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BY A. NESBIT,

MASTER OF THE CLASSICAL, COMMERCIAL, AND MATHEMATICAL ACADEMY, KENNINGTON LANE, LAMBETH, LONDON;

AND AUTHOR OF

"A Treatise on Practical Arithmetic; "A complete Treatise on Practical Land-Surveying ;""A Treatise on Practical Gauging;"" Keys to the Arithmetic, Mensuration, and Gauging;' ""An Introduction to Parsing, adapted to Murray's Grammar; "An Essay on Education; " &c. &c.

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NEW EDITION, ENLARGED, AND GREATLY IMPROVED.

TO WHICH IS ADDED,

A TREATISE ON LEVELLING.

The whole illustrated by nearly seven hundred Practical Examples, and nearly three hundred Woodcuts.

LONDON:

LONGMAN, BROWN, GREEN, LONGMANS, & ROBERTS.

1857.

ΤΟ

ELLIS CUNLIFFE LISTER, ESQ., M.P.

OF

MANNINGHAM-HOUSE,

Near Bradford,

AS AN ACKNOWLEDGMENT OF GRATITUDE FOR NUMEROUS

FAVOURS RECEIVED,

AND AS

A TOKEN OF ESTEEM FOR HIS GENERAL KNOWLEDGE

OF SCIENTIFIC SUBJECTS,

THIS TREATISE

ON

PRACTICAL MENSURATION,

In all its Departments,

IS

MOST HUMBLY AND RESPECTFULLY DEDICATED,

BY HIS MUCH OBLIGED,

AND MOST OBEDIENT SERVANT,

A. NESBIT.

EIAN

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IN revising the present Edition of this work, the Proprietors have spared neither labour nor expense in order to render it as valuable as possible; and for this purpose they have engaged competent persons, who have made several important and necessary improvements. They have commenced with the Geometrical Definitions, Problems, and Theorems, by arranging the subjects in a more concise, elegant, and systematic order, the Geometrical Theorems being much improved and rendered more complete by prefixing a description to the respective theorems. In the Mensuration of Superficies the same order of arrangement has been strictly regarded, and several additional and important notes have been added to the respective problems. On the subject of Land Surveying, great improvements have been made, by introducing a simple method of surveying without the use of the cross-staff. Similar arrangements and improvements have been observed throughout the Mensuration of Solids, Conic Sections, and their Solids, and the other parts of the book. Thus a large

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