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WE the subscribers have carefully perused a Treatise on Surveying, prepared for the Press' by the Rev. Abel Flint of Hartford ; and find it worthy of the public patronage. Every thing not immediately necessary for the practical Surveyor has been excluded ; while it comprises all which is requisite in Field Surveying, both on the old and new plan; elucidated and explained with a degree of conciseness and perspicuity not usually to be found in Treatises on the same subject. The Mathematical Tables are reduced to less than half the size occupied by others; and any inconvenience which might result from such reduction, is obviated by the insertion of a Table of Natural Sines, not usually found in works of this nature. The Surveyor who shall own this will not be under the necessity of purchasing GIBSON, which is a more expensive work.
ASHER MILLER, Surveyor General.
for Tolland County
MIDDLETOWN, Oct. 3, 1804.
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 calculating the Area of Fields arithmetically, without drawing a plot of them and measuring with a Scale and Dividers, as has been the common practice; 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 intelligible that a Learner will require but little assistance from an Instructer, 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 Decimal 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 occur. 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 conscale ; and the system of Geometry and Trigonometry with which it is introduced, with the Prob. lems 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 introduced 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 wanted, and that if judiciously executed it would be useful. It is more particularly 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 experience.
A GENERAL VIEW OF THE CONTENTS OF THIS WORK.
THE System of Geometry is divided into two parts. The first contains Geometrical Definitions respecting Lines, Angles, Superficies, &c. The second part contains a number of Geometrical Problems necessary for Trigonometry and Survey. ing.
The System of Trigonometry is also divided into two parts: and teaches the solution of questions in Right and Oblique angled Trigonometry, by Logarithms and also by Natural Sines.
The Treatise on Surveying is divided into three parts. Part first treats of measuring Land, and is divided into three Sections. The first contains several Problems respecting Mensuration, and for finding the Area of various Right-lined Figures and Circles.
The second Section teaches different methods of taking the Survey of Fields; also to protract them, and find their Área in the manner commonly practised, and likewise by Arithmetical and Trigonometrical calculations, without measuring Diagonals and Perpendiculars with a Scale and Dividers ; interspersed with sundry useful rules and directions.
The third Section is a particular explanation and demonstration of Rectangular Surveying, or the method of computing the Area
of Fields from the Field Notes, by Mathematical Tables, without the necessity of plotting the Field. To this Section is added a useful Problem for ascertaining the true Area of a Field which has been measured by Part second treats of laying out Land in various shapes.
Part third contains sundry Problems and Rules for dividing Land and determining the true Course and Distance of dividing Lines, or from one part of a Field to another. To this is added an Appendix concerning the Variation of the Compass and Attraction of the Needle ; also, a rule to find the difference between the present Variation, and that at a time when a Tract was formerly surveyed, in order to trace or run out the original lines.
The Mathematical Tables, are a Traverse Table, or Table of Difference of Latitude and Departure, calculated for every Degree and quarter of a Degree, and for any distance up to 50; a Table of Natural Sines calculated for every Minute ; a Table of Logarithms comprised in four pages, yet sufficiently extensive for common use; and a Table of Logarithmic or Artificial Sines, Tangents, and Secants, calculated for every 5 Minutes of a Degree. To these Tables are prefixed particular explanations of the manner of using them.