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EUCLID's

ELEMENTS

OF

GEOMETRY,

The First Six, the Eleventh and Twelfth
BOOK S;

Tranflated into ENGLISH,

From Dr. GREGORY's EDITION, TIRE

WITH

NOTES and ADDITIONS.

For the Ufe of the BRITISH YOUTH.

By

E. STO N E.

The SECOND EDITION, with ADDITIONS.

Ptolemy, King of Egypt, having afked Euclid whether there

was any other more compendious way of arriving at Geometry,
than by thefe his Elements, is faid to have anfavered: M
εἶναι βασιλικὴν ἀτραπὸν ἐπὶ γεωμετρίαν, There is no other way,
or royal paffage, to Geometry.

Proclus's Commentary upon Euclid's fecond book,

LONDON,

Printed for JOHN RIVINGTON, in St. Paul's Church-Yard,
WILLIAM JOHNSTON, in Ludgate-freet, and THOMAS
LONGMAN, in Pater-nofter-row.

M.DCC.LXY.

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ISDOM is certainly one of the main springs of human happiness. And the more of it each individual of a fociety acquires, the more happy, all things elfe alike, will that fociety be; for the wifer a man is, the better will he know how to preserve his own health, and pleasantly lengthen out his own life: he will better avoid the injuries of weather; better provide food and cloathing; better avoid pain and fickness; better footh, leffen, and command his own and other people's paffions; better obferve the laws of his country; and, in fhort, better promote his own and neighbours happiness in all refpects foever. Accordingly, fince wildom is fo neceffary to happiness, that learning, which is best adapted to promote and extend it, is undoubtedly the most valuable, and ought by all to be most encouraged, cultivated, and ufed. And therefore, fince true wisdom very much confifts in, and is obtained from, the knowledge of the comparative numbers and magnitudes of the qualities, powers, efficacies, matter, and motions of fenfible objects, their various increase and decrease, &c. and as thefe may be acquired in a great measure from arithmetic and geometry: these two fciences may truly be faid to be the two great fountains from whence much of the wifdom and happiness of mankind flow: And therefore, if poffible, they should be learned by every member of a fociety. No ftate ever did or scarcely could flourish without them. They have always been in efteem and cultivated proportionably to the greatnefs and riches of a country, and as thefe have declined, fo have those.

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