Shatrinshika Ya Shatrinshatika Ek Adhyayan

Here's a comprehensive summary of the provided Jain text "Shatrinshika ya Shatrinshatika Ek Adhyayan" by Anupam Jain and Sureshchandra Agarwal:

Book Title: Shatrinshika ya Shatrinshatika Ek Adhyayan (A Study of Shatrinshika or Shatrinshatika) Authors: Anupam Jain, Sureshchandra Agarwal Publisher: Z_Aspect_of_Jainology_Part_3_Pundit_Dalsukh_Malvaniya_012017.pdf Catalog Link: https://jainqq.org/explore/212084/1

Core Subject:

This article is a scholarly study of a lesser-known Jain mathematical work called "Shatrinshika" or "Shatrinshatika." The authors aim to establish its identity, authorship, content, and historical context, particularly in relation to the prominent Jain mathematician Mahaviracharya.

Key Findings and Arguments:

1. Identity of the Work:

   • The study argues that "Shatrinshika," "Shatrinshatika," and "Chattisi Ganita" (Thirty-six Mathematics) are essentially the same work. Evidence from manuscript descriptions and colophons across different collections (Jaipur, Karanja) supports this conclusion.
   • The title "Shatrinshika" (meaning thirty-six) refers to the thirty-six topics or sections discussed in the text, as indicated by the early inscriptions and the content itself (8 sections on Parikarma, 8 on fractional Parikarma, 6 on fractional types, 10 on Prakirnaka, and 4 on Trairashika).

2. Authorship and Time Period:

   • The primary author identified is Madhavachandra Trividya.
   • The text's own colophon explicitly states that Madhavachandra Trividya composed it by researching and refining (shodh kar) the "Ganita Sara Sangraha" of the renowned Jain mathematician Mahaviracharya (c. 850 CE).
   • While there are multiple individuals named Madhavachandra in Jain tradition, the study points to Madhavachandra Trividya, the disciple of Nemicandra Siddhanta Chakravarti, as the most likely author of Shatrinshika. Nemicandra was a successor to Virasena and likely lived around the late 10th or early 11th century CE. This places the composition of Shatrinshika in the 10th-11th century CE.

3. Relationship with Mahaviracharya's Ganita Sara Sangraha:

   • Shatrinshika is not an entirely original work but rather an adaptation and augmentation of Mahaviracharya's "Ganita Sara Sangraha."
   • Madhavachandra Trividya took several chapters and sections from Mahaviracharya's work verbatim and added new material, particularly in the later sections.
   • The study highlights a confusion in historical scholarship, where some early catalogers and scholars mistook Shatrinshika manuscripts for incomplete versions of Ganita Sara Sangraha due to similar introductory passages and colophons mentioning Mahaviracharya.
   • The authors critique Dr. Mukut Bihari Lal Agarwal for incorrectly attributing the entire Shatrinshika to Mahaviracharya and for his assertion that it solely discusses algebra, noting that Agarwal likely did not examine the manuscript closely.

4. Content of Shatrinshika:

   • The text covers various mathematical topics. Based on the analyzed Jaipur manuscript, the chapters include:
     • Sangya Adhikara (Definition/Terminology)
     • Parikarma Vyavahara (Arithmetic Operations)
     • Kala Savarna Vyavahara (Operations with Fractions/Time Ratios)
     • Prakirnaka Vyavahara (Miscellaneous Problems)
     • Trairashika Vyavahara (Rule of Three)
     • Varga Sankalitadi Vyavahara (Sum of Squares, Cubes, etc.)
   • The last section, Varga Sankalitadi Vyavahara, contains detailed explanations of 13 specific formulas related to the summation of squares and cubes, along with examples.
   • A notable feature of the final section is the inclusion of a 34-cell Magic Square, which is a common element in Jain mathematical and astrological texts. A 15-cell Magic Square is also mentioned as a marginal note.

5. Manuscript Descriptions:

   • The study provides detailed descriptions of several key manuscripts of Shatrinshika, particularly those found in the Jaipur (Tholiyan Temple) and Karanja (Balaatkara Gana Temple) collections.
   • It clarifies that Manuscript No. 468 from Jaipur is the actual Shatrinshika, while No. 469 is likely a different work or a different manuscript altogether.
   • Descriptions of the Karanja manuscripts (referred to as "Chattisi Ganita" and "Shatrinshatika") further confirm the identity of the work.
   • The writing date of the Jaipur manuscript is given as 1608 CE, indicating it's a copy, not the original. The Karanja manuscripts have later dates (1702 CE and 1725 CE).

6. Scholarly Reception and Neglect:

   • The article points out that despite its significance, Shatrinshika has been largely overlooked by many prominent scholars of Jain mathematics (e.g., Jyoti Prasad Jain, Nemicandra Jain Shastri, Parmanand Jain) and general histories of Indian mathematics.
   • The misattribution by Dr. Kasliwal (who identified it as Mahaviracharya's work) and subsequent interpretations by others like Agarwal led to a misunderstanding of its true nature and authorship.

Conclusion:

The study concludes that "Shatrinshika" is a distinct mathematical work composed by Madhavachandra Trividya, a disciple of Nemicandra Siddhanta Chakravarti, around the 10th-11th century CE. It is a significant but not entirely original contribution, building upon Mahaviracharya's "Ganita Sara Sangraha" by incorporating existing material and adding new mathematical concepts, notably the inclusion of magic squares. The research aims to bring this important Jain mathematical text to greater scholarly attention.