By JOHN BONNYCASTLE,

OF THE ROYAL MILITARY ACADEMY, WOOLWICH.

THE THIRD EDITION.

LONDON:

PRINTED FOR J. JOHNSON, NO.72, ST. PAUL'S

CHURCH-YARD,

BY BYE AND LAW, ST. JOHN'S-SQUARE, CLERKENWELL.

:

PREFАСЕ. EFACE.

OF all the works of antiquity which have been tranfmitted to the present 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 science the moderns have far furpassed their masters; but, after a lapse of more than two thousand 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 system.

T

It is, however, generally allowed, that the Elements, as they now stand, are attended with many difficulties, which greatly retard the progress of learners, on their first entrance upon this study, and prevent them from applying to other branches of knowledge, which, in the present advanced state of the fciences, are equally useful and im portant. Among other obstacles of this kind