Yuktibhāṣā

[2] The treatise, written in Malayalam, is a consolidation of the discoveries by Madhava of Sangamagrama, Nilakantha Somayaji, Parameshvara, Jyeshtadeva, Achyuta Pisharati, and other astronomer-mathematicians of the Kerala school.

[2] It also exists in a Sanskrit version, with unclear author and date, composed as a rough translation of the Malayalam original.

[5] It is considered an early text to give some ideas of calculus like Taylor and infinite series of some trigonometric functions, predating Newton and Leibniz by two centuries.

For example, both Oxford University and the Royal Society of Great Britain have given attribution to pioneering mathematical theorems of Indian origin that predate their Western counterparts.

[2] Beyond this, the continuous text does not have any further division into subjects or topics, so published editions divide the work into chapters based on editorial judgment.

Apart from these, the Yuktibhāṣā contains many elementary and complex mathematical topics, including,[citation needed] Chapters eight to seventeen deal with subjects of astronomy: planetary orbits, celestial spheres, ascension, declination, directions and shadows, spherical triangles, ellipses, and parallax correction.

[12] The topics covered in the eight chapters are computation of mean and true longitudes of planets, Earth and celestial spheres, fifteen problems relating to ascension, declination, longitude, etc., determination of time, place, direction, etc., from gnomonic shadow, eclipses, Vyatipata (when the sun and moon have the same declination), visibility correction for planets and phases of the moon.

[10] Specifically,[1]: xxxviii The importance of Yuktibhāṣā was brought to the attention of modern scholarship by C. M. Whish in 1832 through a paper published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland.

[4] The mathematics part of the text, along with notes in Malayalam, was first published in 1948 by Rama Varma Thampuran and Akhileswara Aiyar.

[2][13] The first critical edition of the entire Malayalam text, alongside an English translation and detailed explanatory notes, was published in two volumes by Springer[14] in 2008.

[1] A third volume, containing a critical edition of the Sanskrit Ganitayuktibhasa, was published by the Indian Institute of Advanced Study, Shimla in 2009.

Pages from the Yuktibhasa
Explanation of the sine rule in Yuktibhāṣā
The first verse from Yukti bhasha in Malayalam language