Arithmetic in India: Pāṭīgaṇita
Pāṭīgaṇita, which literally means “mathematics (gaṇita) by means of algorithms ( pāṭī ),” is the name of one of the two main fields of medieval Indian mathematics, the other being bījagaṇita or “mathematics by means of seeds.” The two fields roughly correspond, respectively, to arithmetic (including mensuration) and algebra.
The compound Pāṭīgaṇita seems to have come into use in relatively later times. In older works, the expressions, gaṇitapāṭī and gaṇitasya pāṭī (mathematical procedure, i.e., algorithm), are common, and sometimes the word pāṭī occurs independently. Pāṭīgaṇita is also called vyaktagaṇita or “mathematics of visible (or known) [numbers],” while bījagaṇita is called avyaktagaṇita or “mathematics of invisible (or unknown) [numbers].” Some scholars maintain that the word pāṭī originated from the word paṭṭa or paṭa meaning the calculating board, but its origin seems to be still open to question.
The division of mathematics (gaṇita) into those two fields was not practiced...
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