Algorithms in Bhāskara’s commentary on Āryabhat. īya 493
Its computation should be known indeed as the shadow of the gnomon 〈measured〉
from its foot.|| 15
Th is procedure involves a multiplication and a division. In modern alge-
braic notation:
(^) EC BE DE
AF
=
×
Th e procedure given in the verse appears to be an arbitrary set of opera-
tions. Bhāskara begins with a general gloss. Th en, as in all his verse com-
mentaries, Bhāskara’s commentary provides a list of solved examples. Th ese
examples have a standard structure: fi rst comes a versifi ed problem, then a
‘setting down’ ( nyāsah. ) section, and fi nally a resolution ( karan. a ).
Th us, in his ‘reinterpretation’ of the above procedure aft er a solved
example, Bhāskara writes:
Th is computation is the Rule of Th ree. How? If from the top of the base which is
greater than the gnomon [AF], the size of the space between the gnomon and the
base, which is a shadow, [FD = BE] is obtained, then, what is obtained with the
gnomon [DE]? Th e shadow [EC] is obtained.^16
15 śa ̇nkugun. am. śa ̇nkubhujāvivaram. śa ̇nkubhujayor viśes. ahr. tam|
yal labdam. sā chāyā jñeyā śa ̇nkoh. svamūlād hi|| (Shukla 1976 : 90).
Figure 14.2 A schematized gnomon and light.
AFB
E CD16 etatkarma trairāśikam/ katham? sa ̇nkuto ’dhikāyā uparibhujāyā yadi śa ̇nkubhujānt-
arālapramān. a m. chāyā labhyate tadā śa ̇nkunā keti chāyā labhyate/ (Shukla 1976 : 92.)