TRACT 19. HISTORY OF TRIGONOMETRICAL TABLES. 279

into 360, or 6 times 60, equal parts or degrees, the wholecircumference being equal to 6 times the first are, whosechord is equal to the radius : unless perhaps we are rather toseek for the division of the circle in the number of days inthe year; for thus, the ancient year consisting of 360 days,the sun or earth in each day described the 360th part of theorbit; and thence might arise the method of dividing everycircle into 360 parts; and, radius being equal to the chordof 60 of those parts, the sexagesimal division, both of the ra-dius and of the parts, might thence follow. Trigonometryhowever must have been cultivated long before the time ofPtolemy ; and indeed Theon, in his commentary on Ptolemy’sAlmagest, 1. i. ch 9, mentions a work of the philosopher Hip-parchus, written about a century and a half before Christ,consisting of 12 books on the chords of circular arcs; whichmust have been a treatise on trigonometry. And Menelausalso, in the first century of Christ, wrote 6 books concerningsubtenses or chords of arcs. He used the word nadir , of anarc, which he defined to be the right line subtending thedouble of the arc; so that his nadir of an arc was the doubleof our sine of the same arc, or the chord of the double arc ;and therefore whatever he proves of the former, may beapplied to the latter, substituting the double sine for thenadir.

The radius has since been decimally divided; but the sexa-gesimal divisions of the arc have continued in use to this day.Indeed our countrymen Briggs and Gellibrand, having ageneral dislike to all sexagesimal divisions, made an attemptat some reformation of this custom, by dividing the degreesof the arcs, in their tables, into centesmsor hundredth parts,instead of minutes or 60th parts. The same was also re-commended by Vieta and others; and a decimal division ofthe whole quadrant might perhaps soon have followed, hadit not been for the tables of Vlacq, which came out a littleafter, to every 10 seconds, or 6th parts of minutes.—But thecomplete reformation would be, to express all arcs by theirreal lengths, namely in equal parts of the radius decimally