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# Lilavati: Definitions^{[1]}

Image courtesy of Silk-Elephant Sculptures

**1.** Having bowed to [Ganesa] who causes the joy of those who worship him, who, when thought of, removes obstacles, the elephant-headed one whose feet are honored by multitudes of gods, I state the arithmetical rules of true computation, the beautiful Lilavati, clear and providing enjoyment to the wise by its concise, charming and pure quarter-verses.

**2.** Two times ten *varataka*s [cowrie] are a *kakini* [shell], and four of those are a *pana* [copper coin]. Sixteen of those are considered here [to be] a *dramma* [coin, "drachma"], and so sixteen *dramma*s are a *niska* [gold coin].

**3.** Two *yava*s [barley grain (a weight measure)] are here considered equal to a *gunja* [berry]; three *gunja*s are a *valla* [wheat grain] and eight of those are a *dharana* [rice grain]. Two of those are a *gadyanaka*, so a *ghataka* is defined [to be] equal to fourteen *valla*s.

**4.** Those who understand weights call half of ten *gunja*s a *masa* [bean], and sixteen of [the weights] called *masa* a *karsa*, and four *karsa*s a *pala*. A *karsa* of gold is known as a *suvarna* [lit. "gold"].

**5.** An *angula* [digit] is eight *yavodara*s [thick part of a barley grain]; a *hasta* [hand] is four times six *angula*s. Here, a *danda* [rod] is four *hasta*s, and a *krosa* [cry] is two thousand of those.

**6.** A *yojana* is four *krosa*s. Likewise, ten *kara*s [hand, *hasta*] are a *vamsa* [bamboo]; a *nivartana* is a field bounded by four sides of twenty *vamsa*s [each].

**7.** A twelve-edged [solid] with width, length, and height measured by one *hasta* is called a cubic *hasta*. In the case of grain and so forth, a measure [equal to] a cubic *hasta* is called in treatises a "Magadha *kharika*".

**8.** And a *drona* [bucket] is a sixteenth part of a *khari*; an *adhaka* is a fourth part of a *drona*. Here, a *prastha* is a fourth part of an *adhaka*; by earlier [authorities], a *kudava* is defined [as] one-fourth of a *prastha*.

The remaining definitions concerning time and so forth are to be understood [as they are] generally known from common usage. So much for the definitions.

Now, the explanation of the places of numbers.

**9.** Homage to Ganesa, delighting in the writhing black snake playfully twining about his neck, bright as a blue and shining lotus.

**10.** In succession, one, ten, hundred, thousand, *ayuta* [10^{4}], *laksa* [10^{5}], *prayuta* [10^{6}], *kota* [10^{7}], *arbuda* [10^{8}], *abja* [10^{9}], *kharva* [10^{10}], *nikharva* [10^{11}], *mahapadma* [10^{12}], *sanku* [10^{13}]; after that,

**11.** *jaladhi* [10^{14}], *antya* [10^{15}], *madhya* [10^{16}], *parardha* [10^{17}]: these, increasing by multiples of 10, are the designations of the places of the numbers for practical use, produced by the early [authorities].

That is the explanation of the places of numbers.

^{[1]}Reformatted from the version found at: Brown University, Department of Mathematics, History of Mathematics, Lilavati: Definitions. [link gone missing] Permission to reproduce for educational purposes is granted there. No title page of this document, but presumably from someone's translation of the Lilavati of Bhaskaracarya, a summary of the state of mathematics in India c 1150AD according to the Vedic traditions. These measurements may not have any relationship to those used c.500BC (But I suspect the Magadha Karika is about this size in that the definition used in the suttas is 20 Karis which is further identified as a description of a beggars "load" of requisites...still looks like a lot to me, more than a bushel, not the load of a well-trained Buddhist Bhikkhu.