PREFACE.

T

HE Word Geometry imports no more than to meafure the. Earth, or to measure Land yet in a larger and more proper Senfe, it is applied to all Sorts of Dimenfions. It is generally fupposed to have had its Rife among the Egyptians, from the River Nile's deftroying and confounding all their Land-marks by its annual Inundations, which laid them under the Neceflity of inventing certain Methods and Measures, to enable them to diftinguish and adjust the Limits of their refpective Grounds, when the Waters were withdrawn. And this Opinion is not entirely to be rejected, when we confider that Mofes is faid to have acquired this Art, when he refided at the Egyptian Court. And Achilles Tatius in the Beginning of his Introduction to Aratus's Phenomena, informs us, that the Egyptians were. the firft who measured the Heavens and the Earth (and of courfe the Earth firft) and that their Science in this Matter, was engraven on Columns, and by that means delivered to Pofterity,

It is a Matter of fome Wonder, that though Surveying appears to have been the firft, or at least one of the first of the Mathematical Sciences, that the reft have met with much greater Improvements from the Pens of the most eminent Mathematicians,

maticians, while this feems to have been ne glected; infomuch that I have not been able to meet with one Author, who has fufficiently 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.

Thefe Confiderations induced me to attempt a methodical, eafy and clear Courfe of Surveying, how far I have fucceeded 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, you have Decimal Fractions, the Square Root, Geornetrical Definitions, fome neceffary. Theorems and Problems; with the Nature and Ufe of the Tables of Logarithm Numbers, Sines, Tangents, and Secants.

The fecond Section contains Plane Trigonometry. right angled and oblique, with its Application in determining the Meafures of inacceffible Heights and Distances.

The third Section gives an Account of the Chains and Measures ufed in Great-Britain and Ireland, Methods of Surveying and of taking inacceffible Distances by the Chain only, with fome neceffary Problems; alfo a particular Defcription of the feveral Inftruments ufed in Surveying, with their refpective Ufes.

The fourth Section contains five various Methods of finding the Areas of Maps, from their Geome

trical

trical Construction: two of which more concife than the reft, were never before made public.

The fifth Section contains four new, and much more concife Methods of determining the Areas of Surveys from the Field Notes, or by Calculation than any hitherto published; and I venture to affert that it is impoffible (from the Nature of rightlined Figures) that any Method or Methods more concife than thefe can be inveftigated.

To these Methods is annexed a fhort Table of Difference of Latitude and Half Departure, to every Degree and Quarter of a Degree of the Quadrant, the ftationary Distance being one Chain; which will be found as ready, by a little Practice, and perhaps more exact, than thofe already publifhed. To this is annexed a Table for reducing Degrees of the Circumferentor to thofe of the Quarter Compafs, and the contrary; alfo the Method of changing Angles of the Field, taken by Theedolite, Semicircle, or Plane Table, to thofe from the Meridian; for the greater Readiness and Accuracy in Protraction, as well as to prepare them for Calculation.

Truth calls upon me to acknowledge, that the Methods by Calculation, herein fet forth, got their Rife from thofe of the late Thomas Burgh, Efq; who firft difcovered an univerfal Method for determining the Areas of right-lined Figures, and for which he obtained a parliamentary Reward. I hope therefore it cannot be conftrued as an Intention in me to take from his great Merit, when I fay, that the Methods herein contained are much more concife and ready than his

Section

Section the fixth contains the Nature of Off-fets, and the Method of cafting them up by the Pen: The Nature and Application of Interfections: The Methods of enlarging, diminishing, and connecting of Maps: The Method of tracing defaced Mearings from the Down (or any other) Surveys: The Variation of the Compafs by Amplitudes and Azimuths, with fome of its Ufes; to which is added, a Table of the Sun's Declination: The Method of reducing one Measure to another; how to find by what Scale a Map is laid down, having the Map and Area given: How to find the Content of Ground that is furveyed by a Chain that is too long or too fhort: The Method of dividing Lands: And the whole concludes with fome neceffary Directions and Remarks on Surveys in general.

THE

THE

PRINCIPLES

O F

SURVEYING.

SECT. I. ·

Containing Decimal Fractions, the Square Root, Geometrical Definitions, Theorems and Problems; with the Nature and Use of the Tables of Logarithm Numbers, Sines, Tangents, and Secants.

SUR

DEFINITION,

URVEYING is that Art which enables us to a give a Plan, or juft Representation, of any Piece or Parcel of Land, and to determine the Content thereof, in fuch Measure as is agreeable and cuftomary to the Country or Place where the Land is.

This Science depends on fome Part of the Mathematics, which must be known before we can treat of it, wherefore we shall begin with

DECIMAL FRACTION S.

If we suppose Unity or any one Thing to be divided into any affigned Number of equal Parts, this Number is called the Denominator; and if we chuse to take any Number of fuch Parts lefs than the Whole, this is called the Numerator of a Fraction.