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

RATIONAL SOLUTION 253
get the greater root as 3. Hence the statement for the com-
position is
m=11 l=1 g=3 i=-2
l=1 g=3 i=-2
Here m=multiplier (guṇaka or prakṛti), l=lesser root
(kaniṣṭha-mūla), g=greater root (jyeṣṭha-mūla) and i=interpola-
tor (kṣepa).
Here we have set down successively the lesser root, greater
root and interpolator, and below them again set down the same
(See Brahmagupta's Lemmas described by Bhāskara II). Now
proceeding as before we obtain the roots for the additive 4 :
l=6, g=20, (for) i=4.
Then by the rule :
"If the interpolator (of a varga-prakṛti or Square-nature)
divided by the square of an optional number be the
interpolator (of another Square-nature), then the two
roots (of the former) divided by that optional number
will be the roots (of the other). Or, if the interpolator
be multiplied, their roots should be multiplied."¹
are found the roots for the additive unity
l=3, g=10 (for) i=1.
Whence by the Principle of Composition of Equals, we get
the lesser and greater roots : l=60, g=199 (for) i= 1. In this
way an infinite number of roots can be deduced.
Alternative method:—Bhāskara II has given another method
for finding the two roots for the additive unity :
Or divide twice an optional number by the difference
between the square of that optional number and the
prakṛti. This (quotient) will be the lesser root (of a
Square-nature) when unity is the additive. From that
(follows) the greater root.²

1. इष्टवर्गहृतः क्षेपः क्षेपः स्यादिष्टभाजिते ।
   मूले ते स्तोऽथवा क्षेपः क्षुण्णः क्षुण्णे तदा पदे ॥
   Bījagaṇita II. 5.
2. Siddhānta-śekhara, XIV. 32.