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Lilavati: Definitions[1]

Ganesa
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 varatakas [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 drammas are a niska [gold coin].

3. Two yavas [barley grain (a weight measure)] are here considered equal to a gunja [berry]; three gunjas 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 vallas.

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

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

6. A yojana is four krosas. Likewise, ten karas [hand, hasta] are a vamsa [bamboo]; a nivartana is a field bounded by four sides of twenty vamsas [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 [104], laksa [105], prayuta [106], kota [107], arbuda [108], abja [109], kharva [1010], nikharva [1011], mahapadma [1012], sanku [1013]; after that,

11. jaladhi [1014], antya [1015], madhya [1016], parardha [1017]: 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.