OF GEOMETRY: CONTAINING THE FIRST SIX BOOKS OF EUCLID, WITH A SUPPLEMENT ON THE QUADRATURE OF THE CIRCLE AND THE TO WHICH ARE ADDED ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY. BY JOHN PLAYFAIR, F. R. S. LOND. & EDIN. PROFESSOR OF NATURAL PHILOSOPHY, FORMERLY OF MATHEMATICS, FROM THE LAST LONDON EDITION, ENLARGED. NEW-YORK: PRINTED AND PUBLISHED BY GEORGE LONG, 1819. 4-2-45ADE Brussel PREFACE. 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 composition. Of these |