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OF

G E O M E T R Y.

CONTAINING THE

PRINCIPAL PROPOSITIONS

IN THE

FIRST SIX, AND THE ELEVENTH AND

TWELFTH BOOKS

OF

E U CL I D.

WITH NOTES CRITICAL AND EXPLANATORY.

By JOHN BONNYCASTLE,

OF THE ROYAL MILITARY ACADEMY, WOOLWICH.

THE THIRD EDITION.

LONDON:
PRINT ÉD FOR J. JOHNSON, NO:72, st. PÅ U L'S

CHURCH-YARD;
$Y BYE AND LAW, ST, JOHN'S-SQUARE, CLERKENWELL.

1803.

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PREF A C E.

OF all the works of antiquity which have been transmitted to the present times, none are more universally and deservedly esteemed than the Elements of Geometry which go under the name of Euclid. In many other branches of science the moderns have far surpassed 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 fyftem.

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 sciences, are equally useful and important. Among other obstacles of this kind A 2

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