Bija Ganita; Or, the Algebra of the Hindus
Bija Ganita; Or, the Algebra of the Hindus

Author: Bhascara Acharya

Publisher: Cambridge University Press

Published: 2013-02-28

Total Pages: 133

ISBN-13: 1108056016

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An important twelfth-century treatise on algebra by medieval India's greatest mathematician, first published in English translation in 1813.

Līlāvatī of Bhāskarācārya
Līlāvatī of Bhāskarācārya

Author: Bhāskarācārya

Publisher: Motilal Banarsidass Publ.

Published: 2001

Total Pages: 240

ISBN-13: 9788120814202

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In 1150 AD, Bhaskaracarya (b. 1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of his larger work called Siddhanta Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics. Lilavati has been used as a standard textbook for about 800 years. This lucid, scholarly and literary presentation has been translated into several languages of the world. Bhaskaracarya himself never gave any derivations of his formulae. N.H. Phadke (1902-1973) worked hard to construct proofs of several mathematical methods and formulae given in original Lilavati. The present work is an enlargement of his Marathi work and attempts a thorough mathematical explanation of definitions, formulae, short cuts and methodology as intended by Bhaskara. Stitches are followed by literal translations so that the reader can enjoy and appreciate the beauty of accurate and musical presentation in Lilavati. The book is useful to school going children, sophomores, teachers, scholars, historians and those working for cause of mathematics.

Geometry in Ancient and Medieval India
Geometry in Ancient and Medieval India

Author: T. A. Sarasvati Amma

Publisher: Motilal Banarsidass Publ.

Published: 1999

Total Pages: 304

ISBN-13: 9788120813441

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This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.

The History of Mathematical Proof in Ancient Traditions
The History of Mathematical Proof in Ancient Traditions

Author: Karine Chemla

Publisher: Cambridge University Press

Published: 2012-07-05

Total Pages: 522

ISBN-13: 1139510584

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This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

Lilawati: Or A Treatise on Arithmetic and Geometry
Lilawati: Or A Treatise on Arithmetic and Geometry

Author: Bhāskarācārya

Publisher:

Published: 1816

Total Pages: 242

ISBN-13:

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An important mathematician and astronomer in medieval India, Bhascara Acharya (1114-85) wrote treatises on arithmetic, algebra, geometry and astronomy. He is also believed to have been head of the astronomical observatory at Ujjain, which was the leading centre of mathematical sciences in India. Forming part of his Sanskrit magnum opus Siddhānta Shiromani, the present work is his treatise on arithmetic, including coverage of geometry. It was first published in English in 1816 after being translated by the East India Company surgeon John Taylor (d.1821). Used as a textbook in India for centuries, it provides the basic mathematics needed for astronomy. Topics covered include arithmetical terms, plane geometry, solid geometry and indeterminate equations. Of enduring interest in the history of mathematics, this work also contains Bhascara's pictorial proof of Pythagoras' theorem.