English
from which data I Digitized by Google 154 THE MODERN ASTRONOMY find the longitude to be GS'^ 5', and latitude lO^'SO' S. Hence it appears that the error is on the side of Aryabhatta, unless he meant another star ; but this we can hardly suppose, because there is no other star 3° more to the east with the same latitude. On the other hand, Aryabhatta makes the longitude of the star in the seventh Lunar Mansion Punarvasu, 92° 53'. I make it, from the data in the Brahma Siddkanta, 92° 52', differing but one minute ; but the Sarva Bfiauma makes it 94° 53', differing 2°, which shows that there are errors on both sides, which, after all, may have arisen from carelessness in copying, and therefore it would be needless to offer any further observations on the differences in the table, as copies of the Art/a Siddhanta are not now procurable. In the fifteenth chapter, Aryabhatta treats of the several rules of arithmetic, as addition, subtraction, multiplication, division, squares and cubes of num- bers, and their roots, progressions, and other matters relating to the doctrine of numbers, after which he treats on geometrical problems; the whole of which appears to be the same, or very nearly so, and in the same order, as given in the Litdvati of Bhaskara Acharya ; with this difference, that Aryabhatta only gives the problems and rules of solution generally, and withput numbers, whereas in the Lilavati, they are exemplified by figures and numercial solutions, so that the latter maybe taken as a perpetual com- mentary on this part of the Arya Siddhanta : but in the problems relating to the circle, of which there are about eighteen in the Arya Siddhanta, Bhaskara Acharya differs from him, particularly in the propor- tions of the diameter to the circumference. For instance, the diameter being given to find the cir- Digitized by Google OF THE HINDUS. 155 cumference, one of Aryabhatta's rules is, '* Multiply the square of the diameter by 10, the square root of the product is the circumference." Thus, suppose the diameter 10, then 10* x 10 = 1000, and i/1000 = 31.6228: this appears to be from Brahma Gupta. Bhaskara's rule is. Multiply the diameter by 3927, and divide by 1250, the quotient is the near cir- cumference. Thus, suppose the diameter 10, then ^=^=31.416. The following rule is given by Aryabhatta for finding the arc from the chord and arrow (or verse sine) : Multiply the square of the arrow (v. s.) by 6, add the square of the chord, the root is the arc. Thus, suppose the diameter of a circle is 10, and we wanted to know the circumfe- rence, then 10 will be the chord and 5 the arrow; and we shall have -•6x6+io*=\/ 250 = 15.8114 for the arc or semicircumference ; its double, therefore = 31.6228, the same as above from Brahma Gupta. The following is another of Aryabhatta's rules for finding the arc : Multiply the square of the arrow (v. s.) by 288, divide the product by 49, to the quotient add the square of the chord, the root of the sum is the near arc. Thus, suppose the chord = 10 = the diameter of a circle, then the arrow will ^e 5, or the semidiameter, and ^^=146.938 and \/ 146,938 +iua=\/ 246.938 = 15.7 143, the arc of a semi- circle, and its double 31.4286, the whole circum- ference of a circle whose diameter is 10 ; whence, the proportion is as 1 : 31.4286. But Aryabhatta, in the l/th chapter, in speaking of the orbits of the planets, gives us a nearer approach to the truth ; for he there states the proportion as 191 to 600, or as 1:31.4136, which gives the circumference a small matter less than the proportion of Bhaskara in the Lilavati. This, however, is not the invention of Digitized by Google 156 THE MODERN ASTRONOMY Aryabhatta ; for it is employed in the Brahma Sidd- hanta, Surya Siddhanta, and by all the astronomers before the time of Aryabhatta, as well as since, for computing the tables of sines, &c. though not imme- diately apparent. Thus, in computing the sines, they take the radius at 3438', and the circumference they divide into 21600', the diameter is therefore 6876, hence the proportion is 6876 : 21600 : reduce these numbers to their least terms by dividing them by 36, the result will be 191 : 600, as stated by Aryabhatta. Aryabhatta next proceeds to the doctrine of exca- vations, and the contents of solids ; but unfortunately, after proceeding as far as Chiti (piles or stacks), the remainder of the chapter is lost, together with the whole of the sixteenth, which contained his algebra, and a few stanzas of the seventeenth — a loss the more to be regretted, as I fear it cannot be restored. If we had this part, we should have been able to ascertain what improvements were introduced by Bhaskara Acharya, who, it appears, lived 200 years after Aryabhatta, as will be shown in the next sec- tion. Aryabhatta, like many other Hindu writers, is now thrown back into antiquity, the cause of which will be explained when we come to speak of Bhaskara and Varaha Mihira in the next section. Digitized by Google OF THE HINDUS. 157 SECTION IV. Varaba Mihira, lik* Aryabhatta, endeavaura to iuppart the new order qf things — Perverts the rmemwtg of a passage relating to the epoch qf Yudhist'hira, who he ptaees 2448 before Christ — Yaraha Mihira menti&ns the Surya Siddhanta and Aryabhatta — States the heliacal rising of Canopus at Ujein, when the Sun was 7^ short of Virgo — Gives the positions of the aphelia qf the Planets in the Jatakamava for the year 1450 Sacay or A. D. 1528— DUr hdiaeal rising qf Canopus ai Vjeim eompmted for that tfear^ the result agrees with that which Varaba stated, being 7^ short qf Virgo — The point qfheUacal rising of Canopus at Ujein, in the Hindu sphere, shown The next person we have to notice, in point of antiquity and celebrity, is Varaha Mihira. Like Aryabhatta, he contributed his mite towards sup- porting the modernorder of things, by endeavouring to pervert the meaning of a passage respecting the epoch of YudhishtTiira. When the modern system was first introduced, the epochs of ancient kings were referred to it, as they really stood, and amongst the rest, Yudhisht'hira, who lived about 575 years before Christ. The epoch or time of Yudhist'hira ascending his throne, transferred to the modern Kali Yuga, corresponded to the year 2526 . The meaning of this, Varaha Mihira thought fit to pervert, by say- ing that it was the number of years Yudhist'hira lived before the era of Saca ; placing him there for 2448 B. C. The era of Saca, it seems, then, fell very conveniently in his way ; but if it had not, he would have hit on some other contrivance, equally as plau- sible and convincing. He also supported the notions of the motions of the stars in the Great Bear first broached by Aryabhatta, that of their being 100 Digitized by Google 158 THE MODERN ASTRONOMY years in each Lunar Asterism, and that they were in Magha in the time of Yudhishtliira. To dwell longer on such childish absurdities would be a waste of time : we shall, therefore, proceed to what is of much more importance, that of determining the period when Varaha Mihira lived, which will enable us to point out a great number of forgeries and im- positions of the moderns, that were not in the least suspected. I have noticed on a former occasion, that Varaha Mihira mentions the Surya Siddhanta, which would of course place him after the period to which that work has been referred. Varaha Mihira also men- tions Aryabhatta ; consequently he must have been posterior to him, that is, since A. D. 1322. But what he states himself is still better than all this, because it brings us at once to the point. He tells us in one of his works, the Varaha Sanhita, that Canopus rose heliacally zi Ujein, when the sun was 7° short of Virgo; that is, when he was in 23° of Leo. This is a most important fact, because it serves to decide a point of time that has been long disputed. In calculating the time, we may make choice of any particular year since the time of Aryabhatta: but as Varaha Mihira has given us his time in another of his works called the Jatakarnavaj in which the positions of the aphelia of the planets for the year of Saca 1450, or A. D.