WORDS AND SYMBOLS FOR NUMBERS USED BY THE ANCIENT SINHALESE [3 Cent BC – 4 Cent AD].
Brig Siri Munasinghe.
The early Sinhalese and those of the Indians Continent appear to have developed their words and symbols for numbers from a common source. We are fortunate that our ancestors left traces of these words and the symbols on their rock inscriptions. These traces are extracted and listed for information of scholars interested in research .
THE BASIC SINHALA NUMBER WORDS .
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 ^{1}meaning one lot of land , do^{ 1}– kahapana to indicate two silver kahapanas donated by the officer in charge of canals ,the tini^{1} silapatani –the word for three stone steps donated by Upasika Tisaya, catara^{1} –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 [1] [Six], sata^{1} [Seven], ata^{1} [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 Nava^{1} [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 dasa^{1 }[ten] directions, visiti^{1} [Twenty] appears in an inscription of King Lanjatissa in regard an donation of twenty five cool cave to the Sanga, other numbers such as of tisa^{2} [Thirty], catalisa 3[Forty], panasa 4[Fifty], sati 5[Sixty], satati ^{5} [ Seventy], atasti 6 [ eighty, ?[Ninety], sata ^{ 7} [Hundred], sahasa ^{1} [ Thousand] and an extra number word to indicate very large numbers –lak ^{1} [Lakh]of Money[ Kahapanas] or land measures[ Karihas] are all in the two volumes of the ‘Inscription of Ceylon’ by Dr S Paranavitane.[The Volume II is published in two parts], 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 8is listed alongside for comparison in Table I.
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 9[41] . 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 10in Dakkina Stupa inscription and thirty ekuna tisa ^{10}is used. 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.
LAND MEASURE 

108  eka sataka Kiriha ata11  100  KA 8  
300  tini kariha sata ca12  3 KA  100 and  
367  tini Kariha sata ca satisataka Kiriha13  3 KA  100 and  67 KA 
400  catara kiraha sateka14  4 KA  100  
420  Catara Kriha sata ca visiti kariha ca15  4KA  100 and  20 KA 
477  Catari Kariha Sate ca sata satati Kariha16  4KA  100 and  77 KA 
500  paca kiraha sati17  5 KA  100  
603  Kariha Sasata ca tini kariha18  KA  600 and  3 
884  ata kiraha sata ca catuasati kiriha19  8 KA  100 and  84 KA 
904  Nava Kariha sate ca catara Kiriha ca20  9 KA  100 and  4 KA 
950  nava kiriha sata ca panasa Kiraha21  9 KA  100 and  50 KA 
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 22
Four Kiraha Hundred and seven seventy Kiraha
HOW KAHAVANAS WERE EXPRESSED.
100  eka sataka 23kahavana  One hundred 
500  Paca sata23a Kahavana  Five Hundred 
600  sata kala stataka 24Kahavana  6 times 100 
600  sa sata 24^{a} kahavana  Six hundred 
833  Ata sate tetisa 25kahavana  Eight hundred thirty three 
An interesting observation made by Dr Paranavitane about expressing 600 as six times Hundred ‘The expression sata kala sateka 24has been taken to mean seven times hundred i.e multiplied by seven . 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 English24.
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 or Massa.
Number  Thousands  Hundreds  Tens/units 
1120  Eka Kariha Sahasa25
KA 1000 
ca eka Kariha sata
and 1 KA 100 
ca visiti .
and 20. 
2041  Sari ca do karihi Sahasa26
An assessment of 2 KA 1000 
ca eka catalisa
and 41 KA 

4000  Catara sahasa27  
5000  paca sahasa 28
Five thousand 

100663  Sata sahasa29
Hundred Thousands 
ca ana sata sate
and another 600 
ca ana se sate ca
and another 63. [ Kahapanas] 
LINKING NUMBERS WITH SYMBOLS.
The traces of symbols to express the written number were used on Inscriptons. 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. Some 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 Lanka30’. 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 order31 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 products32. 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 remainder33.The construction of large Dagobas, the construction of Tanks and Canals, the creation of the Calendar, Surveying of land and the record keeping for commerce required a numerical system and precise mathematical language free of ambiguities and misleading statements. All these subjects should be studied in greater detail, as a lot of factors could be deduced from Rock Inscriptions, Ancients Texts and other evidence.
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[625547 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.
[1]S.Paranavitane – Inscription of Ceylon Volume I . 1970 Pg xlii
3 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 337
4 ibid. Pg 335
5 ibid. Pg 343
6 ibid. Pg 357
7 ibid. Pg 327
8 Iravatham .Mahadevan – Early Tamil Epigraphy 2003 Pg 283
9 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 328
10 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 329
11 Rev Habarakada Varira Abeyagiri Inscription Sanskrutika Puranaya 1994 JanMarch Pg 12
12 S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg 168
13 ibid. Pg 165
14 ibid 2001.
15 ibid. Pg 168
16 ibid. Pg 168
17 ibid. Pg 168
18 ibid. Pg168
19 ibid. Pg 167
20 ibid. Pg 167
21 ibid. Pg 167
22 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 168
23 ibid. Pg 259
23a S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 61
24 ibid. Pg 19
24^{a} S.Paranavitane – Inscription of Ceylon Volume II Part II 2001. Pg
25 ibid. Pg 126
24 S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 19
25 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg168
26 ibid. Pg160
27 S.Paranavitane – Inscription of Ceylon Volume II Part I 1983. Pg 98
28 ibid. Pg 92
29 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 146
30 A. Aryasinghe SAMSKRTI Cultural Quarterly Vol 17 No 3. 1983. Pg 3150
31 David M BurtonHistory of Mathematics, 1997 Pg 12.
32 ibid. Pg 35
33 ibid .Pg 36.
34 David M BurtonHistory of Mathematics, 1997 Pg 59
35 ibid, 1997 Pg 86
ANCIENT SINHALA , SANSKRIT, PALI AND TAMIL WORDS FOR NUMBERS
3 CENT BC TO 3 CENT AD
ReferenceInscriptions of Ceylon Vol I S Paranavitane  SINHALA  SANSKRIT  PALI  ELU  TAMIL
ReferenceEarly Tamil Epigraphy 9– I Mahadevan 

One  No 786,815  EKA1  EKA  EK  
Two  Nos791, 208  DO/DUVA1  DUVU  DO  IRU
2CentBC1 Cent AD 

Three  Nos 95,123,314,540,1152  TE /TINI/TI1  TRINI  TINI  TIN  
Four  Nos 9 , 331,1120  CATARA1  CATVARA  CHATTRO  SATARA  
Five  Nos 294, 428,978  PACA1  PANCA  PAS  
Six  No 150  SA/SAYE1  SAT  CHATTRO  SATARA  AIM 56 Cent AD 
Seven  Kanitha tissa
2 CentAD 
SATA1  SAPTA  SATTA  SAT  EL 56 Cent AD 
Eight  Nos 538,502  ATA1  ASTAN  ATTHA  ATA  
Nine  Nos 851,1199  NAVA1  NAVAM  NAVA  NAVA  
Ten  Nos 34,251  DASA1  DASAN  DASA  PATIN/PAT
2CentBC1Cent AD 

Twenty  VISITI1  
Thirty  TISA2  
Forty  CATALISA4  CATVARIMSAT  CATTALISA  SATALIS  
Fifty  PANASA5  PANCASA  PANNASA  PANAS  
Sixty  SATI/SATA6  SASTI  SATTHI  SATA  
Seventy  SATATI7  SAPTATI  SATTATI  SATTA  
Eighty  ASATI8  ASITI  ASITI  ASU  
Ninety  
Hundred  No 857  SATA1  SATA  SIYA  NARU 56 Cent AD  
Thousand  Nos 251,1199  SAHASA1  SAHASRA  SAHASSA  DAHAS  
Lakh  No 1199  LAKA1 
NUMBER WORD FROM 10 TO 100
10 TO 19  20 TO 29  30 TO 39  40 TO 49 
DASA 10  VISITI 20  TISA 30  CATALISA 40 
EKA DASA36 1 & 10  EKA TISA36  EK CATULISA36 1 & 40  
DO DASA37 2 & 10  DO VISITI 37 2 & 20  DO TISA37  
TERASA38 3 & 10  TE VISITI 38 3& 20  
CATARA VISA 4 & 20  CATA CATALISA43 4 & 40  
PACA VISITI42 5 & 20  
SOLASA 39 6 & 10  
ATA DASA/atalosa40 8&10  
EKUNA VISITI 36
1 LESS THAN 20 
EKUNA TISA36
1 LESS THAN 30 
50 TO 59 
60 TO 69 
70 TO 79  80 TO 89  90 to 99 
PANASA44 50  SATI47 60  SATATI49 70  ASITI50 80  None 
SESATI48 3 AND 60  
CATA PANASA45  CATA ASITI46 4 & 80  
PASA PANASA46  
SA SATI48 6 & 60  SATA SATATI49 7 & 70  
9 Iravatham .Mahadevan – Early Tamil Epigraphy 2003 Pg 283
2 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg
4 ibid. Pg 335
5 ibid. Pg 343
6 ibid. Pg 358
7 ibid. Pg 357
8 ibid. Pg 327
36 S.Paranavitane – Inscription of Ceylon Volume II Part II ,2001. Pg 329
37 ibid. Pg 339
38 ibid. Pg 337
43 ibid, Pg 111
42 ibid. Pg 341
39 ibid. Pg 360
40 ibid. Pg 324
44 ibid. Pg 169
47 ibid. Pg 357
49 ibid. Pg 358
50 ibid. Pg 327
48 ibid. Pg 146
45 ibid. Pg 334
46 ibid. Pg 167
46 ibid. Pg 167
48 ibid. Pg 359
49 ibid. Pg 357
DAKKINA STUPA INSCRIPTION.
This is the largest inscription in the Island ,inscribed on 17 slabs. These are 17 of many slabs which are placed around the stupa, People walk on this inscription when worshiping the Caitiya which on this inscription was known as the Tisa maha cheitiya. This inscription is of the period King Sirinaga of 2 Cent AD and lay buried under the debris, which is now cleared. Most visitors to this site is unaware of the historical importance of this inscription. I visited this site in November 2004 and I asked the Watcher about this inscription, unfortunately he was unaware of its existence. I walked around this Stupa on the stone pavement which ran around its circumferance. I notice to my horror that I was walking on the inscription which is on 17 of the slabs that make up the pavement. All visitors walk over this inscription most without even noticing it. A few photo are attached , there were remnants of pieces of bottles broken on the inscription.
The traces of the Numbers or Numerals used by our ancestors is found on this inscription. These numbers symbols are similar to the Indain Numerals which the Arabs copied and introduced to the west about the 14 Cent AD. The trace of 6 Numbers are found an Asokian inscription at Nanghat in Bombay. Which is the earliest available, The Nasik Inscription dated to the 2 Cent AD is also famous for the ancient Hindu numerals.
This inscription which is about the same period as of Nasik and is of great significance to the Sri Lankans. There are many other inscription of the Island where traces of ancient Numerals, these are dated from 2 Cent BC to 3 Cent AD. Except for that at Situlpavu which is of the 1 Cent AD, the other has only one to three ancient Numerals to express symbolically the number of Kahapanas[ Silver Coins] and Karisa[ Measure of land 4 Acres in extent] transacted for various purposes. The Situlpavu Inscription has traces of fair amount of numerals depicting Tens and Hundred.
This inscription is a lengthy account of a large number allotments of lands which are named by various personalities including Royalty . The extent of land is given in the ancient measure of land the Karisa which is equivalent to about 4 acres in extent. In addition to the Numerals an symbol for karisha is always placed beside it. The placement of this symbol follows a uniform set proceedure. These allotments of lands and Fields to this Monastery for its upkeeps is described in detail by Dr Paranavitane in Inscriptions of Ceylon Vol II Part 2.
The Karisa Symbol followed by Numeral 100 symbol 6 Karisa symbol Numeral 3. Drparanavitane identifies the worn letters in line 4 end as kariha sa sata ca tini kariha , which is 603 karihas.
Kariha symbol Numeral 100 Numeral 4 karina symbol sybol 70 and symbol 7. Line 5and continued to 6 is catara kariha ca sata satati Kariha, which is four hundred and seventy seven karihas.
Slab 9 line 7
Kariha symbol Numeral 100 Numeral 9 Kariha symbol Numeral 4. Line six is Nava kiriha sata ca catara kiriha ca, which means Nine Hundred and four karahas.
The Kariha symbol[ line 5] Numeral 50 Kariha symbol Numeral 5. These symbol are preceded by words Pasa panasa kiraha, which fifty five karihas..
The Kariha symbol Numeral 100 and Numeral 4 Kariha symbol then Numeral 20 . These symbol are preceded by the words in Line
3 catara kiraha sata ca visiti kiraha ca. This is Four hundred and twenty karahas.
Kariha symbol Numeral 1000 kariha symbol Numeral 100 Kariha symbol Numeral 9. Words in line 3 eka krahi sahasa sata ca …….
Which means One thosand and one hundred and …. Kariha.