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PART I.-GEOMETRY AS A SCIENCE.

PART II.--GEOMETRY AS AN ART.
PART III.-GEOMETRY COMBINED WITH ARITHMETIC.

(MENSURATION).

BY

THOMAS LUND, B.D.

RECTOR OF MORTON, DERBYSHIRE;

EDITOR OF WOOD'S ALGEBRA;
KORMERLY FELLOW AND SADLERIAN LECTURER OP-ST JOPN's

COLLEGE, CAMBRIDGE.

TOR

V EW-YOR! LONDON:

LONDON:
LONGMAN, BROWN, GREEN, LONGMANS, AND ROBERTS.

1859

Cambridge: Printed at the University Press.

ADVERTISEMENT TO PART I.

The following short Treatise on Geometry as a Science makes no pretence of entering into competition with Euclid's Elements the most wonderful book perhaps, with one exception, in existence. But as it cannot be denied, that Euclid presents Geometry in a diffuse and somewhat repulsive form, whereby a large proportion of those, who ought to be acquainted with the subject, are deterred from venturing upon it at all, I have thought that good service might be rendered to the cause of popular education by framing a work, which shall neither terrify by its size, nor repel, as Euclid does, by a studied avoidance of all practical illustration. At the same time I have endeavoured, except in a single instance, to preserve the strictness of the ancient geometers, at least to the extent of laying down a solid and trustworthy foundation for that which is to follow. I cannot discover any good reason, why the mensuration taught in our Schools should be built, as it mostly is, upon no foundation but the memory only; I think it need not, and I am sure it ought not, to be so. But as it is, we reap the fruits of this bad system of mental culture in the very general ignorance of right principles of construction and design, which notoriously prevails among English artists and workmen. Public attention has been lately directed to the necessity of removing this stigma from our character as a people by the institution of

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