280

HISTORY OF

TRACT 19.

divided: according to which method I have nearly completeda table of sines and tangents.

It is not to be doubted that many of the ancients wrote onthe subject of trigonometry, being a necessary part of astro-nomy ; though few of their labours on that branch have cometo our knowledge, and still fewer of the writings themselveshave been handed down to us.

We are in possession of the three books of Menelaus , onspherical trigonometry; but the six books are lost which hewrote upon chords, being probably a treatise on the construc-tion of trigonometrical tables.

The trigonometry of Menelaus was much improved byPtolemy (Claudius PtolemaBus) the celebrated philosopherand mathematician. He was born at Pelusiuin; taught as-tronomy at Alexandria in Egypt ; and died in the year ofChrist 147, being the 78th year of bis age. In the first bookef his Almagest, Ptolemy delivers a table of arcs and chords,with the method of construction. This table contains 3 co-lumns; in the 1st are the arcs to every half degree or 30minutes; in the 2d are their chords, expressed in degrees,minutes and seconds; of which degrees the radius contains60; and in the 3d column are the differences of the chordsanswering to 1 minute of the arcs, or the 30th part of thedifferences between the chords in the 2d column. In theconstruction of this table, among other theorems, Ptolemy shows, for the first time that we know of, this property ofany quadrilateral inscribed in a circle, namely, that the rect-angle under the two diagonals, is equal to the sum of the tworectangles under the opposite sides.

This method of computation, by the chords, continued inHse till about the middle centuries after Christ; when it waschanged for that of the sines, which were about that time in-troduced into trigonometry by the Arabians, who in otherrespects much improved this science, which they had receivedfrom the Greeks, introducing, among other things, the threeor four theorems, or axioms, which we make use of at pre*gent, as the foundation of our modern trigonometry,