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THEORY AND PRACTICE
ALL THE INSTRUCTIONS REQUISITE FOR THE SKILFUL
PRACTICE OF THIS ART.
WITH A NEW SET OF ACCURATE
BY ROBERT GIBSON.
ILLUSTRATED BY COPPER-PLATES.
NEWLY ARRANGED, IMPROVED, AND ENLARGED, WITH USEFUL
BY JAMES RYAN,
AUTHOR OF AN ELEMENTARY TREATISE ON ALGEBRA; THE NEW AMERICAN
INTEGRAL CALCULUS, &c. &c.
PRINTED AND PUBLISHED BY J. & J. HARPER,
NO. 82 CLIFF-STREET.
AND SOLD BY THE PRINCIPAL BOOKSELLERS THROUGHOUT THE
Entered according to Act of Congress, in the year 1832, by J. & J. Harper, in the office of the Clerk of the Southern District of New-York.
PREF A C E.
The word Geometry imports no more than to measure the earth, or to measure the land; yet, in a larger and more proper sense, it is applied to all sorts of dimensions. It is generally supposed to have had its rise among the Egyptians, from the river Nile's destroying and confounding all their landmarks by its annual inundations, which laid them under the necessity of inventing certain methods and measures to enable them to distinguish and adjust the limits of their respective grounds when the waters were withdrawn. And this opinion is not entirely to be rejected, when we consider that Moses is said to have acquired this art when he resided at the Egyptian court. And Achilles Tatius, in the beginning of his introduction to Aratus's Phænomeną, informs us that the Egyptians were the first who measured the heavens and the earth, and of course the earth first; and that their science in this matter was engraven on columns, and by that means delivered to posterity.
It is a matter of some wonder, that though Surveying appears to have been the first, or at least one of the first, of the mathematical sciences, the rest have met with much greater improvements from the pens of the most eminent mathematicians, while this seems to have been neglected; insomuch that I have not been able to meet with one author who has sufficiently explained the whole art in its theory and practice. For the most part, it has been treated of in a practical manner only; and the few who have undertaken the theory have in a great measure omitted the practice.
These considerations induced me to attempt a methodical, easy, and clear course of Surveying : how far I have succeeded in it must be determined by the impartial reader. The steps I have taken to render the whole evident and familiar are as follow :
In section the first (Part the First) you have Decimal Fractions. The second section contains Involution and Evolution. The third section contains the nature and power of Logarithms, with their application, arrd the method of computing them.
The fourth section contains geometrical definitions, theorems, and problems, with the description and use of the sector, Gunter's scale, and other mathematical drawing instruments used by surveyors.
The fifth section contaius Plane Trigonometry, rightangled and oblique, with a variety of rules and practical examples.
The first section (Part the Second) gives an account of the chains and measures used in Great Britain and Ireland, methods of surveying and of taking inaccessible distances by the chain only, with some necessary problems; also a particular description of the several instruments used in surveying, with their respective uses.
The second section contains the mensuration of heights and distances, with a great variety of problems and practical examples.
The third section contains the mensuration of areas, or the various methods of calculating the superficial contents of any field; also several new rules and problems, with practical examples, and various methods of finding the areas of maps from their geometrical construction; two of which, more concise than the rest, were first published in this work. Also, it contains four new and much more concise methods of determining the areas of surveys from the field-notes, or by calculation, than any hitherto published ; to these is added the method of calculating the area of a survey, by having the meridian pass through the east or west point of the survey, with the method of discovering these points from the fieldnotes, and the method of correcting the errors by the pen, when the survey does not close : also another new method for calculating the area, by having a parallel of latitude pass through the north or south point of the survey. The whole geometrically considered and demonstrated.*
* The remaining part of the Author's Preface I have altered according to the arrangement and improvement of this new edition.-Editor.