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A RUDIMENTARY TREATISE

ON

LAND AND ENGINEERING

SURVEYING

For Students and Practical Use

By T. BAKER, C.E.

AUTHOR OF

65
SUBTERRANEOUS SURVEYING,"

,“STATICS AND DYNAMICS,"
66
MECHANISM AND CONSTRUCTION OF MACHINES, MENSURATION,

MATHEMATICAL THEORY OF THE STEAM ENGINE, STO. ETO.

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Fifteenth Edition, Revised and Corrected

BY

J. R. YOUNG
FORMERLY PROFESSOR OF MATHEMATICS, BELFAST COLLEGE,
AUTHOR OF A RUDIMENTARY TREATISE ON ARITHMETIC," ETC. ETC.

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OF THE

Capio Lures
REESE LIBRARY
UNIVERSITY
CALIFORNIA

LONDON
CROSBY LOCKWOOD AND SON
7, STATIONERS' HALL COURT, LUDGATE HILL

1891

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PREFACE.

LAND SURVEYING is a branch of the Mathematics applied to practical purposes, and had its origin, it is said, in Egypt, more than 1000 years before the Christian era, where the annual inundations of the Nile, and the consequent large deposits of mud, destroyed the land marks of the different proprietors. It therefore became necessary to determine these land marks by measurement, or to lay out the proper quantities of land claimed by the several proprietors, irrespective of their land marks, thus destroyed. Hence the origin of the science of geometry, so called from its being compounded of two Greek words signifying " to measure the earth."

But, notwithstanding the early origin of this science, in as far as it is applied to land surveying, it has received comparatively very little improvement almost up to the present time. The writers of extensive works on this subject being chiefly practical men, unacquainted with modern analysis, and some of them even ignorant of geometry, have successively produced works which are little more than mere copies of those previously published, their examples being in all cases simple and profuse without variety or elegance, the invariable result of such labours being a large volume immeasurably behind the requirements of the subject as well as the science of modern times.

In the following work, the author trusts, it will be found that he has avoided such profusion and want of variety in the subjects proposed, and made, at the same time, the most important parts sufficiently clear to those students who have not had an opportunity of studying geometry and the higher branches of mathematics,—the demonstrations of all rules and formulæ not previously published being given in notes, apart from the practical matter; while the demonstrations of all rules previously given in

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