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District of New-York, ss.

BE IT REMEMBERED, That on the twenty-seventh day of April, in the forty-fifth year of the Independence of the United States of America, Evert Duyckinck, of the said district, hath deposited in this office the title of a book, the right whereof he claims as pros prietor, in the words following, to wit:

" The Theory and Practice of Surveying ; containing all the Instructions requisite for the skilful practice of this Art. By Robert Gibson. Illustrated by Copper-Plates. Newiy arrangea, improved,

and enlarged, with useful Selections, and a new set of accurate Maiheinarical Tables By James Ryan, Teacher of the Mathematics."

In conformity to the act of the 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 an act, entitlerl, “ 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."

G. L. THOMPSON,

Clerk of the District of New-York,

gh.
C. B. vanis

3

PREFACE.

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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 its rise among the Egyptians, from the river Nile's destroying and confounding all their Land-marks 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and measures, to enable them to distinguish and adjust the limits of their respective grounds, when the waters were withdrawn.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 bis introduction to Aratus's Phenomena, 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, that 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 remaining part of the Author's Preface, I have altered according to the arrangement and improvement of this New Edition.

Editor,

The third section contains the nature and power of Logarithms, with their application, and 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 contains Plane Trigonometry, right angled 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 content of any field; also several new Rules and Problems, with practical exampies, 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 Field Notes, 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 fourth section contains the nature of Off-Sets, and the method of casting them up by the pen.

The fifth section contains the method of finding the Areas by intersections.

The sixth section shows how to enlarge or diminish a map, or to reduce a map from one scale to another; also the man. ner of uniting separate maps of lands which join each other, into one map of any assigned size.

The seventh section contains the method of dividing land, or of taking off or inclosing any given quantity

Section the eighth treats of surveying Harbours, Shoals, Sands, &c.

Section the ninth treats of Levelling, adapted to the surveying of roads and billy ground, with Promiscuous Questions.

Section the first (Part the Third) contains the Astronomical methods of finding the Latitude, Variation of the Compass, &c. with a description of the instruments used in these operations.

Section the second contains a description of the instruments requisite in Astronomical Observations.

Section the third shows how to find the Latitude by the Meridian Altitude of the Sun.

Section the fourth shows how to find the Variation of the Compass, with a description of the Azimuth Compass, and its

use.

In this Edition is introduced a new set of accurate Mathematical Tables.

Truth calls upon me to acknowledge, that the methods of cal ation hereio set forth, got their rise from those of the late Thomas Burgh, Esq.* who first discovered an universal method for determining the Areas of right-lined figures, and for which he obtained a parliamentary reward, I hope, therefore, it cannot be construed as an intention in me to take from his great merit, when I say, that the methods herein contained are much more concise and ready than his.

* This method, with very little alteration and improvement, in this cours try, is usually called the Pennsylvania Method of Calculation,

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