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ELEMENTS

OF

PLANE GEOMETRY.

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AN ATTEMPT IS MADE TO IMPROVE THE ARRANGEMENT AND SUPPLY THE

DEFECTS OF THAT BOOK, AND ALSO TO GIVE A DIRECT DEMONSTRATION

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EDINBURGH :
OLIVER AND BOYD, TWEEDDALE COURT.

LONDON : SIMPKIN, MARSHALL, AND CO.

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PRINTED BY OLIVER AND BOYD, EDINBURGH.

PREFACE.

GEOMETRY, as the name imports, appears to have been at first limited in its application to the measurement of small portions of the earth's surface. By the accession of successive discoveries and improvements, however, it has now become a science, not only of the greatest practical utility, as applicable to the measurement of the heavens as of the earth, but likewise a very efficient and successful instrument of investigation in several departments of physical inquiry. The elementary principles of geometrical science are indeed deposited by the wise and beneficent Creator in every rational mind, and therefore the simplest applications of its truths are to be found among men of all nations at an early part of their progress towards civilisation. At such a period, doubtless, the minds of men would be too much occupied in procuring the necessaries of life and securing their own safety to have any leisure or relish for abstract speculation. The elements of science, obscurely apprehended, might then float loosely in the minds of men long before they were collected and arranged in any regular order. The progress also of different nations in the path of geometrical discovery would

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