The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

Proposition IV. How to divide a Circle into 120 Parts, and by consequence into 360.

Draw the Diameter BC, and upon the point A, describe the Circle CDBL, then draw the Diameter DAN, at Right Angles, to the Diameter CAB.

2. The Semidiameter or Radius of a Cir∣cle will divide the Circle into 6 equal parts, and so is equal to the Chord of 60 degrees, AC, therefore being set from D to F, shall mark out the Arch DF, 60 degrees.

3. The side of a Pentagon of fifth part of a Circle, is 72 degrees; now then, if you bisect the Radius AC in the point E, and

make EG = ED; then shall DG = DM, the side of a Pentagon or Chord of 72 degrees, and FM the difference between DM, 72 and DF 60, that is the Chord of 12, which by bisection shall give the Chord of 6 and 3 degrees, and so the Circle may be divided into 120 parts, as was propounded.

4. A Circle being thus divided into 120 degrees, the Arches are so equal, that the third part of the Chord of 3 degrees will subdivide it into 36, without sensible error; and your Circle being thus divided into 360 parts, lines at every degree, or half degree, drawn parallel to the Diameter, shall consti∣tute the line of Chords, & half those Chords the line of sines; and the Segments of the Diameter, the line of versed sines, and as for the Tangents and Secants, a line touching the Circle drawn perpendicular to the end of the Diameter, and continued to the seve∣ral lines drawn from the Centre, through every degree of the Quadrant, shall consti∣tute the line of Tangents, and those lines drawn from the Center to the Tangents, shall constitute the line of Secants also. And thus may a Scale be made with the lines of Sines, Tangents, Secants, and equal parts.