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Genre/Form: Electronic books
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.

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