000			nam a22 4500
999			_c86858 _d86858
008			190629b xxu||||| |||| 00| 0 eng d
020			_a9789386278651
082			_a520.954 _bPai
100			_aPai, Venketeswara
245			_aKaranapaddhati of putumana somayaji _b: Culture and history of mathematics - Vol.9
260			_aNew Delhi _bHindustan Book Agency _c2017
300			_axlvi; 450p. _bhb _c25x16cm
440			_aCulture and history of mathematics _n;12 Volumes _v; Vol.9
520			_awith translation and explanatory notes This book is an important text of the Kerala school of astronomy and mathematics, probably composed in the 16th century. In the Indian astronomical tradition, the karaṇa texts are essentially computational manuals, and they often display a high level of ingenuity in coming up with simplified algorithms for computing planetary longitudes and other related quantities. Karaṇapaddhati, however, is not a karaṇa text. Rather, it discusses the paddhati or the rationale for arriving at suitable algorithms that are needed while preparing a karaṇa text for a given epoch. Thus the work is addressed not to the almanac maker but to the manual maker. Karaṇapaddhati presents the theoretical basis for the vākya system, where the true longitudes of the planet are calculated directly by making use of certain auxiliary notions such as the khaṇḍa, maṇḍala and dhruva along with tabulated values of changes in the true longitude over certain regular intervals which are expressed in the form of vākyas or mnemonic phrases. The text also discusses the method of vallyupasaṃhāra, which is essentially a technique of continued fraction expansion for obtaining optimal approximations to the rates of motion of planets and their anomalies, involving ratios of smaller numbers. It also presents a new fast convergent series for π which is not mentioned in the earlier works of the Kerala school. As this is a unique text presenting the rationale behind the vākya system and the computational procedures used in the karaṇa texts, it would serve as a useful companion for all those interested in the history of astronomy. The authors have provided a translation of the text followed by detailed notes which explain all the computational procedures, along with their rationale, by means of diagrams and equations.
650			_aMathematics
700			_aRamasubramanian, K.
700			_aSriram, M.S.
700			_aSrinivas, M.D.
942			_cBK