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South Asia (6th–10th c.)Science and technology

Mahavira writes the Ganitasarasangraha

Around 850 the Jain mathematician Mahavira, who enjoyed the patronage of the Rashtrakuta king Amoghavarsha I, wrote the Ganitasarasangraha (‘Compendium of the Essence of Mathematics’), one of the earliest surviving Indian treatises devoted to mathematics alone rather than forming part of an astronomical work. Its nine chapters cover arithmetic and fractions, the rule of three, algebraic problems and the measurement of areas, excavations and shadows.

Date
c. 850year known, approximate
Place
Manyakheta (Malkhed), the Rashtrakuta capitalapproximate locationtoday: Malkhed, Kalaburagi district, Karnataka, India · South Asia
Participants
Mahavira (mathematician), Amoghavarsha I
Threads
South Asia (6th–10th c.)
Also known as
Ganitasarasangraha; Gaṇita-sāra-saṅgraha; Ganita Sara Samgraha; Mahaviracharya; Ганита-сара-санграха; Махавирачарья

After two verses of homage to the Jina Mahavira, the treatise praises in six verses a king who ‘propounds the logic of syadvada’ and is known as Amoghavarsha Nripatunga, and wishes his rule prosperity; since Amoghavarsha reigned from 814/815 to 877/878, the work is placed in the middle of the 9th century. Mahavira then extols the science of calculation as useful in worldly and religious affairs, in love, wealth, music and drama, cookery, medicine, architecture, prosody, poetics, logic and grammar, and in the movements of the sun and the other heavenly bodies.

The nine chapters deal with terminology, arithmetical operations, fractions, miscellaneous problems, the rule of three, mixed problems, the measurement of areas, calculations concerning excavations, and shadows. The work gives systematic rules for breaking fractions into sums of unit fractions, treats permutations and combinations — a favourite topic of Jain mathematics — and gives an approximate rule for the perimeter and area of an ellipse. M. Rangacarya, who translated it into English in 1912, thought that Mahavira knew the work of Brahmagupta and tried to improve on it, with a simpler classification of operations, fuller rules and many more examples. The book was widely known in South India and was rendered into Telugu verse by Pavuluri Mallana, probably in the 11th century.

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Sources

  1. Wikipedia (English): Gaṇita-sāra-saṅgraha
  2. Wikipedia (English): Mahāvīra (mathematician)
  3. Wikipedia (English): Amoghavarsha
  4. MacTutor History of Mathematics: Mahavira
  5. The Ganita-sara-sangraha of Mahaviracarya / With English translation and notes by M. Rangacarya. — Madras: Government Press, 1912
  6. Wikidata: Q12423185