283 ShSahitg rate &nd only time the Greek method of measuring the moon's disraet, by equi bwelbas, or digits : from this scale a farther reduction is made to the propeak Hindu scale, as determined by the methods of the fourth chapter (see above, v, 2-8, 26), by another proportion : S रंwelve is to be brue diameter in digits, so is bhe result already found to the true measure ot the part of th® diameter Aluminated. t is not to be youdered at that the Indus did not necognize the ellpticity oft bhe line fortung the nner boundary of the moon's luminated part : it is more *trange that they gnored the obvious fact that, while he illuminated portion of the moon's sphatrical surface visible from the earth veries very nearly as he distance from the sunthe apparent breadth ot the bright part of her disk, in which that surface is seen projected, must way rather us the versed 81ne of her distance. 10. Fix a Ount, calling it the sun : fronm that lay of the base, in its own proper direction; then the perpendicula, towards the west; and also the hypothenuse, passing through the extremity of the perpendicular and the central point. 11. From the point of intersection of the perpendicular and the hypothemuBe describe the noon's disk, according to its dinen sions at the given time. Then, by means of the hypothenuse, first make a determination of directions 12. And lay of upon the hypothenuse, from the point of its intersection with the disk, in an inward direction, the measure of bhe illuminated part : between the limit of the luminated part and the north and south points draw to fishfigures (matsge) ; 18. From the point of intersection of the lines passing through their midst describe an are touching the three points : as the disk already drawn appears, such is the moon upon that day . 4. After making a determination of directions by means of the perpendicular, point of the clevated data) cup at the extremity of the arOfA-line : १aving made the perpendicular (koji) to be' erect (atata), that is the appearance of the moon. 15. In the dark lhalf-anonth ultract the longitude of the Bun increased by six signs from that of the moon, and calculate, in the same manner as before, Jer dark part. In this case lay of the base in a reverse irection, and be circe of the moon on the West
