पृष्ठम्:सिद्दान्तदर्पणम्.djvu/११

the hypotenuse of a right-angled triangle (pp. 22-24, below). In the course of this discursion, he makes a mention also of the two methods of approach for solving mathematical problems, wट., that of logical reasoning and that of demonstration on the b0ard try the method of demonstration, for logical reasoning is limited, endless and sometimes inconclusive (alp0-wisayatrvat, ar1071y7d, kvacidapyavisraries ८, p. 23). Eually Instructive are the method of constructing the armillary sphere, the defining of the situation of ra5-ऽ therein (p. 14), and the exposition of the computation of the geocentric position of the planets (pp. 25-31) The following observations of Nilakatha are noteworthy : 1. 2. 3. 4. 11 5. 4y27dia52 (measure in minutes of the precession of the equinoxes) should be derived by observation, if it has to be accurate (p. 17) The use of 7airnsika (Rule of three) is justified even in computations concerning moving bodies, Since the factors involved are considered only for specific moments at which they might be taken as stationary (p. 25) In astronomical computation it does not make any diffe rence whether the eastward m10tion of the earth (or the westward motion of the planets are taken because the motion is relative (p. 5). The Bhagola (Rasigola, ecliptic sphere) revolves as a whole and not Yayugola (having the Gloatikar101ala or Celestial equator as one of its great circles) ; thus the relative distances between the stars remain constant, from which other results follow (pp. 16-17) The wikSep0 (celestial latitude) of stars beyond five or six degrees on either side of the ecliptic have to be observed and determined by means of instrumental observation, for they cannot be gauged in relation to the planets, which all 1ie within the said limit (p. 16) It is unfortunate that the only available manuscript of the commentary is incomplete . The loss is especially significant, for the 1ast portion should have contained the lucidatory examples about