“Next we have the Vārttikas or "Notes" of Kātyāyana (probably third century B. C.) on 1245 of Pāṇini's rules, and, somewhat later, numerous grammatical Kārikās or comments in metrical form: all this critical work was collected by Patanjali in his Mahābhāshya or "Great Commentary," with supplementary comments of his own. He deals with 1713 rules of Pāṇini.”

—  Pāṇini

Appendix A History of Sanskrit Literature

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ancient Sanskrit grammarian

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“The Mahābhāshya was commented on in the seventh century by Bhartṛihari in his Vākyapadīya which is concerned with the philosophy of grammar, and by Kaiyaṭa (probably thirteenth century). About 650 A. D. was composed the first complete commentary on Pāṇini, the Kāçikā Vṛitti or "Benares Commentary," by Jayāditya and Vāmana.”

Pāṇini ancient Sanskrit grammarian

Appendix A History of Sanskrit Literature

“Among the earliest attempts to explain Pāṇini was the formulation of rules of interpretation or paribhāshās; a collection of these was made in the last century by Nāgojibhaṭṭa in his Paribhāshenduçekhara.”

Pāṇini ancient Sanskrit grammarian

Appendix A History of Sanskrit Literature

“Pāṇini's grammar defines Classical Sanskrit, so Pāṇini by definition lived at the end of the Vedic period. He notes a few special rules, marked chandasi ("in the hymns") to account for forms in the Vedic scriptures that had fallen out of use in the spoken language of his time. These indicate that Vedic Sanskrit was already archaic, but still a comprehensible dialect.”

Pāṇini ancient Sanskrit grammarian

An Analytical Study of 'Sanskrit' and 'Panini' as Foundation of Speech Communication in India and the World

“Pāṇini had before him a list of irregularly formed words, which survives, in a somewhat modified form, as the Uṇādi Sūtra. There are also two appendixes to which Pāṇini refers: one is the Dhātupāṭha, "List of Verbal Roots," containing some 2000 roots, of which only about 800 have been found in Sanskrit literature, and from which about fifty Vedic verbs are omitted; the second is the Gaṇapāṭha, or "List of Word-Groups," to which certain rules apply. These gaṇas were metrically arranged in the Gaṇaratna-mahodadhi, composed by Vardhamāna in 1140 A. D.”

Pāṇini ancient Sanskrit grammarian

Appendix A History of Sanskrit Literature

“Pāṇini had before him a list of irregularly formed words, which survives, in a somewhat modified form, as the Uṇādi Sūtra.”

Pāṇini ancient Sanskrit grammarian

There are also two appendixes to which Pāṇini refers: one is the Dhātupāṭha, "List of Verbal Roots," containing some 2000 roots, of which only about 800 have been found in Sanskrit literature, and from which about fifty Vedic verbs are omitted; the second is the Gaṇapāṭha, or "List of Word-Groups," to which certain rules apply. These gaṇas were metrically arranged in the Gaṇaratna-mahodadhi, composed by Vardhamāna in 1140 A.D.
Appendix A History of Sanskrit Literature

“While Pāṇini's work is purely grammatical and lexicographic, cultural and geographical inferences can be drawn from the vocabulary he uses in examples, and from his references to fellow grammarians, which show he was a northwestern person. New deities referred to in his work include Vasudeva (4.3.98). The concept of dharma is attested in his example sentence dharmam carati "he observes the law"”

Pāṇini ancient Sanskrit grammarian

cf. Taittiriya Upanishad 1.11
An Analytical Study of 'Sanskrit' and 'Panini' as Foundation of Speech Communication in India and the World

“The Pāṇinian commentator Kātyāyana (c. 3rd–4th century BCE) knew of the coexistence of Middle Indic forms with earlier ones. There is a Pāṇinian rule that provides that verb bases listed in an appendix to the Aṣṭādhyāyī have the class name dhātu (verbal base, root). Kātyāyana discusses whether one could define verbal bases semantically and thereby possibly do without the verb list. He remarks that even if one defines a verbal base as denoting an action, the roots must be listed in order to preclude the possibility that constituents of terms such as āṇapayati/āṇavayati ‘commands’ be assigned the class name in question; āṇapayati/āṇavayati is a Middle Indic counterpart of Sanskrit ājñāpayati.”

Pāṇini ancient Sanskrit grammarian

Prof. George Cardona in:"Indo-Aryan languages".

“It is not certain whether Pāṇini used writing for the composition of his work, though it is generally agreed that he knew of a form of writing, based on references to words such as "script" and "scribe" in his Ashtadhyayi. These must have referred to Aramaic or early Kharosthi writing. It is believed by some that a work of such complexity would have been difficult to compile without written notes, though others have argued that he might have composed it with the help of a group of students whose memories served him as 'notepads' (as is typical in Vedic learning). Writing first reappears in India in the form of the Brāhmī script from the 3rd century BC in the Ashokan inscriptions.”

Pāṇini ancient Sanskrit grammarian

An Analytical Study of 'Sanskrit' and 'Panini' as Foundation of Speech Communication in India and the World

David Eugene Smith photo

“It is difficult to say when algebra as a science began in China. Problems which we should solve by equations appear in works as early as the Nine Sections (K'iu-ch'ang Suan-shu) and so may have been known by the year 1000 B. C. In Liu Hui's commentary on this work (c. 250) there are problems of pursuit, the Rule of False Position… and an arrangement of terms in a kind of determinant notation. The rules given by Liu Hui form a kind of rhetorical algebra.
The work of Sun-tzï contains various problems which would today be considered algebraic. These include questions involving indeterminate equations. …Sun-tzï solved such problems by analysis and was content with a single result…
The Chinese certainly knew how to solve quadratics as early as the 1st century B. C., and rules given even as early as the K'iu-ch'ang Suan-shu… involve the solution of such equations.
Liu Hui (c. 250) gave various rules which would now be stated as algebraic formulas and seems to have deduced these from other rules in much the same way as we should…
By the 7th century the cubic equation had begun to attract attention, as is evident from the Ch'i-ku Suan-king of Wang Hs'iao-t'ung (c. 625).
The culmination of Chinese is found in the 13th century. …numerical higher equations attracted the special attention of scholars like Ch'in Kiu-shao (c.1250), Li Yeh (c. 1250), and Chu-Shï-kié (c. 1300), the result being the perfecting of an ancient method which resembles the one later developed by W. G. Horner”

David Eugene Smith (1860–1944) American mathematician

1819
Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra

“Grammars (vyākaraṇas) concern the description of speech forms (śabda) considered to be correct (sādhu) through derivation and thereby serve to make understood the usage found in the Vedas. The grammar that was granted the status of a Vedāṅga is that of Pāṇini. This work is referred to in toto as a śabdānuśāsana (means of instruction of correct speech forms); since the core of Pāṇini’s work comprises the eight chapters of sūtras that serve to describe both the current language of his time and features particular to Vedic, it also bears the name Aṣṭādhyāyī”

Pāṇini ancient Sanskrit grammarian

“Collection of Eight Chapters”
Prof. George Cardona in: Indo-Aryan languages http://www.britannica.com/EBchecked/topic/286348/Indo-Aryan-languages/74594/Characteristics-of-Old-Indo-Aryan-texts#ref603388, britannica.com., 20 January 2014.

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