ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

194 BRAHMAGUPTA AS AN ALGEBRAIST
flourished, seems then, from the concurrence of all these
arguments, to be satisfactorily settled as antecedent
to the earliest dawn of the culture of sciences among
the Arabs; and consequently establishes the fact, that
the Hindus were in possession of algebra before it was
known to the Arabians.
Brahmagupta's treatise, however, is not the earliest
work known to have been written on the same subject
by an Indian author. The most eminent scholiast of
Bhāskara II (Gaṇeśa) quotes a passage of Āryabhaṭa
specifying algebra under the designation of Bīja, and
making separate mention of Kuṭṭaka, which more par-
ticularly intends a problem subservient to the general
method of resolution of indeterminate problems of the
first degree : he is understood by another of Bhāskara's
commentators to be at the head of the elder writers, to
whom the text then under consideration adverts, as
having designated by the name of Madhyamāharaṇa
the resolution of affected quadratic equations by means
of the completion of the square. It is to be presumed,
therefore, that the treatise of Āryabhaṭa then extant,
did extend to quadratic equations in the determinate
analysis, and to indeterminate problems of the first
degree; if not to those of the second likewise, as most
probably it did.
This ancient astronomer and algebraist, so says Cole-
brooke, was anterior to both Varāhamihira and
Brahmagupta, being repeatedly named by the latter;
and the determination of the age when he flourished
is particularly interesting as his astronomical system,
though on some points agreeing, essentially dis-
agreed on others, with that which the Hindu astrono-
mers still maintain.
He, as Colebrooke says, is considered by the commen-
tators of the Sūryasiddhānta and Śiromaṇi, as the
earliest of uninspired and mere human writers on the
science of astronomy, as having introduced requisite
corrections into the system of Parāśara, from whom he
took the numbers for the planetary mean motions; as