Gaṇita-yukti-bhāṣā (Rationales in Mathematical Astronomy) of Jyeṣṭhadeva Volume I: Mathematics

Title

Gaṇita-yukti-bhāṣā (Rationales in Mathematical Astronomy) of Jyeṣṭhadeva
Volume I: Mathematics

Language of Original Text

Malayalam

list of authors

Jyeṣṭhadeva

list of editors

K. V. Sarma

K. Ramasubramanian

M. D. Srinivas

M. S. Sriram

Subject

Mathematics

Value Annotations

Description

Kerala School

Language of Edited Volume

English

Publisher

Hindustan Book Agency

volume

1

issue

4

isbn

978-81-85931-81-4

Date Issued

2008

Source

Malayalam Version of Yukti-bhāṣā:

A. The edition of Part I alone of the work covering general mathematics, issued under the title Yukti-bhāṣā: Onnāmbhāgam: Sāmānyagaṇitam, edited
by Rāma Varma Maru Thampuran and A. R. Akhileswarayyar, (Mangalodayam Ltd., Trissur, M.E. 1123 : A.D. 1948, pp. 394), now out of print.

B. Ms. No. 486 of the Sree Sarada Education Society Research Centre, containing both Parts I and II of the work.

C. A well-preserved palm-Ieaf manuscript belonging to the Sree Sarada Education Society Research Centre, in 199 folios.

D. Ms. No. 12513 of the Oriental Research Institute and Manuscripts Library of the Kerala University, Trivandrum.

E. Ms. No. T. 90 of the Malayälam Section of the Oriental Research Institute and Manuscripts Library of the Kerala University, Trivandrum.

F. Ms. No. D. 332 of the Malayālam Section of the Madras Govt. Oriental Manuscripts Library, as printed by the Library issued under the title Gaṇita-yukti-bhāṣā T. Chandrasekharan (Madras, 1953).

G. A paper transcript of Part II of the work preserved in the Sree Sarada Education Society Research Centre, Madras.

H. A copy of Ch. VIII alone of the work written in pencil on foolscap paper presented to the present Editor by H. H. Rāma Varma Maru Thampuran of the Cochin royal family.

Sanskrit version of Yukti-bhāṣā: Paper transcript No. R. 4382 of the Madras Govt. Oriental Manuscripts
Library. It had been copied from a palm-leaf manuscript with the Raja of Chirakkal (Malabar) in 1923-24 by N. Parthasarathi Acharya.

Value Annotations

Description

While the author of Yukti-bhāṣā has obviously composed the work only in
Malayālam, there is available a Sanskrit version as well of the work.

abstract

Gaṇita-yukti-bhāṣā (Rationales in Mathematical Astronomy) of Jyeṣṭhadeva (c.1530) is a seminal text of the Kerala School of Astronomy. It is composed in the Malayalam language and presents detailed yuktis or explanations and demonstrations for the results and processes of Mathematical Astronomy. The text comprising fifteen chapters is naturally divided into two parts, Mathematics and Astronomy, and purports to give an exposition of the techniques and theories employed in the computation of planetary motions as set forth in the great treatise Tantrasaṅgraha (c.1500) of Nīlakaṇṭha Somayāji. Even though the importance of Gaņita-yukti-bhāṣā was brought to the notice of modern scholarship by C.M. Whish in 1830s, a critical edition of the entire Malayalam text is being brought out for the first time along with an English translation and detailed explanatory notes.

The Mathematics part is divided into seven chapters and the topics covered are Parikarma (logistics), Daśapraśna (ten problems), Bhinnagaņita (fractions), Trairāśika (rule of three), Kuțțākāra (linear indeterminate equations), Paridhi and Vyāsa (infinite series and approximations for the ratio of the circumference and diameter of a circle) and Jyānayana (infinite series and approximations for sines). A distinguishing feature of the work is that it presents detailed demonstrations of the famous results attributed to Mādhava (c.1340-1420), such as the infinite series for π, the arc-tangent and the sine functions, the estimation of correction terms and their use in the generation of faster convergent series. Demonstrations are also presented for some of the classical results of Āryabhața (c.499) on Kuṭṭākāra or the process of solution of linear indeterminate equations, of Brahmagupta (c.628) on the diagonals and the area of a cyclic quadrilateral and of Bhāskara (c.1150) on the surface area and volume of a sphere.
The work should be of interest to the historians of Mathematics and Astronomy and to philosophers of Science.