Algebra

Algebra is one of the broad areas of Mathematics. The Hindu name for the science of algebra is bijaganita. Bija means "element" or "analysis" and ganita means " the science of calculation". Bijaganita literally means "science of calculation with elements or the science of analytical calculation.

Brahmagupta (628) calls algebra as Kuttaka-ganita or Kuttaka. Kuttaka means pulveriser. Algebra is also called as avyakta-ganita or the science of calculation with unknowns (avyakta means unknown) in contrast to the name vyakta-ganita the science of calculation with knowns (vyakta means known) for arithmetic including geometry and mensuration.

Definition

Bhaskara II (1150) has defined Algebra as "Analysis (bija) is certainly the innate intellect assisted by the various symbols (varna), which, for the instruction of duller intellects, has been expounded by the ancient sages who enlighten mathematicians as the sun irradiates the lotus; that has now taken the name algebra (bijaganita)".

That algebraic analysis' requires keen intelligence and sagacity has been observed by him on more than one occasion.

"Neither does analysis consist in symbols, nor are there different kinds of analyses; sagacity alone is analysis, for wide is imagination. "Analysis is certainly clear intelligence". "Or intelligence alone is analysis".In answer to the question, "if (unknown quantities) are to be discovered by intelligence alone what then is the need of analysis ?" he says, "Because intelligence is certainly the real analysis; symbols are its helps. The innate intelligence which has been expressed for the duller intellects by the ancient sages, who enlighten mathematicians as the sun irradiates the lotus, with the help of various symbols, has now obtained the name of algebra.

Thus, according to Bhaskara II, algebra may be defined as the science which treats of numbers expressed by means of symbols, and in which there is scope and primary need for intelligent artifices and ingenious devices.

Origin

The .origin of Hindu algebra can be definitely traced back to the period of the Sulba (800-500 B.C.) and the Brahmana (c. 2000

B.C.).

Technical Terms

Unknown Quantiy

The unknown quantity was called in the Sthananga-sutra (before 300 B.C.) yavat-tavat (as many as or so much as, meaning an arbitrary quantity). In the so-called Bakhshali treatise, it was called yadrccha, vancha or kamika (any desired quantity).This term was originally connected with the Rule of False Position. Aryabhata I (499) calls the unknown quantity as gulika (shot). This term strongly leads one to suspect that the shot was probably then used to represent the unknown. From the beginning of the seventh century the Hindu algebraists are found to have more commonly employed the term avyakta (unknown).

Equation

The equation is called by Brahmagupta (628) sama-karana or sami-karana (making equal) or more simply sama (equation). Prthudakasvami (860) employs also the term samya (equality or equation); and Sripati (1039) sadrsi-karana (making similar). Narayana (1350) uses the terms sami-karana, samya and samatva (equality). An equation has always two paksa (side).

References

Citations

1.History of Hindu Mathematics by Bibhutibhusan Datta and Avadesh Narayan Singh