES OF
BY WHICH AREAS MAY BE ACCURATELY CALCULATED WITHOUT
PLOTTING, ARE FULLY EXPLAINED :
PRACTICAL ILLUSTRATIONS ON SURVEYING,
AND SURVEYING ROADS, &c.
BY GEORGE GILLET,
ALSO, A CONCISE
BY F. A. P. BARNARD,
LATE TUTOR IN YALE COLLEGE.
DISTRICT OF CONNECTICUT, ss. BE IT REMEMBERED, That on the second day of August, in the L. S. fifty-fifth year of the Independence of the United States of America,
Oliver D. Cooke, of the said District, hath deposited in this office the title of a book, the right whereof he claims as proprietor, in the words fol. lowing, to wit: “A system of Geometry and Trigonometry, with a Treatise on Surveying ; comprising various methods of taking the survey of a field, with directions for protracting and finding areas ; in which, also, the principles of Rectangular Surveying, by which Areas may be accurately calculated without plotting, are fully explained : with a complete series of Mathematical Tables, and the necessary Explanations. By Abel Flint, A. M. With improvements by George Gillet, Surveyor General of Connecticut. Sixth edition, revised and enlarged, by the addition of copious notes and illustrations, and a concise Trea. tise on Logarithms, by Frederic A. P. Barnard, A. B., Instructor in Mathematics in the Hartford Grammar School, and author of a Treatise on Arithmetic." In conformity to the act of Congress of the United States, entitled, “An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein mentioned.” And also to the act entitled, "An act supplementary to an act, entitled, ' An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
CHARLES A. INGERSOLL,
Clerk of the District of Connecticut. A true copy of record, examined and sealed by me,
CHARLES A. INGERSOLL,
Clerk of the District of Connecticut.
Entered according to act of Congress, in the year 1833, by EDWARD P.
TO THE SEVENTH EDITION.
The original compiler of the following work designed, in preparing it, to furnish a plain and concise system of PRACTICAL SURVEYING.
That he did not fail of success, has been proved, by the high estimation in which this treatise has been, and is, at the present time, held by Surveyors, and by the continued and increasing demand for it. The publishers have used exertions to render the present edition more worthy of patronage.
About thirty pages of practical matter have been added by GEORGE GILLET, Esq., Surveyor General of the state of Connecticut. A distinguishing feature of the present as well as of the previous edition, is the introduction of a new and elegant set of tables, more extensive than those which have before been attached to this work, and on a superior type.The numbers in the traverse table are carried to 100.
In the table of logarithms, and of logarithmic sines, &c., the decimals are carried to six figures, and a column of differences is added for the purpose of finding intermediate numbers.
When logarithms are carried to six places, they may be taken to as few, or as many within that limit, as is desired. Prefixed to the tables will be found a brief explanation of the nature and use of logarithms by Mr. BARNARD, which will be found a valuable addition.
The articles on distributing estates, locating and surveying roads, and on levelling, cannot fail of being highly useful.
The subscribers have examined in manuscript, the additions to the seventh edition of Flint's Surveying, by GEORGE GILLET, Esq., Survey. or General of Connecticut, and find them to embrace a system of correct, useful, and practical matter, judiciously arranged, and clearly ex. plained to the understanding of the learner. Having long acted as Sur. veyors under public authority, we recommend this work as containing all the elementary science, and requisite tables, necessary or convenient for the learner, and the practitioner. The present is a more full and complete system than any former edition.
MOSES WARREN, Dep. Sur. N. London Co.
JONATHAN NICHOLS, Dep. Sur. Windham Co.
PREFACE TO THE FIRST EDITION.
The following work is chiefly a compilation from other Books; and but very little new is added, except a more full explanation, than has yet been published, of RECTANGULAR SURVEYING, or the method of calcu. lating the area of fields arithmetically, without drawing a plot of them and measuring with a scale and dividers, as has been the common prac. tice; and also a more particular explanation of the use of natural sines, than is contained in most mathematical books.
The compiler has endeavoured to render this work so easy and intel. ligible, that a learner will require but little assistance from an Instruc. ter, except with regard to the construction and use of mathematical and surveying instruments. Before, however, he enters on the study of this book, he must be well acquainted with common Arithmetic, with deci. mal fractions, and the square root; and he must also know the various characters or marks used in Arithmetic.
A surveyor will doubtless find many questions arise in the course of his practice, for the solution of which, no particular directions are here given; nor is it possible to give directions for every case that may oc
In all practical sciences, much must be left to the judgment of the practitioner, who, if he is well acquainted with the general principles of his art, will readily learn to apply those principles to particular cases.
The primary design of this treatise is to teach common Field Surveying; at the same time it contains the elements of Surveying upon a larger scale ; and the system of Geometry and Trigonometry with which it is introduced, with the problems for the mensuration of superficies, as also the mathematical tables at the end, will be found useful for many other purposes. It would be well, therefore, for those who do not intend to become practical surveyors, to acquaint themselves with what is here taught; and with this view the following work is very proper to be in. troduced into academies and those higher schools which are designed to fit young men for active business in life. Indeed every person who frequently buys and sells land, should learn to calculate the contents of a field arithmetically; a knowledge which may be acquired in a very little time, from the particular explanation here given of that method.
Notwithstanding the many books already published on the subjects here treated upon, it was thought a work of this kind was really want. ed, and that if judiciously executed it would be useful. It is more par. ticularly necessary at the present time in Connecticut, as the legislature of the State have lately enacted a law on the subject of surveying, in consequence of which more attention must be paid to the theory of that art than has been common.
These considerations induced the compiler to select from various publications what appeared to him important; and to arrange the whole in a method best adapted, in his view, for teaching that useful art. How far he has succeeded in his endeavours to simplify the subject, and render it easy to the learner, must be submitted to the test of expe. rience.