227 
1893.] Pandit Bapu Dora Sastri — A brief account of BJidskara. 
dentally and briefly treated of by liim, and his followers, not compre- 
hending it fully, have hitherto neglected it entirely. 
4. The ancient astronomers Lalla and others say that the differ- 
ence between the mean and true motion of a planet becomes nothing 
wlien the planet reaches the point of intersection of the concentric and 
excentric. But Bhaskara, denying this, says that when the planet 
reaches the point where tne transverse diameter of the concentric cuts 
the excentric, the difference of the mean and true motions becomes 0.* 
For let p bo the mean place of a planet at any time on a certain 
day, and p that at the same time on the next day ; and e and e be the 
amounts of the equation respectively: then p + e and p' + e will be 
the true places of the planet ; p'—p + (e — e) will be the true motion 
of the planet ; taking p' ~p the mean motion from this, the remainder 
e - e is the difference between the amounts of the equation. Thus, 
it is plain, that the difference between the mean and true motions of 
the planet is the rate of the increase or decrease of the amount of the 
equation. Therefore where the amount of the equation becomes 
greatest, the rate of its increase or decrease will be nothing ; or the 
difference between the mean and true motions equals 0. But as the 
amount of the equation becomes greatest, when the planet reaches the 
point of the excentric cut by the transverse diameter of the concentric 
(see the note on verses 15, 16 and 17 of Chapter V), the rate of its 
increase or decrease must be nothing ; that is, the difference between 
the mean and true motions will be nothing at the same point. This 
is the principle of the maxima and minima, with which, it is thus evident, 
Bhaskara was acquainted. 
5. He ascertained that when the arc corresponding to a given 
sine or cosine is found from the table of sines, this will be not far from 
its exact value, when it is not nearly equal to 90° or 0° respectively .+ 
6. He discovered the method of finding the altitude of the sun, 
when his declination and azimuth and the latitude of the place are 
given. This is a problem of Spherical Trigonometry, which he first 
solved by two rules in the Ganitadhydya. Of these two rules, we 
have shown one in the note on verse 46 of the 13th Chapter of the Gola- 
dhyaya, and the other is the following : — 
shown by Bhaskara in his analysis, is in the highest degree remarkable ; that the 
formula which ho establishes, and his method of establishing it, bear more than a 
mere resemblance— they bear a strong analogy — to the corresponding process in 
modern mathematical astronomy ; and that the majority of scientific persons will 
learn with surprise the existence of such a method in the writings of so distant a 
period, and so remote a rogion.’ Ed.] 
*' [Siddhanta-S' iromani. Chap. V, 39. Ed.] 
t [ Siddhanta-S’ iromani . Appendix. Ed.] 
