अङ्कानां वामतो गतिः

[Arvind Kolhatkar]

Dear Group,

In the book ‘History of Hindu Mathematics’ by Bibhutibhushan Datta and Avadhesh Narayan Singh, published in 1935, I came across a comprehensive list of ‘word numerals’, i.e., words employed to record numbers, especially in inscriptions, copper-plate grants, in works on mathematics etc.  I enclose it as a .pdf enclosure for those who may be interested in it. 

As an example of the use of word-numerals, Leelavati says:

व्यासे भनन्दाग्निहते विभक्ते

खबाणसूर्यैः परिधि: सुसूक्ष्मः।

द्वाविंशतिनिघ्ने विहृतेऽथ शैलैः

स्थूलोऽथवा स्याद् व्यवहारयोग्यः॥

 

“if the diameter be multiplied by 3 अग्नि 9 नन्द 27 भ, and divided by 12 सूर्य 5 बाण 0 ख, (the resultant is) the circumference, which is very accurate. Or, if the diameter is multiplied by 22 and divided by 7 शैल, (the resultant circumference) is sufficiently accurate for common tasks.”

As the grants and the mathematical texts were often composed in meters, the wide choice presented by word numerals was very useful.

I am trying to understand the well-known rule अङ्कानां वामतो गतिः (the numbers go towards the left, or, alternatively, the words go in the opposite direction, as compared to the normal direction of writing that goes towards the right).  It appears to me the rule is applied when the numbers are spoken out and then written down.  In that case, the speaker starts with digit (or a group of digits like 27 in the above extract) that, in the written form of the number, appears on the extreme right.  He next speaks out the digit next on the left and so on till he reaches the end.  This is meant by अङ्कानां वामतो गतिः.

This rule is also seen in the names of cardinal numbers in Sanskrit.  In एकादशन् द्वादशन् त्रयोदशन् एकविंशति द्वाविंशति त्रयोविशति and in several other cardinals the digit in the unit place is spoken first and the digit in the tens place comes after it.  The way to correctly write down the number thus spoken out is to record the digit first spoken out in the unit place and record the next digit in the tens place to its left, thus moving leftwards.

 

I request other learned members to comment upon the rule अङ्कानां वामतो गतिः.

(An interesting aside.  Devanagari, Roman and most other scripts are written and read from the left to the right and putting down or reading a number or a date is done in the natural flow.  Some scripts like the Arabic and Persian are written and read from the right to the left.  However, even they record numbers and dates from the left to the right.  It creates a minor obstacle in the process of reading and writing as the eye has to change its direction of movement.)

Arvind Kolhatkar, Toronto, April 19, 2011.

[S. L. Abhyankar]

नमो नमः !
केचित् प्रश्नाः -
(१) कुत्र पठ्यते अयम् नियमः "अङ्कानां वामतो गतिः" ? कः अस्य मूलस्रोतः ?
(२) तः = ? वामतः = from left or towards left ?
(2-1) Ref.:- http://spokensanskrit.de/index.php?script=HK&beginning=0+&tinput=%E0%A4%B5%E0%A4%BE%E0%A4%AE%E0%A4%A4%E0%A4%83&country_ID=&trans=Translate&direction=AU

Sanskrit word

Transliteration

Grammar

English word

Edit (Login)

	वामतः	vaamataH	indecl.	to the left	edit
	वामतः चल	vaamataH cala	sentence	Keep to the left!	edit

(2-2) What is the meaning of this News report -

श्री देवड़ा द्वारा स्वेच्छानुदान राशि तः भोपालस्यपञ्च निर्धन जनान् नवतिः सहस्र स्वीकृतानि

Bhopal: Thursday, March 17, 2011: Updated 20:18IST

(Ref. :- http://www.mpinfo.org/mpinfonew/NewsDetails.aspx?newsid=110317N31&flag1=2 )

(३) "वयं पञ्चाधिकं शतम्" अस्मिन् विख्याते वाक्ये गतिः वामतः वा दक्षिणतः ?
(४) गोपीभाग्यमधुव्रात .... अस्यां रचनायां गतिः वामतः वा दक्षिणतः ?
(५) कथम् भणितव्या संख्या २०१२ ? "द्विसहस्र-द्वादश" इति सुष्ठु खलु ? का अत्र गतिः ?
(६) यदि संस्कृतभाषायां शब्दक्रमे स्वतंत्रता भवति तर्हि किमर्थं अयम् नियमः "अङ्कानां वामतो गतिः" ?
(७) "वक्ता दशसहस्रेषु" अत्र "दशसहस्रेषु" इति सामासिकः शब्दः ? कः अस्य विग्रहः ?

• ७-१ दश सहस्राः दशसहस्राः तेषु ?
• ७-२ सहस्राणां दशं दशसहस्रं तस्मिन् ?
• ७-३ दशं च सहस्रं च दशसहस्रम् (= १०१०) ---> तेषु ?
  

विनम्रं प्रार्थये स्पष्टीकरणानि  ।
सस्नेहम् ,
अभ्यंकरकुलोत्पन्नः श्रीपादः |
"श्रीपतेः पदयुगं स्मरणीयम् ।"

2011/4/20 Arvind Kolhatkar <kolhat...@gmail.com>

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[hnbhat B.R.]

2011/4/21 S. L. Abhyankar <sl.abh...@gmail.com>

नमो नमः !
केचित् प्रश्नाः -
(१) कुत्र पठ्यते अयम् नियमः "अङ्कानां वामतो गतिः" ? कः अस्य मूलस्रोतः ?

सर्वत्र प्रयोगेषु गणितग्रन्थेषु दृश्यन्ते, न साहित्यग्रन्थेषु; क्वचित् छन्दोग्रन्थेषु स्यात्।

मूलान्वेषणं तु भिन्नः प्रश्नः, अयं नियमः दृष्टां पद्दतिमानुसृत्य कल्पित इत्याभाति।

 

(२) तः = ? वामतः = from left or towards left ?
(2-1) Ref.:- http://spokensanskrit.de/index.php?script=HK&beginning=0+&tinput=%E0%A4%B5%E0%A4%BE%E0%A4%AE%E0%A4%A4%E0%A4%83&country_ID=&trans=Translate&direction=AU

Sanskrit word

Transliteration

Grammar

English word

Edit (Login)

	वामतः	vaamataH	indecl.	to the left	edit
	वामतः चल	vaamataH cala	sentence	Keep to the left!	edit

As usual, Sanskrit spoken today coins many well-framed sometimes ill-framed words. Questions based on the meaning depends on the context of news preparation exactly or according to the original words from which they are coined. Sanskrit language has nothbing to add or to loose the meaning of its native words.

With regards to question of meaning of this particular word, it specifically depends upon the context. As native usages can suggest:

वामेनात्र वटस्तमध्वगजनाः सेवते

The banyan tree to the left; can be conveyed by वामतो ऽत्र वटः but for metrical purpose it is conveyed with तृतीया विभक्तिः।

सो ऽभिगम्य महात्मानं कृत्वा रामं प्रदक्षिणम् । 

न्यवेदयदमेयात्मा दृष्टा सीतेति तत्त्वतः ।। 1.1.78 ॥

तत्त्वतः । सार्वविभक्तिकस्तसिः । दृष्टा सीतेति तत्त्वं न्यवेदयदित्यर्थः । 1.1.78 ।। 

used in the sense of द्वितीयाविभक्तिः।

"मन्त्रो हीनः स्वरतो वर्णतो वा" स्वरेण वर्णेन वा हीन इत्यर्थः। तृतीयार्थे।

5-4-45 अपादाने च अहीयरुहोः

इति पञ्चम्या विकल्प्यते - ग्रामाद् आगच्छति, ग्रामत आगच्छति

Strictly speaking it वामतः - वामाद् (दक्षिणं) चल from left to right. But it depends on from which direction you moving on the road. Not always the same direction, 

Aṣṭāṅgahṛdayasaṃhitā

AHS, Cikitsitasthāna, 15, 108.2

pāṭayed udaraṃ muktvā vāmataścaturaṅgulāt //

 

ArthaśāstraArthaŚ, 10, 1, 6.1
prathame purastān mantripurohitau dakṣiṇataḥ koṣṭhāgāraṃ mahānasaṃ ca vāmataḥ kupyāyudhāgāram // 

Arthasastra describes the position of Manti, treasure, kitchen, etc. in the sense of सप्तमीविभक्तिः to the left.

एते प्रामाणिकप्रयोगाः | 

Now it is left to you to decide the answer to your other questions in the light of the principle as highlighted by Mr. Aravindji who has authentically referred to a reliable text and on referring to the text you may find the answers for the rest of your questions..

Or wait till the principle is subjected to further analysis and a satisfactory explanation and scope of the principle is provided by some enlightened member of the group. I am out of the question as I am not गणितज्ञ either traditional or mathematician of modern times.. 

(2-2) What is the meaning of this News report -

श्री देवड़ा द्वारा स्वेच्छानुदान राशि तः भोपालस्यपञ्च निर्धन जनान् नवतिः सहस्र स्वीकृतानि

Bhopal: Thursday, March 17, 2011: Updated 20:18IST

(Ref. :- http://www.mpinfo.org/mpinfonew/NewsDetails.aspx?newsid=110317N31&flag1=2 )

 

(३) "वयं पञ्चाधिकं शतम्" अस्मिन् विख्याते वाक्ये गतिः वामतः वा दक्षिणतः ?
(४) गोपीभाग्यमधुव्रात .... अस्यां रचनायां गतिः वामतः वा दक्षिणतः ?
(५) कथम् भणितव्या संख्या २०१२ ? "द्विसहस्र-द्वादश" इति सुष्ठु खलु ? का अत्र गतिः ?
(६) यदि संस्कृतभाषायां शब्दक्रमे स्वतंत्रता भवति तर्हि किमर्थं अयम् नियमः "अङ्कानां वामतो गतिः" ?
(७) "वक्ता दशसहस्रेषु" अत्र "दशसहस्रेषु" इति सामासिकः शब्दः ? कः अस्य विग्रहः ?

• ७-१ दश सहस्राः दशसहस्राः तेषु ?
• ७-२ सहस्राणां दशं दशसहस्रं तस्मिन् ?
• ७-३ दशं च सहस्रं च दशसहस्रम् (= १०१०) ---> तेषु ? 
  

For the analysis of the 4th question, please refer to the page where the numeral value of the verse is given. I am not sure it has followed the principle. Like the title of his work Vedic Mathematics, he need not follow the convention practiced by astronomers and गणितज्ञ-s of ancient time. About the other questions, you are hurrying before the nature and scope of the principle is clearly understood for which this topic was started.

 

“if the diameter be multiplied by 3 अग्नि 9 नन्द 27 भ, and divided by 12 सूर्य 5 बाण 0 ख, (the resultant is) the circumference, which is very accurate. Or, if the diameter is multiplied by 22 and divided by 7 शैल, (the resultant circumference) is sufficiently accurate for common tasks.”

Regarding the above example cited by Aravindji, the counting depends on the mythological representations by those numbers.

Agni represents the three Agni-s, called Treta which also can be used if occasion demands. 

"दक्षिणाग्नि-र्गार्हपत्याहवनीयौ त्रयोऽग्नयः. ८५०) अग्नित्रयमिदं त्रेता"

called दक्षिणाग्नि  गार्हपत्य  आहवनीय 

In the same way, नन्द-s are nine, popularly associated with Chanakya and Chandragupta. 

भम् = नक्ष्त्र २७ beginning with अश्विनी, भरणी etc. ending with रेवती.

नक्षत्रमृक्षं भं तारा तारकाऽप्युडु वा स्त्रियाम् ( १. ३. २१८) दाक्षायिण्योऽश्विनीत्यादितारा 

सूरसूर्यार्यमादित्यद्वादशात्मदिवाकराः।
भास्कराहस्करब्रध्नप्रभाकरविभाकराः ।।१-३-२८।। 

For बाण 5 it is the number of arrows of Kama:

Five floral Arrows of Kamadeva ( १. १. ५७) अरविन्दमशोकं च चूतं च नवमल्लिका ( १. १. ५८) नीलोत्पलं च पञ्चैते पञ्चबाणस्य सायकाः Five physical arrows of Kamadeva ( १. १. ५९) उन्मादनस्तापनश्च शोषणः स्तम्भनस्तथा ( १. १. ६०) संमोहनश्च कामश्च पञ्च बाणाः प्रकीर्तिताः

खम् - आकाशम् - empty space; number  0

शैल - ७; सप्त कुलाचलाः;

 तत्रापि रैवतकविन्ध्यसह्यकुमारमलयश्रीपरवतपारियात्राः। सप्त कुलाचलाः।

or 

महेन्द्रो मलयः सह्यः शुक्तिमान् ऋक्षवानपि | विन्ध्यश्च पारियात्रश्च सप्तैते कुलपर्वता ||

similar counting here from some commentary on Brihadaranyaka:

वसवः अष्टसंख्यो गुणः, तथैकादश रुद्राः; द्वादश आदित्याः, विश्वे देवाः त्रयोदश विश्वाया अपत्यानि --- सर्वे वा देवाः,

मरुतः सप्त सप्त 

If my guess is right, अङ्कानां वामतो गतिः is applicable to the numeral system  कटपयादि . Whether it is applied to this numbering system is yet to be verified.  It is seen in other texts applied to this system too:

शुद्धभेदैः सह शरेषुयुगखेन्दवः (१०४५५)

Kavyaprakasha.

Here is one more citation using कटपयादि from नारायणीयम् -

That word is: आयुरारोग्यसौख्यम् - aayuraarogyasaukhyam.  Using (कटपयादि संख्या) katapayaadi protocol, this word translates to the number 1712210. Scholars think that this meant the work was completed on the 1712210th day of kaliyuga (कलियुग).  Also, astrologers and scholars worked this out to conclude that that day was the 28th day of the month of Vrischkam (वॄश्छिकम्) of the Kollam Era year 762.

The related discussion on the quoted can be seen in this page:

http://annaswamynatarajan.sulekha.com/blog/post/2010/11/sriman-narayaneeyam-by-melpathur-narayana-bahattathiri.htm

Any body can verify the application of both the systems in these two examples from literature.

Further analysis of the convention is welcome.

With regards

Dr. Hari Narayana Bhat B.R.
EFEO,
PONDICHERRY

[P.K.Ramakrishnan]

There are two methods of denoting numbers in Sanskrit.

One is called bhutasamkhya.  This name has come from the idea that bhutas are

five in number.   Therefore to denote 5 it is sufficient to say bhuta.  If we want to say

1 it can be said by saying prithivi, the first of the pancha-bhutas.  To mean 14 we

can say manu.  Here is a quotation from Varahamihira using bhuta-samkhya -

दश-शिखि-मनुयुक्-तिथी-न्द्रियांशै: 

दश = ten

शिखि = अग्नि = 3 referring to the third of

the pancha-bhutas - पृथिवी, अप्, तेज:, वायु:, आकाश:

मनुयुक् = Two manus = 28 (there are 14 manus)

तिथि = 15

इन्द्रिय = 5 (there are 5 indriyas to know श्ब्द रूप रस स्पर्श घ्राण 

(ear, eyes, tongue, skin and nose).

अंश refers to degree of the zodiac.

Bhutasamkhya is mostly followed in North India

The second system is  aksharasamkhya - denoting numbers by letters. 

The most common is katapayaadi system  which was followed in South India.

Vararuchi is supposed to be the author of this system.      

Members may be well aware of this system.

When this system is followed each letter has a value from 0 to 9.

A number may consist of any number of letters. The magnitude of the

number increases from left to right. 

For example 

eka = 1:

dasa  = 10 

satam  = 100

sahasram =  1000

ayutam= 10000

niyutam = 100000

and so on unending.

Therefore the statement -  

 अंकानां वामतो गति:

The number increases from left to right.

Melpathur Narayana Bhattathiri has used this method to denote the kalidinasambhya when he completed his treatise called Narayaniyam.

आयुरारोग्यसौख्यम्

0 1 2 2 1 7 1

But according to the rule -left to right,

this becomes 1712210.

Aryabhata has used another method of using letters to denote very large numbers.

-----------------------------------
P.K.Ramakrishnan
http://peekayar.blogspot.com

---

From: Arvind Kolhatkar <kolhat...@gmail.com>
To: sams...@googlegroups.com
Sent: Wed, 20 April, 2011 10:26:03 PM
Subject: [Samskrita] अङ्कानां वामतो गतिः

Dear Group,

In the book ‘History of Hindu Mathematics’ by Bibhutibhushan Datta and Avadhesh Narayan Singh, published in 1935, I came across a comprehensive list of ‘word numerals’, i.e., words employed to record numbers, especially in inscriptions, copper-plate grants, in works on mathematics etc.  I enclose it as a .pdf enclosure for those who may be interested in it. 

As an example of the use of word-numerals, Leelavati says:

व्यासे भनन्दाग्निहते विभक्ते

खबाणसूर्यैः परिधि: सुसूक्ष्मः।

द्वाविंशतिनिघ्ने विहृतेऽथ शैलैः

स्थूलोऽथवा स्याद् व्यवहारयोग्यः॥

 

“if the diameter be multiplied by 3 अग्नि 9 नन्द 27 भ, and divided by 12 सूर्य 5 बाण 0 ख, (the resultant is) the circumference, which is very accurate. Or, if the diameter is multiplied by 22 and divided by 7 शैल, (the resultant circumference) is sufficiently accurate for common tasks.”

[hnbhat B.R.]

Thanks for the explanation. I had already quoted Ayurarogyasaukhyam.

--

[hnbhat B.R.]

Just reading the first message of Aravindji, it is not special to Sanskrit as he has interpreted एकादश, द्वादश, त्रयोदश  etc. numerals.

Yes. In writing using numerals they are written from right to left =

11, 12, 13, 14 etc.

It is the same with English also. 

Eleven, twelve (two+ten), thirteen (three - tens), fourteen (four+ten) the phonetic changes may be explained in the same way as एकादश, etc. where the individual numbers have undergone little change. Now, Hindi speaker, Aravindji will attest the Hindi numerals too:

दस, ग्यारह्, तेरह्, etc. undergoing the changes to from एकादश, द्वादश, etc. sanskrit numbers through Prakrit languages.

Is the rule applicable then to Sanskrit only? Possibly not. This is with the pure numerals without any encoding complicated. 

The two other systems add only change of encoding system. But the same principle is seen applicable in both the examples cited for each. as I have already cited a large number:

शुद्धभेदैः सह शरेषुयुगखेन्दवः (१०४५५) 

शर - ५,

इषु - ५,

युग - ४,

ख - ०

इन्दु - १ ===== will make the figure given above arranging from right to left beginning from 1 as can be seen in the above example.

The same with आयुरारोग्यसौख्यम्  denoting a large numeral counting the day of Kali Era as explained by me and Mr.Ramakrishnan.

Now the question is which one is meant by अङ्क the first one occurring in the verses or the numeral digits written corresponding to them in the maxim अङ्कानां वामतो गतिः। Strangely enough from our side we are reading it from left to right and while decoding it we have to read it from right to left (from our side). From the page, it will be reverse. It numeral digits has to be decoded by reading towards left of the page. Is this meant by the maxim?

In any case, it is too applicable numerals in English. I don't know about other numerals in words and fitures. But 1, 2, 3 are called Arabic numerals even though they are used in English language. I remember having read that 0 was Indian contribution. Comparing numbers in words and figures may help to arrive at the origin  of the principle.

In Dravidian languages, it is the revers, pattu + randu (10+12) = 12, pattu + onnu - padinonnu 11 etc. there is no change of order between the words denoting them and figures written denoting the numerals.

May be the characteristic inherited from Indo European group. representing with figures, it has to change the order. 

Little farther continued the scrutiny.

[Vasantha Lakshmi]

भोः अभिवादये।
मम नाम वसन्थ लक्ष्मी ।
अहं भवत्यः लेखः  'अन्कानां वामनो गथि' पथितवथि।
एतत् विवरणं बहु सम्यक अस्थि।
मया किञ्चित्  संस्कृतं आगचथि।
यदि दोषाः संथि चेतः क्षम्यतां ।
पुनर्मिलामः।
वसन्थ लक्ष्मी ,
Visakhapatnam

2011/4/21 P.K.Ramakrishnan <peek...@yahoo.com>

[hnbhat B.R.]

Here is the Vikipeadia link to both the systems;

Aryabhatiya and bhutasamkhya as they are called in the article. Both are interlinked.

http://en.wikipedia.org/wiki/Bhutasamkhya_system#cite_note-Sircar-0

Interested people may directly read the details there.

Thanks once again to Mr. Ramakrishnan for providing the information about the two systems.

[Arvind_Kolhatkar]

Dear Group,

I too, like Abhyankarji, was not sure about the proper meaning of
अङ्कानां वामतो गतिः. However, every authority seems certain that it
means that ‘numbers proceed to the leftward’. Datta and Singh say the
following and also give an explanation as to how this expression got
created.

<The extensive use of word numerals by early mathematicians such as
Pulisha, Varahamihira, Lalla and others appears to have set the
fashion to write the word numerals with a right to left arrangement,
which was generally followed by later writers.

No explanation as to why the right to left arrangement was preferred
in the word system is to be found in any of the ancient works. The
following explanation suggests itself to us, and we believe that it is
not far from the truth. The different words forming a number
chronogram were to be so selected that the resulting word expression
would fit in with the meter used. To facilitate the selection the
number was first written down in numerical figures. The selection of
the selection of the proper words would then, naturally, begin with
the figure in the unit place, and proceed to the left just as in
arithmetical operations. This is in accordance with the rule “ankanam
vamato gatih”, i.e., ‘the numerals proceed to the left’ which seems to
have been very popular with the Indian mathematicians. The right to
left arrangement is thus due to the desire of the mathematicians to
look upon the formation of the word chronogram as a sort of
arithmetical operation.> p. 62

Dr. Bhat’s observes that English also follows the same pattern as that
of Sanskrit (putting the smaller number first and the larger next to
it) for numbers like eleean, twelve, thirteen, fourteen. Indeed, but
that is true only till twenty. From twenty-one onwards, English
reverses itself and starts putting the larger number first as in
twenty-one, twenty-two etc. Sanskrit continues with the original
pattern.

The Russian language follows the same pattern as that of English. See
одиннадцатЬ, двенадцать, тринадцать etc. for eleven, twelve, thirteen
till nineteen. The smaller component comes first. However, this is
reversed from twent-one onwards. двадцать is twenty. The numbers
thereafter are двадцать один, двадцать два, двадцать три etc., the
larger component coming first and the smaller following it.

Arvind Kolhatkar, Tornto, April 21, 2011.

[Arvind_Kolhatkar]

Dear Group,

Dr Bhat observes “But 1, 2, 3 are called Arabic numerals even though

they are used in English language. I remember having read that 0 was

Indian contribution. “

They are called Arabic numerals because they travelled from India to
Europe some time before the 10th century through the Arabs. It is now
widely known that their true origin was in India but ‘social drag’
ensures that the old name continues.

0 and the important concept of positional value to digits was another
very important contribution of the Indians. Just as no one knows who
invented the first wheel, so also the person or persons who thought of
this ingenious system of writing numbers are not known. What is
certain is, however, that this system ‘tamed’ numbers. Any number, no
matter how large, can be easily worked upon and manipulated with the
help of the four easily learnt basic operations, when it is expressed
as per the ‘Indian’ system . The Romans could never have multiplied
two large multi-digit numbers with the same ease that a schoolboy can
display today. It is no exaggeration to say that renaissance science
progressed in Europe only because Indian numeral system had reached
there by that time, making arithmetical calculations very easy.

Arvind Kolhatkar, Toronto, April 21, 2011.

[Adolf von Württemberg]

प्रिय Arvind,
Good comment!
Re: your statement - They are called Arabic numerals because they travelled from India to Europe some time before the 10th century through the Arabs. It is now widely known that their true origin was in India but ‘social drag’

ensures that the old name continues.

My comment: One of my colleagues who teaches Arabic said that in Arabic they call the numerals the 'Hindu number system'!

"It is worthy of remark that a belief constantly inculcated during the early years of life, whilst the brain is impressible, appears to acquire almost the nature of an instinct; and the very essence of an instinct is that it is followed independently of reason."
- Charles Darwin (1809 – 1882), The Descent of Man, 1871

Dear Group,

--

[hnbhat B.R.]

Thanks Arvindji for taking into consideration my observations.

To come to the the comparison of English and Sanskrit counting, again, up to the count twenty follows the same in between 11 - 19 and there after too it is changed in English for the intermediate numbers like twenty-one to -nine, thirty-one to -nine and so on.

The multiples of 10s are counted in the same order as before. dashat is used for the group of tens in sanskrit as can be seen in the list below. 

two tens - twenty

dvau dashatau - dvaa-viM-shati

three-tens - thirty

tisro dashataH - triM-shat

four tens - four-ty

catvaraH dashataH - catvaariM-shat 

 

five tens - fig-ty

pa~nca dashataH - panca-shat

six tens - sixty

Shat dashataH 

seven tens - seventy

sapta dashataH - sapta-tiH (hereafter the sanskrit words loose the trace of dashat)

astha dashataH - ashItiH (only remainder is ti as in vimshati)

nava dashataH - navatiH 

Hereafter both lost the trace of the multiples and multipled.

dasha dashataH - shataM (only remainder of dashat plus)

ten tens - hundred

Dravidian languages maintain through out the same system.

3 tens munRu pattu - murpadu (30) p muppadu  _ Onnru (31)

With regards

[Sunder Hattangadi]

Would someone kindly post how the decimal fractions are pronounced? (one-tenthe, 3-hudredths, etc)  Thanks.

 

 

 

Regards,

 

sunder

[Vasu Srinivasan]

Quoting Bhat-ji's

"If my guess is right, अङ्कानां वामतो गतिः is applicable to the numeral system  कटपयादि . Whether it is applied to this numbering system is yet to be verified.  It is seen in other texts applied to this system too:"

The katapayaadi system is prevelant in the naming of melakarta ragas in current carnatic system too (kanakangi, ratnangi - all the way to rasikapriya) - the first two letters represent 01, 02, 03 ...upto  72.

If ankaanaam vaamato gati: applies here too, then "kana = 10" becomes "01" which means the number is being read from left-to-right from the number's perspective (from a reader's perspective it is right-to-left).


--
Regards,
Vasu Srinivasan
-----------------------------------
vagartham.blogspot.com
vasya10.wordpress.com

2011/4/22 Sunder Hattangadi <sun...@yahoo.com>

--

[Krishnanand Mankikar]

 

 

We were told in our school that decimal numbers have to be pronounced as individual numbers. e.g. 64.36 is to be pronounced as sixtyfour point three six (and not sixtyfour point thirysix -- since the weight of the number place is to be stated for the numbers to the left of the decimal point, according to our maths teacher)

(I hope, I have understood the question correctly)

 

Regards

k.

 

 

2011/4/22 Sunder Hattangadi <sun...@yahoo.com>

--

[Sunder Hattangadi]

Thank you. Actually, I meant how to pronounce it in Sanskrit.

 

 

Regards,

 

sunder