**WORDS AND SYMBOLS FOR NUMBERS USED BY THE ANCIENT SINHALESE [3 Cent BC – 3 Cent AD]**.

Brig Siri Munasinghe.

We are fortunate that our ancestors left traces of these words and the symbols for numbers on their rock inscriptions. These traces are extracted and listed for information of scholars interested in research. Few other numeration system existed and was practiced in Sri Lanka until the Portuguese reintroduced the numeral they obtained through the Arabs from India.

THE BASIC SINHALA NUMBER WORDS [.S.Paranavitane – Inscription of Ceylon Volume I . 1970 Pg xlii

The historical records of Twenty basic words that are required to express all numbers is found on rock inscriptions of ancient Sri Lanka. The number words for one in ** Ek**

*patake*meaning one lot of land ,

*do**– kahapana*to indicate two silver kahapanas donated by the officer in charge of canals ,

*tin*

*i**silapatani*–the word for three stone steps donated by Upasika Tisaya,

*catara**–disa*to indicate four directions mentioned often in the donations made to the Sanga, the cave of the

*paca*

^{1}*– batikana*– of the five brothers, and number words for

*saye**[Six]*

*,*

**[Seven]**

*sata**,*

**[Eight] is similarly found. Then a chief named Uba during the time of Mahasenpathi[ Dr S Paranavitane believes him to be King Dutugemeunu himself] builds a cave for the Sanga or a King spending**

*ata***[nine] lakhs for labour of hands and feet for construction of a cave , a Princess whose father was King Gamini Uttiya donating a cave in the memory of her father and mother to the Sanga of the**

*Nava***[ten] directions,**

*dasa***[Twenty] appears in an inscription of King Lanjatissa in regard an donation of twenty five cool cave to the**

*visiti**Sanga*, other numbers such as of

*[Thirty],*

**tisa**

*catalisa**for Forty on Pg 337],*

*panasa**[Fifty onPg 335 ],*

**[Sixty on Pg 343],**

*sat*i

*satati**[ Seventy on Pg 343 ],*

*atasti**[ eighty for Pg 357], [The the pages given are those on Volume II Inscriptions of Ceylon- S Paranaviyane is published in two parts]*

*[Ninety- on Gold nugget Abeyagirri Vihare],*

**Anu**

**sata***[Hundred],*

**[ Thousand] and an extra number word to indicate very large numbers –**

*sahas*a

*lak**[Lakh]of Money[ Kahapanas] or land measures[ Karihas] are all in the two volumes of the ‘Inscription of Ceylon’ Volume I by Dr S Paranavitane., the word for Ninety has not yet been traced in those Inscriptions available to the author . These words are similar to the words of Sanskrit and Pali, that were used in India and Sri Lanka during this ancient period. These words later developed into Elu and these are different to the early Dravadian words used by our closest neighbor. Those Dravidian number names which are described in the recently published book ‘Early Tamil Epigraphy’- I Mahadevan 2003 Pg 283,is listed alongside for comparison in Table I.*

^{1}

NUMBER WORDS FOR ROUND NUMBERS AND THEIR MULTIPLES.

The Number Words for expressing multiples of Tens, Hundreds and Thousands or the round numbers are also found on inscriptions from 3 Cent BC to 3 Cent AD was obtained from Dr Paranavitane’s three volumes ‘The Inscriptions of Ceylon’. These words for numbers used express the measures of land in Karihsa , sums of money such as Ranas [ Gold Coins], Kahavanas{ Silver], and Massas[ Copper or Alloy], dates of the lunar Month, etc in the inscriptions. The words for the Multiples of Tens are a combine of the Initial letters of the nine digits as the first member with the words with *sa* in case of Tisa, Catalisa, Panasa or with *ti *in Visiti, Sati, Satati, Asati, as the second member. The number word for ten ending with *ti* sounds more like the English Twenty, thirty, forty etc. Perhaps the rhythm made it easy to memorize the numbers. The Sinhala word for multiples Hundred and Thousands is a Compound of the Nine words for Sinhala Digits as the first member of the combined with the word for Hundred [ *Sata*] and Thousand[ *Sahasa*] as the second member. This way of expressing number names is similar to the present system adopted in present day Sinhala and English.

**The construction of number words from 11 to 99**.

The words for many numbers from eleven to eighty four is recorded on rock before the 3 Cent AD are shown on Table II . These words were expressed as a compound of the two word , the first word for Units and then the word for tens. The name for units as a rule came first. * EK CATALISA* [41

**S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 328**] . It was One and forty instead of Forty and one . In the present day Sinhala this is different as its is a compound of the word for Tens is expressed as the first word followed by the word for Units[ Hatalis eka], which is closer to the expression in English[ Forty One]. Both these system are in use in modern languages.

An exception is the word for nineteen and twenty nine the word one less than twenty- *ekuna visiti* in Dakkina Stupa inscription and thirty- *ekuna tisa* is used[ S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 329]. The One less than twenty or one less than Thirty statement gives some indication of Number – sense such as less than or greater than. The Sinhala name numbers was very flexible and akin to the Roman written numerals for 19 or 29 which was IXX or IXXX , placing * *I to the left of XX or XXX for less than and to the right for one greater than .

### CONSTRUCTION OF NUMBER WORDS FROM 101 TO 999

There are many records of the donations of allotments of land for temples and purchases or payment of money which provides an incite as to how the ancient Sinhala constructed name for numbers using Hundred ,Tens and Units free from ambiguities and misleading statements .The expression for land measurements are different to those expressing a sum of money. Traces of these from inscriptions are separately shown below, and there had been a separate tradition for these different transactions.

When expressing three digit numbers in the measurement of land, the word Karisha which was a measure equivalent of four acres is interspersed between the word for *sata* [hundred ] examples . *eka Kiriha sataka, tini Kariha sata, catara ,kiraha sateka,Etc.*** this is followed by the word Ca the ancient word for **and.

**The rest of the numbers from 1 to 99 were constructed in the manner described below.**

These Written or Verbal notations seems to have a adopted a general rule in constructing Thousands , Hundreds , Tens and Units into a precise mathematical language free of ambiguities and misleading statements. Was this a requirement for the additions and subtractions of numbers, which was essential until the Zero was introduced after the 3 Cent AD in India?.

The sentence for four hundred seventy seven was written as below.

*Catari Kariha Sate ca sata satati Kariha * * * [S.Paranavitane – Inscription ofCeylon Volume II Part II ,2001. Pg 168]

*Four Kiraha Hundred and seven seventy Kiraha *

* *

HOW KAHAVANAS WERE EXPRESSED.

An interesting observation made by Dr Paranavitane about expressing 600 as six times Hundred ‘The expression *sata kala sateka*has been taken to mean seven times hundred i.e multiplied by seven[ Bakki Ala Inscription] . He states that it is interesting to find the same expression to denote the idea of multiplication in old Sinhalese as well as in modern English[S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 19 ].

**CONSTRUCTION OF NUMBER WORDS ABOVE 1001.**

There are interesting inscriptions where traces of names for Numbers consisting of thousands, Hundreds, Tens and units. These amounts on inscriptions give the cost of purchases and donations of Tanks to Monasteries. Few examples of these are shown below

The ancients were flexible in expressing these numbers specially in the case land measurements , they interspersed the units of measurement, the * Kariha* in between the unit word and the word for Hundred or thousand when expressing the number of Hundred or thousands. In case of expressing numbers over ten and up to ninety nine they sometimes used the *Kariha * after the number word. How ever when large numbers expressing money * Kahapana* they wrote the whole word beginning with the highest denomination the thousand then hundred and the tens and units followed by the word Kahavana orMassa.

Page 8

LINKING NUMBERS WITH SYMBOLS.

The traces of symbols to express the written number were used on Inscriptions. Most of the number words described in table 1 that is required to express any number was represented by symbols. The traces of these symbols or Numerals of the ancient Sinhalese found in the ancient inscriptions are shown in Table III. The two main inscription where these Numeral are seen are those of Situlpavu and of the Dakkina Stupa Inscriptions. Others are shown under Inscriptions with numerals page.

Most of these symbols for numbers [Numerals] appear next to and are attested by written number words. These are well described in Dr Abya Aryasinghe in ‘A Short Study of Brahmi Numerals in Sri Lanka- ’SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg 31-50. These numerals bear a close resemblance to the Indian counterparts. The Sinhala numbering system in written form or in numerical representation was based on the powers of Ten[ Decimal]. It was similar to the Indian counterpart and to the Egyptian Hieratic Script. All three had 20 symbols or numerals which could be written in free form on Palm leaves/ Papyrus.The simple additions and Subtractions may have been the same as the present day arithmetic where it was necessary only to collect numerals of the same order and exchange ten like symbols for the next higher order[ David M Burton-History of Mathematics, 1997 Pg 12.] and subtraction was performed by the same process in the reverse order. Some times borrowing was used when the a symbol was exchanged for a larger number was exchanged for ten lower order symbol to provide enough for the smaller number to be subtracted. Multiplications and Divisions were additive according to the Rhind’s Papyrus , where the product of two numbers was obtained by repeated doubling of one of the numbers and then adding the appropriate duplications to from the products. Division was multiplication in the reverse and was not easy when fractions were involved. To divide one would begin by doubling the divisor to a point at which the next duplication would exceed the dividend, then he would start halving the divisor in order complete the remainder.The construction of large Dagobas, the construction of Tanks and Canals, the creation of the Calendar,

One such example is the constructions of a Stupa of the magnitude of the Maha seya at Anurhadapura. This stupa is tall and where a truncated hemisphere rests on three concentric short cylinder of descending diameters. On top of the this is placed a Cube and on which is built a spire in the shape of Cone. All from of two and three dimensional shapes available to the ancient has been utilized in its construction. Precise formulas for their areas and volumes would have been available either those of the Greeks , but more so the Hindu Mathematics. To quote one such formula that the Hindus and perhaps the Sinhalese used was that for the area of a Circle. This was Half the circumference multiplied by the half the Diameter34. This eliminated the value of Phi which is now 22/7 an approximate. This would not be that accurate when large diameters are considered. Perhaps they had there own Geometrical treaties now lost to us.

Perhaps King Sadhatissa was aware of the Thales of Miletus[625-547 BC] method of measuring the height of the pyramid35. The King may have measured the length of the Shadow from the Dagabo to the tip of the Pinnacle of the Maha- seya, when his own shadow equal in length to his own height. He had only to add the half the diameter at the base to get the true height of the Maha- seya.

51 S.Paranavitane – Inscription of Ceylon.Volume II Part I ,1983.Pl XXIII No 48

52 ibid.Pl XXIV No 49

53 S.Paranavitane – Inscription of Ceylon.Volume II Part II ,2001.Pl VII to XII & Siri Munasinghe- The Island-Midweek Review 16.02. 2005, Pg IV

54 A. Aryasinghe- SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg43

55 S.Paranavitane – Inscription of Ceylon.Volume II Part I ,1983.Pl XXXI No 65

56 ibid.Pl XXXI No 146

57 MH Sirisoma & Gita Amerasinghe- Has Ebu Kahavana 1986, Pg 148

58 DMDe Silva Wickremasinghe- Epigraphia Zeylanica Vol I 1912 Pl 13(b).

59 S.Paranavitane – Inscription of CeylonVolume II Part II ,2001.Pl XLVII No 168

60 S.Paranavitane – Inscription of CeylonVolume II Part I ,1983.Pl VIII No 14(2)

**61**** Rev Habarakada Varira- Abeyagiri Inscription Sankrutika Puranaya 1994 Jan-March Pg 12**

The inscription that says “sata kala sataka” is vry important. It means multiplication not addition.

Do you know the date of that inscription?

Its in the above table “How kahavans expressed?

This could be the oldest decimal notation if it goes to BC times

The Bakki-Ala inscription is a grant of King Lajaka Tissa [59-50 BC], as you said is important in the history of mathematics of ancient Sri Lanka, it also mentions fractional shares or water rates that need be calculated and paid up, as many inscriptions of the period. This includes of interest paid for deposits of Kahavanus and grain to monasteries. Very Interesting, any way I placed the scans of the pages on the blog for your info.Please call me Mune. Thanks.

sorry the page you read is a big mess, I have corrected a little of it, I need to put the tables etc and also placed a brief note on Katapaya Numeration system with the Zero, used in SL before the Portuguese reintroduced the numeral to the Island.