Algorithms in Bhāskara’s commentary on Āryabhat. īya 505
- I do not know the 〈monthly-〉 interest on a hundred. However, the 〈monthly-〉
〈interest on a hundred increased by the interest〉|
Obtained in four months is six. State the interest of a hundred produced within a
month||
Th is example states a case in which:
m = 100
k 2 = 4
p 1 + p 2 = 6
By the procedure given in Ab.2.25, the value of p 1 is 5.
Bhāskara then adds: 35
Ve r i fi cation ( pratyayakaran. a ) with the Rule of Five: ‘If the monthly interest
( vr. ddhi) 36 on a hundred is fi ve, then what is the interest of the interest [of value
( dhana )-fi ve] on a hundred, in four months?’
Setting down:
1
100
54
5
0Th e result is one. Th is increased by the〈monthly〉 interest on the capital is six rūpa s, 6.
Simply stated, the verifi cation consists of knowing m , p 1 and k 2 , fi nding
p 2 and confi rming that its value increased by p 1 will give the same value for
p 1 + p 2 as stated in the problem.
Th e Rule of Five, as seen above, returns the value of p 2. Th is procedure
does not deliver the same result but gives a method of inverting the pro-
cedure to check independently that the result makes sense. In this case, an
independent procedure is established. Th e use of the Rule of Five, which
Bhāskara describes as a combination of two Rules of Th ree, also imbues the
computation with a mathematical basis in proportionality.
3.3.2 Ve r i fi cation of the area of plane fi gures
Bhāskara interprets the fi rst half of Ab.2.9 as a way to verify procedures for
areas given by Āryabhat. a in the previous verses.
35 pratyayakaran. am pañcarāśikena-yadi śatasya māsikī vr. ddhin pañca tadā caturbhir māsaih.
śatavr. ddheh. [pañcadhanasya] kā vr. ddhih. iti/ nyāsar -1
100
54
5
0labdham. 1 / etatsahitā
śatavr. ddhih. s. ad. rūpān. i 6/ (Shukla 1976: 114–15).
36 From now on, unless otherwise stated this is the word translated as ‘interest’.