पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४४३

245 hastas, and the top-side is 4 hastas. What is the measure of the (basal) segments (caused by the inner perpendicular) and what of the inner perpendicular (itself) ? . 186. In the case of the (quadrilateral) figure above-mentioned, the measures of the top-side and the base are each to be taken to be less by 1 hasta From the top of each of the two perpendi- culars, a string is stretched so as to reach the foot (of the other perpendicular). You give out the measures of the inner perpendi- cular and of the basal segments (caused thereby). 187. (In the case of a quadrilateral with unequal sides), one side is 13 hastas in measure; the opposite side is 15 hastas; the top-side is 7 hastas; and the base here is 21 hastas What are the values of the inner perpendicular and of the basal segments (caused thereby)? CHAPTER VII-MEASUREMENT OF AREAS. 188-189. There is an equilateral quadrilateral figure, measuring 20 hastas at the side. From the four angles of that VII-54, and then the measures of the perpendiculars from the ends of the top- side to the base as also the measmes of the segments of the base caused by those perpendiculars have to be arrived at by the application of the rule given in stanza VII.49. Then taking these measures of the perpendiculais to be those of the pillars, the iule given in stanza 180 above as applied to arive at the measures of the inner perpendicular and the basal segments caused thereby The problem given in stanza 187 is however worked in a shghtly different way in the Kanarese commentary. The top-side is supposed to be parallel to the base, and the measures of the perpendicular and of the basal segments caused there- by are arrived at by constructing a triangle whose siacs are the two sides of the quadrilateral, and whose base is equal to the difference between the base and the top-side of the quadrilateral. 1881-189. Tho figure contemplated this problem seems to be this - The inner perpendiculars referied to herein are GH and KL. To find out these, FE is first determined FE, ac- cording to the commentary, is said to be equal to DM+DE+ (DM)}. CM² 2 Then with FE and BC or AD taken as pillars, the rule under reference may be applied. A M D F HE L K