Bhaskaracarya II, also spelled as Bhaskaracharya (1114-1185 AD), was a poet, grammarian, astronomer, physician, philosopher, and mathematician. Exceptionally gifted, he made significant contributions to all branches of mathematics. He possessed deep knowledge of Vedanga's plane geometry, Paninian grammar, the epic poetry of the pre-Christian era, and Indian mathematics as it had evolved since 400 AD. He skillfully addressed the gaps left by his predecessors in algebra and expanded its scope significantly. Bhaskarācārya advanced the mathematical tradition that began with Aryabhața I, shaping algebra for further development of astronomy.
Among his works in Sanskrit, Siddhanta-Širomani stands out as a major contribution. It consists of four parts: arithmetic (Lilavati), algebra (Bijaganita), planetary motion, and astronomy.
This book (a translated version of his algebra) presents various algebraic problems and the unique methods he employed to solve them, which are sure to fascinate readers. In brief, it includes discussions on algebraic surds, general and indeterminate equations of the first and second degrees (including those with more than two unknowns), and the product of unknown quantities. His application of zero in algebra, along with his groundbreaking formula for the sine function in planetary calculations, may be considered a precursor to the development of calculus.
KANTA PRASAD SINHA (b. December 1949) hails from West Bengal, India. He pursued higher studies in Chemistry, Economics, and Population Science, and served in the Indian Administrative Service until his retirement. A passionate student of the history of mathematics, he initially focused on ancient Greek mathematics and its associated historical and philosophical context, gradually expanding his interest to include the comparative development of number systems, geometry, astronomy, trigonometry, and algebra across civilizations.
Though self-taught in this field, he has written several research papers in both English and Bengali. He translated Līlāvati and Bijaganita (Algebra) into Bengali, which were subsequently published in Kolkata, West Bengal.
Indian mathematics emerged in the Indian subcontinent from 1000 BCE until the end of the seventeenth century. In the classical (400-1200 AD) and late medieval periods, many milestones were laid that helped shape Mathematics as a subject with its various branches.
Bhāskaracharya (also often as Bhāskarāchārya-II, Bhāskara-II or Bhaskara) of the early twelfth century was a doyen among the classical masters who wrote several important treatises. Bījaganita (Algebra) is one of them. Rules and Examples were all composed in verses in Sanskrit with a great economy of words. Annotation of such verses by himself has also been given. The distinguished commentators followed him.
Bījaganita (Algebra) was translated into English in the early nineteenth Century. In the recent past, the most advanced presentation has been done by Takao Hayashi. Despite that, it is felt needed this book requires more accessible to readers who have a desire to know how the branches of mathematics, especially algebra flourished in the Indian subcontinent ahead of other civilisations.
With the main text of English translation detailing explanation of Rules and Examples (solutions to problems), a brief account of the development of algebra across the civilisations in the ancient and medieval periods and its development in Greece, Arabs and India as observed by Edward Strachey and TH Colebrooke are placed. The purpose of such additions is to give the readers a balanced view of India's standing in the periods mentioned.
I have translated Līlāvati and Bījaganita into Bengali. Those works inspired me to translate Bījaganita into English.
During such endeavour, I got immense support from my wife, Nandita Sinha and daughter, Dr Rajeshwari Sinha
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