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GEOMETRY;

CONTAINING

THE FIRST SIX BOOKS OF EUCLID,

WIT! A

SUPPLEMENT

ON THE

QUADRATURE OF THE CIRCLE AND THE

GEOMETRY OF SOLIDS;

TO WHICR ARE ADDED,

ELEMENTS OF PLANE AND SPHERICAL,

TRIGONOMETRY.

BY

JOHN PLAYFAIR, F. R. S. Lond. & Edin.
LATE PROFESSOR OF NATURAL PHILOSOPHY, (FORMERLY OF MATHEMATICS),

IN THE UNIVERSITY OF EDINBURGH, SECRETARY OF THE ROYAL SOCIETY
OF EDINBURGH, MEMBER OF THE ROYAL ACADEMY OF NAPLES, AND OF
TUB ROYAL MEDICAL AND PHYSICAL SOCIETIES OF EDINBURGH.

SIXTH EDITION, ENLARGED.

EDINBURGH:

PRINTED FOR BELL & BRADFUTE; AND STIRLING & SLADE
EDINBURGH ; LONGMAN, HURST, REES, ORME & BROWN;
OGLE, DUNCAN & CO.; AND G. & W. B. WHITTAKER,

LONDON.

1822.

ENTERED IN STATIONERS' HALL.

P. Neill, Printer, Edinburgh.

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It is a remarkable fact in the history of science; that the oldest book of Elementary Geometry is still considered as the best, and that the writings of EucLID, at the distance of two thousand years, continue to form the most approved introduction to the mathematical sciences. This remarkable distinction the Greek Geometer owes not only to the elegance and correctness of his demonstrations, but to an arrangement most happily contrived for the purpose of instruction-advantages which, when they reach a certain eminence, secure the works of an author against the injuries of time, more effectually than even originality of invention. The Elements of Euclid, however, in passing through the hands of the ancient editors, during the decline of science, had suffered some diminution of their excellence, and much skill and learning have been employed by the modern mathematicians to deliver them from blemishes, which certainly did not enter into their original

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composition. Of these mathematicians, Dr Simi SON, as he may be accounted the last, has also been the most successful, and has left very little room for the ingenuity of future editors to be exercised in, either by amending the text of EucLID, or by improving the translations from it.

Such being the merits of Dr SIMSON's edition, and the reception it has met with having been every way suitable, the work now offered to the public will perhaps appear unnecessary. And indeed, if the geometer just named had written with a view of accommodating the Elements of EUCLID to the present state of the mathematical sciences, it is not likely that any thing new in Elementary Geometry would have been soon attempted. But his design was different: it was his object to restore the writings of EUCLID to their original perfection, and to give them to modern Europe as

nearly as possible in the state wherein they made 30

their first appearance in Ancient Greece. For this undertaking, nobody could be better qualified than Dr SIMSON ; who, to an accurate knowledge of the learned languages, and an indefatigable spirit of research, added a profound skill in the ancient Geometry, and an admiration of it almost enthusiastic. Accordingly, he not only restored the text of Euclip wherever it had been corrupted,

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