The Blackwell Companion to Hinduism

A vowel followed by Tdenotes its own length. (4) This means: “aT” denotes a, “a ̄T” denotes a ̄, “uT” denotes u, etc. Ka ̄tya ̄y ...

Reference to elements of the same number is in the same order. (7) Therefore, i>y,u>v, etc., but not, e.g., i>v. The ru ...

iko yan.aci. (12) As it happens, a language consists of sentences, not just of words. From the perspective of the history of sci ...

writings as a ̄rs.a, “belonging to the seers,” just as the Pra ̄tis ́a ̄khya authors had done with respect to Vedic mantras. A l ...

extensively by Noam Chomsky and his school, and finally replaced by more abstract principles. In classical India, “the arrangeme ...

——. 1963. “Sur le genre du su ̄ tra dans la litterature sanskrite,” Journal asiatique251: 165–216. ——. 1969. “Pa ̄n.ini,”Current ...

CHAPTER 17 Indian Mathematics Takao Hayashi I Vedic Mathematics I.1 Vedas Since the Vedas are religious texts produced by poets, ...

There are also references in the R.gveda to the basic unit-fractions 1/2 (ardha or “a half ”), 1/4 (pa ̄daor “a foot,” from the ...

It has been conjectured that zero is indicated by the word ks.udra(lit. petty, tri- fling) in the Atharvaveda (19.22.6=19.23.21) ...

construction of ritual sites including various altars. It is mostly devoted to the description of various fire-altars (agni) to ...

(tiryan.ma ̄nı ̄)·ropesÒ produce separately.” What “the ropes produce” are not explicitly mentioned, but are no doubt the square ...

A ̄ryabhat.a I’s terminology for series, citi, etc., too, is probably related to the S ́ulbasu ̄tras, whose main theme was the p ...

(747), consists of ten topics, which presumably cover the entire mathematics known to the Indians of those days. They are: basic ...

A ̄ryabhat.a I was one of the most influential mathematicians and astronomers in India through his two works, A ̄ryabhat.ı ̄yaan ...

unknown integer, N, is divided by a set of integers, {a 1 ,a 2 ,..., an}, one by one, the remainders are {r 1 ,r 2 ,..., rr}. Wh ...

II.3 The seventh to eighth centuries – restructuring The seventh century saw a restructuring of Indian mathematics. It was divid ...

negative number. A fraction was expressed, just like our fractions, by placing the numerator above the denominator (without a ba ...

angled triangles and a central square, while discussing the validity of A ̄ryabhat.a’s statement, “A square (varga) is an equi-q ...

Govindasva ̄min shows a keen interest in the logical foundations of the rule of three. He provides a definition, with a detailed ...

Na ̄ra ̄yan.a Pan.d.ita wrote, in ad1356, a book for pa ̄t. ̄-ganı .ita,Gan.itakaumudı ̄, in which he developed, among other thi ...