OF GEOMETRY. CONTAINING THE PRINCIPAL PROPOSITIONS IN THE FIRST SIX, AND THE ELEVENTH AND OF EUCLI D. WITH NOTES CRITICAL AND EXPLANATORY. By JOHN BONNY CASTLE, OF THE ROYAL MILITARY ACADEMY, WOOLWICH. THE THIRD EDITION. LONDON: PRINTED FOR J. JOHNSON, NO. 72, ST. PAUL'S BY BYE AND LAW, ST, JOHN'S-SQUARE, CLERKENWELL. PREFACE. OF all the works of antiquity which have been tranfmitted to the prefent times, none are more univerfally and defervedly esteemed than the Elements of Geometry which go under the name of EUCLID. In many other branches of fcience the moderns have far furpaffed their mafters; but, after a lapse of more than two thoufand years, this performance still maintains its original preeminence, and has even acquired additional celebrity from the fruitless attempts which have been made to establish a different fystem. It is, however, generally allowed, that the Elements, as they now ftand, are attended with many difficulties, which greatly retard the progrefs of learners, on their first entrance upon this ftudy, and prevent them from applying to other branches of knowledge, which, in the prefent advanced state of the fciences, are equally ufeful and important. Among other obftacles of this kind |