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A

TREATISE

ON

PLANE AND SPHERICAL

TRIGONOMETRY.

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PRINTED FOR J, JOHNSON, ST. PAUL'S CHURCH-YARD,

BY R. TAYLOR AND CO., GHOE LANE.

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INTRODUCTION.

At what period Trigonometry first began to be cultivated, as a branch of the mathematical sciences, is extremely uncertain, no records having been left by the antients, which enable us to trace it to a higher age than that of Hipparchus, who flourished about a century and a half before Christ, and is reported by Theon, in his Commentary on Ptolemy's Almagest, to have written a work, in twelve books, on the chords of circular arcs, which, from the nature of the title, must evidently have been a treatise on Trigonometry.

But the earliest work on the subject, now extant, is the Spherics of Theodosius, a native of Tripoli in Bythinia, who, soon after the time above mentioned, collected and brought together, into this performance, the scattered principles of the science which had been discovered by his predecessors, and formed them into a regular treatise, in three books, containing a variety of the most necessary and useful propositions relating to the sphere, arranged and demonstrated with great perspicuity and elegance, after the manner of Euclid's Elements (a).

(a) This work of Theodosius, which came to us through the medium of an Arabic version, has been published both in Greek and Latin by several writers; but the Latin edition of Dr. Barrow, 8vo. London, 1675, and that of Hunt, 8vo. Oxford, 1709, are

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