## Geometry in Ancient and Medieval IndiaThis 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. |

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### Contents

1 | |

14 | |

Early Jaina Geometry | 61 |

The Trapezium | 70 |

The Quadrilateral | 81 |

The Triangle | 117 |

I The Circle | 154 |

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### Common terms and phrases

A. B. Ganitapada abadhas ABCD algebraical altitude Apastamba Aryabhata II Aryabhata School astronomical base Baudhayana Bhaskara Bhaskara II bhuja Brahmagupta's breadth calculated chord circle circum-radius circumference combined commentary construction cord corner cube of side cyclic quadrilateral Datta derived diagonal diameter divided expression face figure flanks formula frustum geometrical given gives gnomon half the sum height Hence hypotenuse Indian mathematics isosceles trapezium isosceles triangle Jaina jatya joined karna Katyayana koti Kriyakramakari length Mahavira mathe mathematicians method middle point multiplied Narayana Pandita Nilakantha perpendicular polygon prakramas prauga proof pyramid quotient radius rational right triangles rational triangles rect rectangle rectangular rhombus right angle Sanskrit segment shadow sides equal similar triangles Similarly sine-chord sphere square of side square root sredhikfetras Sulba Sulbasutras surface area sutra theorem trapezia Trilokasara unit vedi Vedic verse vertical volume word

### Popular passages

Page 3 - Indian aim was not to build up an edifice of geometry on a few self-evident axioms, but to convince the intelligent student of the validity of the theorem so that...