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## Details

Genre/Form: | Electronic books Observations |
---|---|

Additional Physical Format: | Print version: Pai, Venketeswara. Karaṇapaddhati of Putumana Somayājī. Singapore : Springer, 2018 (OCoLC)1004070967 |

Named Person: | Putumana Somayājī |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Venketeswara Pai; K Ramasubramanian; M S Sriram; M D Srinivas |

ISBN: | 9789811068140 9811068143 |

OCLC Number: | 1028979414 |

Description: | 1 online resource |

Contents: | Transliteration scheme -- Foreword -- About the authors -- Introduction -- Mean planets and the śakābdasamṣkāra -- Invocation -- Revolutions of the planets in a mahāyuga -- The number of solar, lunar and intercalary months in a mahāyuga -- The number of omitted tithis and sidereal days -- Revolutions of the planets in a kalpa -- Period elapsed in the present kalpa -- Obtaining the number of elapsed years since the beginning of the present kaliyuga -- Procedure for obtaining the aharganạ -- Technique for simplifying the mathematical operations -- Obtaining the mean longitudes of planets -- Śakābdasamṣkāra for mean planets -- Śakābdasamṣkāra for the number of days elapsed in the present year -- Obtaining the khanḍạs and the dhruvas -- Procedure for obtaining the khanḍạs -- Applying śakābdasamṣkāra to find the dhruvas -- An alternative method for obtaining the khanḍạs and dhruvas -- Speciality in the śakābdasamṣkāra for Rāhu -- The mean motion of the planets -- Śakābdasamṣkāra for the mean motions -- Obtaining the hāra and the dvitīyahāra of a gunạkāra -- Śakābdasamṣkāra for the number of revolutions of the planets -- Relation between the kaksỵās of planets -- Obtaining smaller gunạs and hāras -- Definition of the mahāgunạkāras and mahāhāras of the planets -- The process of apavartana for obtaining the drḍḥagunạhāras -- Mean longitudes of the planets from mahā-gunạkāras and mahāhāras -- Kalyādidhruvas of the planets -- The Vallyupasamḥāra technique -- Vallyupasamḥāra : Method I -- Vallyupasamḥāra : Method II -- Better approximations to the rate of motion : Dvitīya and trṭīya-hārakas -- The dvitīya-hāraka in terms of the remainders in the mutual division -- Gunạkāras and hāras for the difference in rates of motion -- Computation of the khanḍạ, dhruva, etc. of the Moon -- The alpa-gunạkāras and alpa-hārakas of the candra-kendra -- Obtaining the khanḍạs and dhruvas for the Moon -- Algorithm to determine the khanḍạ -- Dhruvas at the end of different hārakas and khanḍạs -- Obtaining the kendraphalas -- An alternative method for obtaining the kendraphalas -- Obtaining the dhruva-samṣkārahārakas -- Obtaining the khanḍạ using a specific hāraka -- A method for finding different khanḍạs -- Obtaining kendraphalas using a special hāraka -- The process of obtaining the multipliers -- The procedure for obtaining the candravākyas -- The relationship between the magnitude of hāraka and the proximity to sunrise -- Obtaining the yogodayāntaraprānạs and yogadhruvas -- General rule for conjunction of planets -- Obtaining the hārakas for the planets -- The mandakendrahārakas of the planets -- Obtaining the śīghrakendra-hārakas of the planets -- Obtaining the khanḍạs of the planets -- Convention in the choice of hāraka -- Procedure for obtaining manḍạlas and dhruvas given in the Vākyakaranạ -- Expression for the manḍạlas and dhruvas -- Rationale behind the expression for manḍạla -- Rationale behind the expression for dhruva -- A general prescription for obtaining śodhyas -- Obtaining the instant at which the śīghrocca-grahayoga occurs -- Another method to obtain the instant of the śīghrocca-grahayoga -- Procedure for obtaining the śodhyadina -- Finding the śodhyadhruva -- Another method to obtain the śodhyadina -- Obtaining the maudḥyāvasāna-khanḍạs -- Obtaining the hārakas mentioned in the Aganịta -- Obtaining the śodhyābdas of the planets -- Obtaining the adhimāsakhanḍạ -- Procedure for obtaining the grahanạhārakas -- Procedure for obtaining the grahanạkhanḍạs -- Examination of the revolution numbers etc. -- Procedure for correcting the revolutions of the planets in a kalpa -- Obtaining the kalpādidhruvas of the planets -- Saṅkramanạdhruva at the beginning of the kalpa -- Corrections to saṅkramanạ and graha-dhruvas -- Eliminating the kalpādidhruvas -- Obtaining zero saṅkramanạdhruva at the beginning of the kalpa -- Different measures of kalpa -- Different divisions of a kalpa -- The duration of krṭa and other yugas -- Time elapsed in the present kalpa -- Relation between the circumference and the diameter and computation of Rsines -- The Mādhava series -- Transformed Mādhava series -- An algebraic identity -- The Putumana Somayājī series -- Ratio of the circumference to the diameter -- Generation of the tabular Rsines from Rsin 30 and Rsin 45 -- Procedure for obtaining the Rsine and Rcosine of the half of any desired arc -- An alternative expression for the Rsine of half the desired arc -- Finding the Rsine and Rcosine of half of the arc from the bānạ -- Series expansion for the Rsine and Rcosine -- Computation of the Rsine and Rcosine values using the vākyas vidvān etc. -- Obtaining the tabular Rsines from the last and the penultimate Rsine -- Another recursive relation for obtaining the Rsines -- Computation of the arc from the corresponding chord -- Computation of the Rsine value of a small arc -- Finding the Rsines from a table of arc-sine differences for small arcs -- Obtaining the planetary longitudes -- The circumferences of the manda and śīghra epicycles of the planets -- Finding the true circumference of the epicycle -- Obtaining the mandaphalas of the planets -- Obtaining the śīghraphalas of the planets -- Obtaining the true bhujā and kotịphalas -- Application of the manda and the śīghraphalas -- Procedure for obtaining the antyaphala -- Obtaining the expression for the śīghraphala in terms of the antyaphala -- Expression for the śīghrakarnạ -- Expression for the śīghraphala in case I when the śīghrakendra is makarādi -- Expression for śīghraphala in case I when the śīghrakendra is karkyādi -- Expression for the śīghraphala in case II when the śīghrakendra is karkyādi -- Another method to obtain the śīghraphala -- An alternate method to obtain the śīghrakarnạ -- Obtaining the circumference of the śīghra epicycle Circumference at the beginning and the end of the odd quadrant -- Obtaining the vyastakarnạ of the Sun -- Finding the mean longitudes of the Sun from vyastakarnạ -- Finding the mandakarnạs of the Sun and the Moon from vyastakarnạ -- Finding the true physical distances of the Sun and the Moon from vyastakarnạ -- Obtaining the māsavākyas, saṅkrāntivākyas and naksạtravākyas -- The māsavākyas -- The saṅkrāntivākyas -- The naksạtravākyas -- The yogyādivākyas : true longitude of the Sun at any instant -- Obtaining the yogyādivākyas -- Finding the true longitude of the Sun from the yogyādivākyas -- Procedure for obtaining the manda-sphutạ -- Manda-sphutạ of exterior planets -- Manda-sphutạ of interior planets -- Obtaining the manda and śīghrakarnạs -- Obtaining the karnạs when the Rsine of the kendra is zero -- Earth-planet distance -- Yojanakarnạs (physical distance in yojanas) of the planets -- Obtaining the hypotenuse at the heliacal rising and setting -- Hypotenuse at heliacal rising and setting of the interior planets -- Latitude of a planet at heliacal rising and setting -- Diameter of the orbs of the Sun, Moon and the Earth in yojanas -- Gnomonic shadow -- Obtaining the Rsine and Rcosine of the latitude from the midday shadow -- Corrections to the Rsine and Rcosine of the latitude -- Obtaining mahāśaṅku and chāyā at any desired instant -- Obtaining the bhujākotịs of mahācchāyā -- Expression for the latitude in terms of the declination and mid-day shadow -- Expression for the Rsine of sum, difference of two arcs -- Another expression for the latitude and co-latitude -- Obtaining the svadeśahāraka -- Obtaining the krāntijya of Sun and the dyujyā -- Different methods of obtaining prānạkalāntaras -- The expression for the ascensional difference or carajyā -- Alternate expressions for the carajyā -- Obtaining the declination of the Moon -- Obtaining the mānyādijyās and the inādijyās -- Lambanahāraka and its application -- Obtaining the lambanajyās -- Obtaining the prītāng̣anādi-lambanajyās -- Obtaining the yogīraktādi-lambanajyās -- Obtaining the dimension of the disc of the planets in minutes -- Obtaining the dimension of the discs of the Sun and the Moon -- Obtaining the diameter of earth's shadow on the Moon's orbit -- Obtaining the bimbaliptās of the planets -- Ascendent at the meridian transit -- Defining kāla-lagna and obtaining the rising times of rāśis therefrom -- The longitudes and latitudes of the "junction stars" commencing with aśvinī -- Obtaining the true declinations of the stars -- Obtaining the madhyāhnakālalagna -- An alternate method for obtaining the madhyāhnakālalagna -- Yet another method for obtaining the madhyāhnakālalagna -- Obtaining the natakāla (RA) and the madhyāhnakālalagna -- The time elapsed in the current rāśi -- Obtaining the Right Ascension, etc. -- Importance of observations with instruments -- Obtaining the natakāla or the vāyukāla (RA) -- An alternate method for obtaining the vāyukāla -- Definition of the natakāla -- Obtaining the latitude from the vāyukāla -- Obtaining the longitude from the vāyukāla -- An alternative method for obtaining the longitude from the madhyāhnakālalagna -- Concluding remarks -- Appendices -- Vallyupasamḥāra and continued fractions -- Simple continued fraction and its convergents -- Properties of the convergents -- Remainder theorem of Karanạpaddhati -- Some applications of the Remainder theorem -- Epicycle and eccentric models for manda and śīghra corrections -- Equation of centre and the manda-sphutạ of planets -- Śīghraphala and the śīghra-sphutạ or the true longitude of planets -- Alpagunạkāras and alpahārakas of the planets -- An introduction to the Vākya method of Indian astronomy -- Introduction -- Vākyas related to the true motion of the Sun -- Vākyakaranạ method -- Vākyas pertaining to the Sun according to Karanạpaddhati -- Obtaining māsavākyas, saṅkrāntivākyas and naksạtravākyas -- The Māsavākyas -- The Saṅkrāntivākyas -- The Naksạtravākyas -- The Yogyādivākyas -- Finding the true longitude of the Sun from the yogyādivākyas -- Some observations -- Vākya method of finding the longitude of the Moon -- Vākya method for finding the true longitudes of the planets -- Manḍạlas, dhruvas and śodhyas -- The candravākyas of Vararuci and Mādhava -- Computing the candravākyas of Vararuci and Mādhava -- Error correction procedure for candravākyas -- Rationale behind the vākyaśodhana procedure -- Vararucivākyas -- Mādhava-vākyas -- Explanation of the vākyaśodhana expression for ... -- Table of candravākyas of Vararuci and Mādhava -- Table of computed candravākyas -- Literal meanings of selected vākyas -- The Manḍalas and dhruvas of the planets -- The gunạkāras and hārakas of the Aganịta system -- Glossary -- Bibliography -- Index -- Index of Half-verses. |

Series Title: | Sources and studies in the history of mathematics and physical sciences. |

Responsibility: | Venketeswara Pai, K. Ramasubramanian, M.S. Sriram, M.D. Srinivas. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"This useful work contains an English translation of the Karanapaddhati of Putumana Somayaji along with extensive explanatory notes. ... In sum, this solid piece of work, invaluable for those studying medieval Indian astronomy and mathematics, especially of Kerala school of astronomy and mathematics." (Ranjan Roy, Mathematical Reviews, October, 2018) Read more...

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