Kuttaka: Algebra (With Introduction, English Translation and Notes along with Illustrative Examples)

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Aryabhata-1 (499) has started a tradition of Including in astronomical treatises, separate and full chapters exclusively devoted to mathematics. Brahmagupta devoted two chapters to mathematics in his Brähmasphuta siddhanta. He has called the twelfth chapter as Gopita and the eighteenth chapter as Kuttoka. The present work Brahmagupta's, Kuttaka [Algebra], contains the Sanskrit text of Kuttakadhyaya of Brahmasphuta-siddhanta with Introduction, English translation exposition, notes, along with solution of illustrative examples according to the methods of Brahmagupta, illustrated by Prthüdakasvami, using modern symbols.

In Kuttaka (algebra), Brahmagupta made a considerable advance surpassing Diophantus (300 A.D.), the Greek algebraist, in the solution of equations involving more than one quantity, in the resolution of equations of a higher order than the second, and, especially, in the complete solution of indeterminate equations of the first degree and partial solution of the second. Brahmagupta also showed extreme Ingenuity in the application of algebra to astronomical investigations.

Engineer Venugopal D Heroor has done yeoman service by bringing out the present work. Readers will definitely find Er. Heroor's present book, Brahmagupta's Kuttaka [Algebra], both charming and exciting as well as enlightening.

Sri Venugopal D. Heroor, is an enthusiastic scholar of Bharatiya-Ganita (Ancient Indian Mathe matics). His books (i) The History of Mathematics & Mathematicians of India, (i) Bharatiya Trikopomiti Sástro (in both Kannada and English), (ii) Srimadbhásko- rdcaryo virocita Lilovati, and (iv) Bharatiya Bijogapita in Kannada, are fascinating, significant and definite contribution the study of the history of Indian mathematics.

His works: 'Development Of Combinatorics From The Pratyayas In Sanskrit Prosody in English, its Kannada version "Ankapása" Chandahsástradimda Vikolpa-Ganitada Vikäsa and its Hindi translation: Chandabśästra Se Vikalpa-Ganita Ka Vikasa are of inter-disciplinary nature.

He has brought out eighteen books related to Indian mathematics, which include Kannada and English transla-tions of: Gapitödhyaya and Kuttakadhyaya of Brahmagupta's Brahma-sphuta- siddhanta, Sridharācārya's Poți Gapita and Trilatika, Bhaskarácārya's Jyotpatti, Bijoganita, and Narayana Pandita's Bijaganitovatamsa. Other Kannada translation of Sanskrit works are Narayana Pandita's Gapita Kaumudi and Sripati's Gapitatilakam.

He has translated many articles and research papers and has also contributed original articles. He has conducted classes for teachers and research scholars; presented papers at various universities, National and International Seminars.

Brahmagupta the most celebrated mathematician born in 598 C.E composed Brahmasphuta siddhänta, his master piece, in šaka 550 or 628 C.E. at the age of thirty (30). Brahmagupta devoted two chapters to mathematics in his Brahmasphuta siddhanta, He has called the twelfth chapter as Gapita and the eighteenth chapter as Kuttaka (Algebra).

Gapitãddhyāya of Brahmasphuta siddhanta with Introduction, English translation and notes along with complete solution of Examples of Prthudaka Svami and others by me under the title Brahmaguptaganitam (ब्रह्मगुप्तगणितम् ) has already been published by Chinmaya International Foundation Shodha Sansthan, Adisankara Nilayam, Vliyanad, Ernakulam, KERALA in 2014.

According to the tradition of those times, "Ganita" (i.e., Pātīganita) includes matter pertaining to arithmetic problems on mixtures, plane figures, shadows, series, piles and excavations.

The Eighteenth Chapter of Brähmasphuta siddhanta, the Kuttakadhyaya (Algebra), contains solutions of the indeterminate equations of both first and second degree.

The name siddhanta has by derivation the meaning "established conclusion." But in reality the name Siddhanta Jyotisa means scientific astronomy giving accurate conclusions. In the discipline of astronomy, a few centuries immediately preceding and following the Christian era witnessed the advent of a class of texts called siddhantas, characterized by a better scientific approach and more comprehensive treatment.

The siddhanta astronomy adopted more sophisticated mathematics, incorporated the planets in the system, devised a system of coordinates for the determination of the periods of planetary revolutions and of the relative sizes of the Earth, the Sun and the Moon. The nakşatra system was dispensed with and replaced by the twelve signs of the zodiac. The mean longitudes were calculated from the number of days elapsed from the beginning of long periods of time called Kalpa or the Kaliyuga.

**Contents and Sample Pages**