Bijganit Purvarddh

Author(s): Bapudev Shastri
Publisher: Medical Hall Press

Page 6

for determining the sine of the altitude of the sun when situated in the vertical circle of which the Azimuth distance is 45. But all the original treatises on Algebra bave perished, and of those compiled since the time of ARYA BHAȚA that of BHASKARACHÁRYA only is in use : the others are rarely to be met with:
The first treatise on Algebra published in Greece was that prepared about 1500 years ago by an ingenious Greek named Diophantus.
The Arabs and Persians have never been the inventors of any science. They have always borrowed from other nations. Algebra therefore could not have been a science of their invention
: bsp. ):= 2 (**+a)=
* +2 a3
Now, since the square of the sine of the zenith distance added to the square of the sine of the altitude is equal to the muare of the radius.
.:.x2 + + y2 + 2 a? = R$
Clearing fractions, 72 22 + på 24 apr + 144 a? = 72 R? or
(p2 + 72) 9 + 24 apx - 72 R? - 144 ao 22+ 24 ap 72 R2-144 4?_144 ( RP-a!) .** +p+72* p? +72 - pi + 72 Now, in the foregoing equation it will be observed, that the voice of the side containing the knowo quantities is wbat has been already spoken of under the naine of KARANÍ, and that the half of the co-efficient of 2 i9 wbat has been already spoker. of uuder tha name of PHALA.
Completing the square
2 fx +
+ Extracting the square root +1 / 2+k
x=vf+Ff (A) From this it is evident thnt PHALA is subtractod from, or added to, the square root of the EaraŅI increased by the syaure of the PHALI according as the sun is south or north of the equinoctial.
in (A), if ft be assumed a negative, then the value of x (i. e. of the KOMASAXKU) will also be negative, (i. e. the sun will be below the horizon).
As the foregoing calculation is effcoted by a method of procedure clearly Alge. braical, it follows that the Hindus were in possession of that science at the date of the earliest of their mathenatical treatises,