History of Hindu Mathematics: A Source Book v2.c17.s14.50

v2.c17.s14.50

**Principle of Composition.** The above results are called by the technical name, *Bhâvanâ* (demonstration or proof, meaning anything demonstrated or proved, hence theorem, lemma; the word also means composition or combination). They are further distinguished as *Samâsa Bhâvanâ* (Addition Lemma or Additive Composition) and *Antara Bhâvanâ* (Subtraction Lemma or Subtractive Composition). Again, when the *Bhâvanâ* is made with two equal sets of roots and interpolators, it is called *Tulya Bhâvanâ* (Composition of Equals) and when with two unequal sets of values, *Atulya Bhâvanâ* (Composition of Unequals). Kṛṣṇa has observed that when it is desired to derive roots of a Square-nature, larger in value, one should have recourse to the Addition Lemma and for smaller roots one should use the Subtraction Lemma.