Ganittilakam Savrtuttikam

Here's a comprehensive summary of the Jain text "Ganitatilakam Savrtuttikam," based on the provided pages, focusing on its content and context:

Book Title: Ganitatilaka (गणिततिलकं) Author: Sripati Commentator: Simhatilaka Suri Critical Edition and Publication:

• Editor: Hiralal R. Kapadia
• Publisher: Oriental Institute, Baroda
• Series: Gaekwad's Oriental Series, Volume No. LXXVIII
• Year: 1937

Summary:

"Ganitatilakam Savrtuttikam" is a critically edited work of the "Ganitatilaka," a treatise on mathematics (specifically Pati-ganita or elementary arithmetic) by the renowned astronomer and mathematician Sripati. The edition includes a detailed commentary by Simhatilaka Suri and an extensive introduction and appendices by the editor, Hiralal R. Kapadia.

I. Introduction by Hiralal R. Kapadia:

The introduction is a comprehensive overview of the presence and significance of mathematics within Jainism, and then delves into the specifics of Sripati's "Ganitatilaka."

• Mathematics in Jainism:

  • Importance: Mathematics is considered an "exact science" and was highly valued by ancient civilizations, including the Greeks, for its role in philosophical study.
  • Jain Contribution: Indians, particularly the Jainas, made significant contributions to mathematics. Mahaviracharya (850 A.D.) highlighted the usefulness of mathematics in various fields like music, logic, medicine, architecture, and grammar.
  • Anuyoga Classification: Jain sacred works were traditionally divided into four anuyogas: Dharmakathānuyoga, Ganitānuyoga, Dravyanuyoga, and Charanakaranānuyoga. Ganitānuyoga is closely linked to the study of time and celestial bodies, essential for religious ceremonies. Therefore, ganitānuyoga (often translated as "Mathematics") was not just a secular subject but integral to Jain religious doctrine and the pursuit of moksha (liberation).
  • Mathematical References in Jain Scriptures: Knowledge of sankhyāna (arithmetic) and jyotiṣa (astronomy) was a key accomplishment of Jain saints, as mentioned in texts like the Bhagavati Sutra and Uttaradhyayana Sutra. The first Tirthankara, Rishabha, reportedly taught arithmetic to his daughter. Lord Mahavira's acumen in mathematics is also alluded to.
  • Jaina Works on Mathematics: The introduction lists several extant and inferred Jain works related to mathematics and astronomy, including Suryaprajñapti, Candraprajñapti, Jyotishkarandaka, Kshetrasamasa, and the works of Mahavira, Municandra Suri, Sridharacharya, and Rajaditya. It also discusses concepts like sankhyāna (calculation types), permutations and combinations (bhanga), notational places, place-value systems, and various number classifications (including different types of infinity).

• Outlines of Ganitatilaka:

  • Title: The work is named "Ganitatilaka" by the commentator Simhatilaka Suri, while the author Sripati calls it "Pati-ganita."
  • Composition: The book is entirely in Sanskrit verse, using various metres.
  • Structure: It begins with a salutation to the soul and then proceeds to discuss mathematical topics.
  • Topics Covered: The introduction details the extensive coverage of mathematical topics within the "Ganitatilaka" and its commentary, including:
    • Definitions of Measures: Various units of measurement for wealth (kaparda, suvarna, meya, dhanya), length (kshetra), time (kala), and substance (dravya).
    • Eight Fundamental Operations: Addition (sankalita), subtraction (vyutkalita), multiplication (gunakara), division (bhāgahāra), squaring (varga), square root extraction (vargamūla), cubing (ghana), and cube root extraction (ghanamūla). The text details multiple methods for each operation.
    • Fractions: Comprehensive treatment of fractions, including their operations (addition, subtraction, multiplication, division), classification (e.g., jāti, bhāga, prabhāga), and compound fractions.
    • Zero: Operations involving zero are explained.
    • Proportion: Discusses the rule of three (trairas'ika) and rule of five (pañcarāśika), including inverse proportion (vyasta).
    • Interest (Mis'ravyaavahara): Problems related to calculating interest.
    • Inverse Operations (Viparitoddes'aka): Methods for solving problems by reversing operations.
    • Miscellaneous Problems: Various problems involving fractions and their applications.
    • Geometrical References: Mentions of geometrical figures like triangles, quadrilaterals, circles, and formulas for their calculations.
    • Values of Pi (π): Discussion of different values of π used in Jain texts (√10, slightly more than 3, and 3.16).

• Sripati's Life and Works:

  • Identity: Sripati appears to have been a follower of Mahesvara (Shaivism) but criticized Jain cosmological doctrines in his work Siddhantas'ekhara.
  • Family: He was the son of Nagadeva, grandson of Bhatta Kesava, and possibly hailed from Rohinikhanda.
  • Works: Besides "Ganitatilaka," he authored several astronomical and astrological works like Dhikoti-karana, Jyautiṣaratnamālā, Siddhanta Sekhara, Daivajñavallabha, and Jatakapaddhati.
  • Dating: He flourished around 1040 A.D., not later than Bhaskaracharya.

• Simhatilaka Suri's Commentary:

  • Identity: The commentator, Simhatilaka Suri, was a pupil of Vibudhacandra Suri.
  • Other Works: He is also credited with works like Mantrarahasya and Vardhamanakalpa.
  • References: His commentary refers to other mathematical works, notably Lilavati, Trishati, and various Jain texts.

• Critical Apparatus: The edition is based on a single palm-leaf manuscript, which, despite some minor inaccuracies, is deemed reliable. The editor has provided a table of contents, appendices with examples and tables, and made efforts to reconstruct the text accurately.

II. The Text of Ganitatilaka and Commentary:

The core of the volume contains Sripati's "Ganitatilaka" in Sanskrit verse, along with Simhatilaka Suri's commentary. The text systematically covers the mathematical topics outlined above, providing definitions, rules (sutras), and numerous examples with their solutions. The commentary clarifies the verses, explains terms, and sometimes offers alternative interpretations or references to other texts like Sridharacharya's Trishati and Bhaskaracharya's Lilavati.

III. Appendices:

The appendices provide valuable supplementary material:

• Appendix I: Examples and Answers: Lists numerical problems posed in the text with their corresponding solutions.
• Appendix II: Tables of Measurements: Reproduces tables of various units of measurement mentioned in "Ganitatilaka" and other ancient works, allowing for comparison.
• Appendix III: Sanskrit Words and their Numerical Significations: A glossary of Sanskrit words used to represent numbers, sourced from various texts, with their numerical values.

In essence, "Ganitatilakam Savrtuttikam" is a significant scholarly contribution that preserves and elucidates an important medieval Indian mathematical text, placing it within the broader context of Jain intellectual history and Indian mathematical traditions. The editor's work is commendable for its thoroughness and the wealth of contextual information provided.