Ganitatilaka (Sanskrit text and English introduction)
by H. R. Kapadia | 1937 | 49,274 words
The Sanskrit text of the Ganitatilaka with an English introduction and Appendices. Besides the critically-edited text, this edition also includes the commentary of Simhatilaka Suri. The Ganitatilaka is an 11th-century Indian mathematical text composed entirely of Sanskrit verses and authored by astronomer-mathematician Shripati. The text itself dea...
Part 6 - Notational places (ankasthanas) in Jainism
In Ganitasarasangraha we come across the following names of the twenty-four notational places commencing with the unit, each of which is 10 times the preceding :- ) Eka (unit), (2) Dashan (ten), (3) S'ata (hundred), (4) Sahasra (thousand), (5) Dashasahasra (ten thousand), (6) Laksa (lac), (7) Dashalaksa (ten lac, million), (8) Koti
(crore), (9) Dashakoti (ten crore), (10) S'atakoti (hundred crore), (11) Arbuda (thousand crore), (12) Nyarbuda (ten thousand crore), (13) Kharva (billion), (14) Mahakharva, (15) Padma, (16) Mahapadma, (17) Ksoni, (18) Mahaksoni, (19) S'ankha (million billion), (20) Mahas'ankha (trillion), (21) Ksiti, (22) Mahaksiti, (23) Ksobha and (24) Mahaksobha (10ª3). If we however refer to Sthananga (II, 4, 95), Jambudvipaprajnapti (sutra 18), Suryaprajnapti ( ), Anuyogadvara (sutra 137), Jivasamasa (v. 113-115) etc., we find names for some of the notational places3 up to the 194 th as under:- (1) Puvvanga (Purvanga), (2) Puvva (Purva), (3) Tudiyanga (Trutitanga), (4) Tudiya (Trutita), (5) Adadanga (Adadanga), (6) Adada (Adada), (7) Avavanga (Avavanga), (8) Avava (Avava), (9) Huluanga (Huhukanga), (10) Huhua (Huhuka), (11) Uppalanga (Utpalanga), (12) Uppala (Utpala), (13) Paumanga (Padmanga), (14) Pauma (Padma), (15) Nalinanga (Nalinanga), (16) Nalina (Nalina), (17) Acchaniuranga (Arthanipuranga), (18) Acchaniura (Arthanipura), (19) Ayuanga (Ayutanga), (20) Ayua (Ayuta), (21) Nayuanga (Nayutanga), (22) Nayua (Nayuta), (23) Payutanga (Prayutanga), (24) Payuta (Prayuta), (25) Culiyanga (Culikanga), (26) Culiya (Culika), (27) Sisapaheliyanga (S'irsaprahelikanga) and (28) Sisapaheliya (S'irsaprahelika).2 Here Purva stands for 75600000000000 years. This is indicated in the following verse quoted by Abhayadeva Suri in his commentary (p. 87") to Sthananga (s. 95) :- "puvvassa u parimanam sayarim khalu homti kodilakukhao | chappanam ca sahassa boddhavva vasakodinam || "" 1 Strictly speaking, these are names for different measures for a number of years. 2 While commenting upon Samavaya (sutra 84), Abhayadeva Suri quotes the following verses:- " puvvatudiyadadavavahuhuya taha uppale ya paume ya | nalicchiniura aue naue paue ya nayavvo || 1 || culiya sisa paheliya coddasa nama u amgasamjutta | atthavisam thana caunauyam hoi thanasayam || 2 || " 3 Sanskrit rendering:- purvasya tu parimanam saptatih khalu bhavanti kotilaksah | patpancasacca sahasrani boddhavyani varsakotinam ||
The Purva as well as each one of the succeeding notational places up to Sirsaprahelika is 84 lacs times the immediately preceeding one, S'irsaprahelika being hence equal to (84 lacs) 2 years. This is suggested in the following karanagatha quoted in this very commentary on p. 87°:- 28 "icchiyathanena gunam panasunnam caurasitigunitam ca | kanam taivare puvamgaina muna samkham || " This subject about notational places is treated by Umasvati, too, in his svopajna bhasya of Tattvarthadhigamasutra (IV, 15, p. 292). He mentions there the names as under:- (1) Ayuta, (2) Kamala, (3) Nalina, (4) Kumuda, (5) Tutya, (6) Adada, (7) Avava, (8) Haha, and (9) Huhu. It may be noted that this enumeration of these notational places does not tally with the one mentioned above. This discordance is noted by Siddhasena Gani while commenting upon this bhasya. There he makes two observations (on pp. 293-294) as under:- (1) This is not the order as found in the Agamas like Suryaprajnapti. (2) It only refers to a few notational places, the complete list being as under:- (1) Tutyanga, (2) Tulika, (3) Adadanga, (4) Adada, (5) Avavanga, (6) Avava, (7) Huhvanga, (8) Huhuka, (9) Utpalanga, (10) Utpala, (11) Padmanga, (12) Padma, (13) Nalinanga, (14) Nalina, (15) Arthaniyuranga, (16) Arthaniyura, (17) Culikanga, (18) Culika, (19) S'irsaprahelikanga and (20) S'irsaprahelika. From this list it appears that either some names have been left out in the Mss. utilized by me for the printed edition or that Siddhasena Gani has dropped six names from Ayuta to Prayuta. Jyotiskarandaka strikes altogether a different note in 1 This remark is made in Samavaya as under :- "pugvaiyanam sisapaheliyapajjavasananam sankanadvanamtaranam corasie gunakare pa0 " 2 Sanskrit rendering:- icchitasthanena gunyam sunyapancakam caturasitigunitam ca | krtva tativaran purvangadinam janihi sakhyam ||
this connection; for, according to it (v. 64-71) S'irsaprahelika is the name of the 250 th place and not of the 194 th place. Moreover, even the names of most of the notational places after Purva are different from those which are mentioned above and which are recorded in works codified at the Mathura council. In order that this remark may be substantiated, the names are mentioned as below:- (1) Puvva (Purva), (2) Layanga (Latanga), (3) Layu (Lata), (4) Mahalayanga (Mahalatanga), (5) Mahalaya (Mahalata), (6) Nalinanga (Nalinanga), (7) Nalina (Nalina), (8) Mahanalinanga (Mahanalinanga), (9) Mahanalina (Mahanalina), (10) Paumanga (Padmanga), (11) Pauma (Padma), (12) Mahapaumanga (Mahapadmanga), (13) Mahapauma (Mahapadma), (14) Kamalanga (Kamalanga), (15) Kamala (Kamala), (16) Mahakamalanga (Mahakamalanga), (17) Mahakamala (Mahakamala), (18) Kumuyanga (Kumudanga), (19) Kumuya (Kumuda), (20) Mahakumuyanga (Mahakumudanga), (21) Mahakumuya (Mahakumuda), (22) Tu- diyanga (Trutitanga), (23) Tudiya (Trutita), (24) Mahatudiyanga (Mahatrutitanga), (25) Mahatudiya (Mahatrutita), (26) Adadanga (Adadanga), (27) Adada (Adada), (28) Mahadadanga (Mahadadanga), (29) Mahadada (Mahadada), (30) Uhanga (Uhanga), (31) Uha (Uha), (32) Mahahanga (Mahohanga), (33) Mahauha (Mahoha), (34) Sisapaheliyanga (S'irsaprahelikanga) and (35) Sisapaheliya (S'irsaprahelika). 28 Each of these represents a number equal to 84 lacs times the preceding; consequently Sirsaprahelika stands for (84 lacs) 38 years, and not for (84 lacs) 23 years. Expressed in numbers it is equal to 18795517955011259541900969981343077- 0797465494261977476572573467186816 x 10130 years." Tattvartharajavartika (p. 149), a lucid commentary of Akalanka on Tattvarthadhigamasutra (III. 382) furnishes us with the following names, each indicating a number equal to 84 lacs times the preceeding one:- 1 See Mahopadhyaya Vinayavijaya Gani's Lokaprakasa (pt. III, Kalaloka, pp. 410), the encyclopadia of Jainism. 2 This is according to the Digambara school; for, according to the S'vetumbaras the number of this sutra is 17 th.
(1) Purvanga, (2) Purva, (3) Nayutanga, (4) Nayuta, (5) Kumudanga, (6) Kumuda, (7) Padmanga, (8) Padma, (9) Nalinanga, (10) Nalina, (11) Kamalanga, (12) Kamala, (13) Tutyanga, (14) Tutya, (15) Atatanga, (16) Atata, (17) Amamanga, (18) Amama, (19) Huhuanga, (20) Huhu, (21) Latanga, (22) Lata and (23) Mahalata. Some names seem to be omitted in this printed edition. For, a Digambara work Trailokyadipaka of which there is a MS. No. 603 of the Govt. Collection of 1875- 76 deposited at the Bhandarkar O. R. Institute, we have the following names after Amama:- hahahuhuamga, hahahuhu, vidyullatamga, vidyullata, latamga, lata, mahalatamga, mahalata, sirsaprakampita, hastaprahelika and acalatmaka . In Abhidharmakosha III, 94 of Vasubandhu we have as the first word of this verse. While explaining it Tripitakacarya Rahula Sankrtyayana makes the following observation in his commentary Nalandika by name:- 66 " kalpanam asamkhyatraye sadhanasamcayena ( paramitapurtya ) buddhatvam bhavati | asamkhya samkhya ca dasottaravrddhya sasti (sti ) sthanam yavath- - dasa - sata - sahasra - prabheda ( 10,000 ) - laksa -'tilaksa-koti- madhya- S -sga- mahayuta- nayuta - mahanayuta prayuta-mahaprayuta-kamkara - mahakamkara - bimbara - mahabimbara- ksobhya - mahaksobhya - vivaha-ma0 - utsamga-ma0 - vahana-ma0 - titibha - ma0 - hetu-ma0- karabha0-ma0 - indra-ma0 - sampata (samapta ) - ma0 - gati - ma0 - nimbarajo-ma0 - mudra -ma0- bala - ma0 - samjna - ma0 - vibhuta-ma0 - balaksa-ma0 - asamkhyeti | atra madhye'stau sthanani gu faegana i ad afg:(fg:) farcaisacara 1" Before another topic is taken up, I may say a few words about the Jaina way of writing the numerals. At present they are written as shown below:- 1, 2, 3, 4, 5, 6, 7, 8, e . 1 As early as the 4 th century or so before the Christian era we find in several agamas, a list of the names of 18 lipis (written characters). Herein are mentioned ankalipi and ganitalipi. Dr. B. Datta mentions that these two names suggest that the forms of numerals used for different purposes 1 See (1) Samavaya (XVIII), (2) Prajnapanasutra (sutra 37) of S'yamacarya (376 A. V.), (3) Avashyakaniryukti (Upodyfataniryukti) and (4) Maladharin Hemacandra's commentary to Vishesavashyakabhasya (v. £64).
were different, the former referring to those used in engraving and the latter, to those used in ordinary writing.1
1 In this connection he has added that in the Jaina literature, as also in the Vedic literature, we ordinarily find that a distinction is made between forms of alphabets used in engravings and in Mss., which are respectively styled by the Jainas as Kasthakarma or wood-work and Pustaka-karma or book-work. He has substantiated his statement by referring to the 10 th and 146 th sutras of Anuyogadvara as well as Maladharin Hemacandra Suri's commentary on the former. I may add that Hemacandra has interpreted pottha as (1) pota, (2) pustaka and (3) tadapatradi. Furthermore, the word pusta occurs also in the bhasya on Tattvarthadhigamasutra (I. 5), and is explained on p. 46 by Siddhasena Gani as . It also occurs in the bhasya on VI. 10 and is explained in the tika on p. 21. On p. 78 of this very tika (VII. 11), the word pusta is used.