पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

best to keep the spirit of the original and have as far as possible
not altered the sequence in the translation.
The translation to each rule is preceded by a sentence
or two giving in brief the contents of the rule and is followed,
where necessary, by relevant notes and comments. Parallel
rules and examples found in other available works on Hindu
mathematics have been indicated in the footnotes. Headings
and sub-headings have been provided to facilitate consulta-
tion.
2. PATIGANITA. Pâtîgaṇita is the name given to that
branch of Hindu Mathematics which deals with arithmetic
and mensuration. It is believed that this subject attained an
independent status sometime before the beginning of the
Christian era, when arithmetic became a separate subject and
geometry, which formerly belonged to a separate group of
Sciences, viz., the Kalpasûtra, came to be incorporated with it.¹
The earliest work exclusively dealing with this subject which
has come down to us is the fragmentary manuscript known as
the Bakhshâlî Manuscript² (text composed about 200 A.D.), which
was discovered in 1881 A.D., at Bakhshâlî, a village near the
city of Peshawar in the north-west of India, in course of ex-
cavation by a farmer. This work shows beyond all doubt that
by the third century A.D., when its text was composed, the
subject of Pâtîgaṇita was already in a state of maturity.
There are references to a number of other works on the
subject which were in use in the fifth and sixth centuries in
India. Bhâskara I (629 A.D.) refers to the works of Maskarî
Pûraṇa, Mudgala, Patana, and others, which were exclusively
devoted to the subject of Pâtîgaṇita. In the Âryabhaṭîya of
Âryabhaṭa I (b. 476 A.D.), written about the end of the
fifth century A.D., there is a chapter which deals with
¹ See B. Datta, 'The Scope and Development of the Hindu Gaṇita,'
Indian Historical Quarterly, Vol. V, No. 3, Sept. 1929, pp. 478-512.
² Bakhshâlî Manuscript—A Study in Mediaeval Mathematics. Edited
by G. R. Kaye. Parts I and II, Calcutta (1927). Part III, Delhi (1933).