LEADER 04676nam 22005775 450 001 9910392743203321 005 20200630104819.0 010 $a981-10-6814-3 024 7 $a10.1007/978-981-10-6814-0 035 $a(CKB)4100000002892602 035 $a(MiAaPQ)EBC5471177 035 $a(DE-He213)978-981-10-6814-0 035 $a(PPN)225548496 035 $a(EXLCZ)994100000002892602 100 $a20180314d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKara?apaddhati of Putumana Somay?j? /$fby Venketeswara Pai, K. Ramasubramanian, M.S. Sriram, M.D. Srinivas 205 $a1st ed. 2018. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (486 pages) 225 1 $aSources and Studies in the History of Mathematics and Physical Sciences,$x2196-8810 311 $a981-10-6813-5 320 $aIncludes bibliographical references and index. 327 $aChapter 1. Mean planets and the ?ak?bdasa?sk?ra -- Chapter 2. Obtaining smaller gu?as and h?ras -- Chapter 3. Computation of the kha??a, dhruva, etc. of the Moon -- Chapter 4. Obtaining the h?rakas for the planets -- Chapter 5. Examination of the revolution numbers etc -- Chapter 6. Relation between the circumference and the diameter and computation of Rsines -- Chapter 7. Obtaining the planetary longitudes -- Chapter 8. Gnomonic shadow -- Chapter 9. Ascendent at the meridian transit -- Chapter 10. Obtaining the Right Ascension, etc. 330 $aKara?apaddhati of Putumana Somay?j? is an important text of the Kerala School of astronomy and mathematics, probably composed in the 16th century. In the Indian astronomical tradition, the kara?a texts are essentially computational manuals and they often display a high level of ingenuity in coming up with simplified algorithms for computing planetary longitudes and other related quantities. Kara?apaddhati, however, is not a kara?a text. Rather, it discusses the paddhati or the rationale for arriving at suitable algorithms that are needed while preparing a kara?a text for a given epoch. Thus the work is addressed not to the almanac maker but to the manual maker. Kara?apaddhati presents the theoretical basis for the v?kya system, where the true longitudes of the planet are calculated directly by making use of certain auxiliary notions such as the kha??a, ma??ala and dhruva along with tabulated values of changes in the true longitude over certain regular intervals which are expressed in the form v?kyas or mnemonic phrases. The text also discusses the method of vallyupasa?h?ra which is essentially a technique of continued fraction expansion for obtaining optimal approximations to the rates of motion of planets and their anomalies, involving ratios of smaller numbers. It also presents a new fast convergent series for ? which is not mentioned in the earlier works of the Kerala School. As this is a unique text presenting the rationale behind the v?kya system and the computational procedures used in the kara?a texts, it would serve as a useful companion for all those interested in the history of astronomy. The authors have provided a translation of the text followed by detailed notes which explain all the computational procedures, along with their rationale, by means of diagrams and equations. 410 0$aSources and Studies in the History of Mathematics and Physical Sciences,$x2196-8810 606 $aMathematics 606 $aHistory 606 $aObservations, Astronomical 606 $aAstronomy?Observations 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aAstronomy, Observations and Techniques$3https://scigraph.springernature.com/ontologies/product-market-codes/P22014 615 0$aMathematics. 615 0$aHistory. 615 0$aObservations, Astronomical. 615 0$aAstronomy?Observations. 615 14$aHistory of Mathematical Sciences. 615 24$aAstronomy, Observations and Techniques. 676 $a520.954 700 $aPai$b Venketeswara$4aut$4http://id.loc.gov/vocabulary/relators/aut$0912807 702 $aRamasubramanian$b K$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSriram$b M.S$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSrinivas$b M.D$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910392743203321 996 $aKara?apaddhati of Putumana Somay?j?$92044216 997 $aUNINA