Bhāskara I

Bhāskara I was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.

Quotes

• Analysis (bija) is the intellect assisted by the various symbols that has now taken the name algebra (bijaganita).
  • (paraphrased for clarity)
  • Datta and Singh, History of Hindu Mathematics: A Source Book, Part II, 1962:quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• The science of calculations with unknowns is the source of the science of calculations with knowns.
  • Datta and Singh, History of Hindu Mathematics: A Source Book, Part II, 1962:quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• What the learned calculators (sankhyah) describe as the originator of intelligence, being directed by a wise being (satpurusha) and which alone is the primal cause (bija) of all knowns (vyakta), I venerate that invisible Supreme Being as well as that science of calculation with unknowns […] Since questions can scarcely be solved without the reasoning of algebra—not at all by those of dull perceptions—I shall speak, therefore, of the operations of analysis.
  • Datta and Singh, History of Hindu Mathematics: A Source Book, Part II, 1962:quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• I bow to Lord Shiva whose Lotus feet are rubbed by the foreheads of the Lotus-born (Brahma) and Krisha, to Him, a mere recollection of whose name is a source of fortune and end of misfortune for gods, demons, and men. (Ganitapada, Aryabhatiyabhashya) I bow to Shambhu, who is the cause of creation and destruction of the universe, (the different parts of ) whose body are the Sun etc., and who is as effulgent as tens of thousands of suns. (Ganitapada, Aryabhatiyabhashya). I bow to God Shiva, the support of the three worlds, who though inconceivable by nature, being mercy incarnate, assumedthe eight forms, viz. The Sun, the Moon, the Ether, Fire, Air, Water, Earth, and the Sacrificer, for the good of the entire world. (Kalakriyapada, Aryabhatiyabhashya)I bow to God Shambhu who bears on His forehead a digit of the moon illumining all directions by its rays, to Him whose feet are adored by the gods and who is a source of all knowledge. (Mahabhaskariya, opening verse)
  • quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• The line which passes through Lanka, Vatsyapura, Avanti, Sthánesvara, and the "abode of the gods" [= Mount Meru = north pole] is the prime meridian [desantara vidhàyani, lit. the prime meridian for longitude differences.]
  • Bhaskara, quoted in C. K. Raju. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe. Pearson Education India, 2007
  • The Indian prime meridian . Avanti is present-day Ujjain, and Sthane$vara is present-day Thanesar in Pakistan

• On any day calculate the longitude of the Sun and the Moon for sunrise or sunset without applying the longitude correction, and therefrom find the time (since sunrise or sunset), in ghatis, of rising or setting of the Moon; and having done this, note the corresponding time in ghatis from the water clock. From the difference, knowledgeable astronomers can calculate the local longitude in time.*?
  • Bhaskara, quoted in C. K. Raju. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe. Pearson Education India, 2007