Simple Sanskrit – Lesson 7
सरलं संस्कृतम् – सप्तमः पाठः 
In Lesson 6, we studied vowelending words up to इकारान्त along with the numerals द्वि त्रि. It would become mundane to keep on detailing declensions of other vowelending words and also consonantending words. Those could possibly be added later on in annexes.
Having detailed in the previous lesson, the declensions of the numerals एक द्वि त्रि and having noted towards the closing, “There is much more to learn about numbers. That merits a separate chapter.” it should be appropriate to discuss “numbers” संख्या: right away.
We use numbers in different ways. For counting we use cardinal numbers. They are adjectival and have gender, case and number, corresponding to the person or thing being counted. That is why we had in the previous lesson, declensions of एक द्वि त्रि in all three genders and in all cases. It should be appropriate to note declensions of चतुर् (= four) right away.
Table 71
Declensions of pronounadjective चतुर् (= four)
विभक्तिः ↓ वचनम् → 
पुंल्लिङ्ग बहुवचनम् 
नपुंसकलिङ्ग बहुवचनम् 
स्त्रीलिङग बहुवचनम् 
प्रथमा

चत्वारः

चत्वारि

चतस्रः

द्वितीया

चतुरः

चत्वारि

चतस्रः

तृतीया

चतुर्भिः

चतुर्भिः

चतसृभिः

चतुर्थी

चतुर्भ्यः

चतुर्भ्यः

चतसृभ्यः

पञ्चमी

चतुर्भ्यः

चतुर्भ्यः

चतसृभ्यः

षष्ठी

चतुर्णाम्

चतुर्णाम्

चतसृणाम्

सप्तमी

चतुर्षु

चतुर्षु

चतसृषु

It would be noted that
 declensions are in plural
 declensions in masculine and neuter genders are same in third case onwards.
For numbers from पञ्च (= five) right up to शत (= hundred), declensions are common in all three genders.
We also need numbers for telling the rank or serial order. Such numbers are called the Ordinals . In Table 72 are listed प्रातिपदिकs both cardinal and ordinal for numbers from 1 to 20.
Table 72
cardinal and ordinal प्रातिपदिकs for numbers from 1 to 20
Number

संख्यावाचकविशेषणम्

Ordinal

क्रमवाचकविशेषणम्

स्त्रीलिङ्गि क्रमवाचकविशेषणम् e.g. for विभक्ति or तिथि

Group of

समेत्य

1

१ एक

First

प्रथम

प्रथमा

–

–

2

२ द्वि

Second

द्वितीय

द्वितीया

Pair or couplet

द्वयम् द्वयी

3

३ त्रि

Third

तृतीय

तृतीया

triplet, trio

त्रयम् त्रयी

4

४ चतुर्

Fourth

चतुर्थ

चतुर्थी

quartet


5

५ पञ्च

Fifth

पञ्चम

पञ्चमी

quintet

पञ्चकम्

6

६ षट्

Sixth

षष्ठ

षष्ठी

sextet


7

७ सप्त

Seventh

सप्तम

सप्तमी

heptad

सप्तकम्

8

८ अष्ट

Eighth

अष्टम

अष्टमी

octet, octave

अष्टकम्

9

९ नव

Ninth

नवम

नवमी



10

१० दश

Tenth

दशम

दशमी

decade

दशकम्

11

११ एकादश

Eleventh

एकादश

एकादशी



12

१२ द्वादश

Twelfth

द्वादश

द्वादशी

dozen


13

१३ त्रयोदश

Thirteenth

त्रयोदश

त्रयोदशी



14

१४ चतुर्दश

Fourteenth

चतुर्दश

चतुर्दशी



15

१५ पञ्चदश

Fifteenth

पञ्चदश

पञ्चदशी, पौर्णिमातिथि: अमावस्यातिथि:


(तिथीनां) पक्षः

16

१६ षोडश

Sixteenth

षोडश

षोडशी



17

१७ सप्तदश

Seventeenth

सप्तदश

सप्तदशी



18

१८ अष्टादश

Eighteenth

अष्टादश

अष्टादशी



19

१९ नवदश एकोनविंशति एकान्नविंशति ऊनविंशति

Nineteenth

नवदश एकोनविंशतितम

नवदशी एकोनविंशतितमा



20

२० विंशति

Twentieth

विंश, विंशतितम

विंशी, विंशतितमा

score

विंशति

Further multiples of ten are ३० त्रिंशत् ४० चत्वारिंशत् ५० पञ्चाशत् ६० षष्टि ७० सप्तति ८० अशीति ९० नवति १०० शत
For cardinal numbers every set of ten has the number of unit’s place first followed by the multiple of ten, e.g.
२१ एकविंशति २२ द्वाविंशति २३ त्रयोविंशति २४ चतुर्विंशति २५ पञ्चविंशति
२६ षड्विंशति २७ सप्तविंशति २८ अष्टाविंशति २९ नवविंशति ३० त्रिंशत्
३१ एकत्रिंशत् ३२ द्वात्रिंशत् ३३ त्रयस्त्रिंशत् ३४ चतुस्त्रिंशत् ३५ पञ्चत्रिंशत्
३६ षट्त्रिंशत् ३७ सप्तत्रिंशत् ३८ अष्टात्रिंशत् ३९ नवत्रिंशत् ४० चत्वारिंशत्
४१ एकचत्वारिंशत् ४२ द्वाचत्वारिंशत् द्विचत्वारिंशत् ४३ त्रयश्चत्वारिंशत् त्रिचत्वारिंशत् ४४ चतुश्चत्वारिंशत्
४५ पञ्चचत्वारिंशत् ४६ षट्चत्वारिंशत् ४७ सप्तचत्वारिंशत् ४८ अष्टचत्वारिंशत् ४९ नवचत्वारिंशत् ५० पञ्चाशत्
५१ एकपञ्चाशत् ५२ द्विपञ्चाशत् ५३ त्रिपञ्चाशत् ५४ चतुःपञ्चाशत् ५५ पञ्चपञ्चाशत्
५६ षट्पञ्चाशत् ५७ सप्तपञ्चाशत् ५८ अष्टपञ्चाशत् ५९ नवपञ्चाशत् ६० षष्टिः
६१ एकषष्टिः ६२ द्वाषष्टिः द्विषष्टिः ६३ त्रयःषष्टिः त्रिषष्टिः ६४ चतुःषष्टिः ६५ पञ्चषष्टिः
६६ षट्षष्टिः ६७ सप्तषष्टिः ६८ अष्टषष्टिः ६९ नवषष्टिः ७० सप्ततिः
७१ एकसप्ततिः ७२ द्वासप्ततिः द्विसप्ततिः ७३ त्रयस्सप्ततिः त्रिसप्ततिः ७४ चतुस्सप्ततिः
७५ पञ्चसप्ततिः ७६ षट्सप्ततिः ७७ सप्तसप्ततिः ७८ अष्टसप्ततिः ७९ नवसप्ततिः ८० अशीतिः
८१ एकाशीतिः ८२ द्वाशीतिः द्व्यशीतिः ८३ त्र्यशीतिः ८४ चतुरशीतिः ८५ पञ्चाशीतिः
८६ षडशीतिः ८७ सप्ताशीतिः ८८ अष्टाशीतिः ८९ नवाशीतिः ९० नवतिः
९१ एकनवतिः ९२ द्वानवतिः द्विनवतिः ९३ त्रयोनवतिः त्रिनवतिः ९४ चतुर्नवतिः ९५ पञ्चनवतिः
९६ षण्णवतिः ९७ सप्तनवतिः ९८ अष्टनवतिः ९९ नवनवतिः १०० शतम्
It has been good to list all the cardinal numbers up to 100. There are two options for 22, 23, 32, 33 …. etc., even if I have missed them at some places.
Although only one option for 29, 39, etc. has been listed, there would be four options for each of them, as noted for the number 19 in Table 72.
In 81, 82 etc. they become एकाशीतिः … etc., since एकाशीतिः = एक + अशीतिः Also द्व्यशीतिः = द्वि + अशीतिः Here, the concept of resultant sound called as conjugation संधि gets naturally applied. Similar is the case for ८६ षडशीतिः, ९६ षण्णवतिः and many other numbers.
It should be noted that all cardinal numbers are to be used as adjectives but in singular and for numbers 5 and above, their declensions are common in all genders. Numbers ending in त् are त्कारान्त and neuter नपुंसकलिङ्गी. Numbers ending in तिः are इकारान्त स्त्रीलिङ्गी and would have declensions as per मति detailed in Table 610.
Masculine ordinal adjectives are found as number of every अध्याय in श्रीमद्भगवद्गीता, e.g. अष्टमोऽध्यायः. Here also concept of resultant sound called as conjugation संधि applies. Much larger ordinal numbers are found in श्रीमन्महाभारतम्. In पर्व १२ शान्तिपर्व there are ३६५ अध्यायs and the ordinal number of this अध्याय is given as पञ्चषष्ट्यधिकत्रिशततमोऽध्यायः
पञ्चषष्ट्यधिकत्रिशततमोऽध्यायः
 पञ्चषष्ट्यधिक = पञ्चषष्टि (65) adding to i.e. अधिक
 त्रिशत = three hundred
 तमोऽध्यायः = तमः अध्यायः = __ th Chapter
 पञ्चषष्ट्यधिकत्रिशततमोऽध्यायः = 365 th Chapter
In Book 4 of an edition of श्रीमन्महाभारतम् there is a tabulation of total number of श्लोकs. The gross count of श्लोकs is given as 100,217 संपूर्णा श्लोकसंख्या सप्तदशाधिकद्विशतोत्तरैकलक्षमिता. Note –
सप्तदशाधिकद्विशतोत्तरैकलक्षमिता =
 सप्तदशाधिकद्विशत = सप्तदश (17) अधिक i.e. adding to द्विशत (200) = 217
 उत्तरैकलक्ष = उत्तरएकलक्ष = after one lakh i.e. after 100,000
 मिता = of so much count is संपूर्णा श्लोकसंख्या i.e. total number of श्लोकs
It is to be noted that in both the examples above, numbers are composed by speaking of numbers in the unit’s place, then ten’s place and so on towards left. This is opposite of English style where we say 365 three hundred sixty five speaking the numbers from left to right.
Before going into such manner of speaking of large cardinal and ordinal numbers, it is pertinent to take note of some interesting points, which should come to notice in Table 72.
 The last column for ‘Group of i.e. समेत्य’ is very much in use. For example, instead of saying “60 boys षष्टिः कुमाराः”, one can say “three twenty’s of boys or three scores of boys कुमाराणां तिस्रः विंशतयः”.
 When saying “60 boys षष्टिः कुमाराः” 60 षष्टिः is numerical adjective of the noun ‘boys कुमाराः’.
 But when saying “three twenty’s of boys कुमाराणां तिस्रः विंशतयः”, ‘twenty’s विंशतयः’ is a noun in plural. तिस्रः is its numerical adjective also in plural.
 It is also to be noted that in “60 boys षष्टिः कुमाराः”, although 60 षष्टिः is numerical adjective of ‘boys कुमाराः’ in this construction षष्टिः the adjective is used only in singular. Also, षष्टिः is feminine, though कुमाराः is masculine. So the rule that adjective and the noun, which the adjective qualifies, must both be of same gender, in same case and of same number
यल्लिङ्गं यद्वचनं या च विभक्तिर्विशेष्यस्य ।
तल्लिङ्गं तद्वचनं सा च विभक्तिर्विशेषणस्यापि ।।
does not apply to numerical adjectives.
5. In the third column, one can see four options for 19. Such four options can be used for all other numbers as 29, 39, …. etc. Here
 ऊन means less. So ऊनविंशतिः means less than 20
 एकोन = एक + ऊन means one less (than); So, एकोनविंशति = one less than twenty
 एकान्न = एकात् न means ‘not due to one’; एकान्नविंशति: = not twenty due to one
6. In columns 4 and 5 the ordinals of numbers 20 and above can be formed in two ways –
 by enjoining a suffix तम or
 by deriving an अकारान्त प्रातिपदिक by dropping ति for example by getting विंश from विंशति.
We also use numbers to say ‘how many times’. In Sanskrit we use a suffix वारम् with the प्रातिपदिक, for example द्विवारम् (=twice, two times) त्रिवारम् (= thrice, three times) वारं वारम् (= again and again) बहुवारम् (= many times)
We also use ‘how many times’ to tell ratio of one quantity with other, e.g. “Four is double of two”, “Nine is triple of three”.
Rishis indulged in evolving a number system counting very large numbers. This involved having in the number system the concept of zero and of decimals दशांश, multiples (10, 20, 30 … etc.) and powers of 10 (10, 100, 1000…. etc.)
Table 73
Sanskrit numbers by powers of ten
Index of power of ten

Value

Number of ‘zero’s after 1

Name of the number

0

1 One 
0

एक

1

10 Ten 
1

दश

2

100 Hundred 
2

शत

3

1000 Thousand 
3

सहस्र

4

10,000 Ten thousand 
4

अयुत

5

100,000 Hundred thousand 
5

लक्ष

6

1,000,000 Million 
6

प्रयुत

7

10,000,000 Ten million 
7

कोटि

8

100,000,000 Hundred nillion 
8

अर्बुद

9

1000,000,000 Billion / Gega 
9

अब्ज

10

10,000.000,000 Ten billion 
10

खर्व

11

100,000.000,000 Hundred billion 
11

निखर्व

12

1000,000.000,000 Trillion 
12

महापद्म

13

10,000,000.000,000 Ten Trillion 
13

शङ्कु

14

100,000.000,000,000 Hundred trillion 
14

जलधि

15

1,000,000.000,000,000 
15

अन्त

16

10,000,000.000,000,000 
16

मध्य

17

100,000.000,000,000,000 
17

परार्ध

All these are summarized in a shloka as follows –
एकदशशत सहस्रायुतलक्षप्रयुतकोटयः क्रमशः 
अर्बुदमब्ज खर्वनिखर्वमहापद्मशङ्कवस्तस्मात् 
जलधिश्चान्तं मध्यं परार्धमिति दशगुणोत्तराः संज्ञाः 
संख्यायाः स्थानानां व्यवहारार्थं कृताः पूर्वैः 
All the above names of powers of 10 are neuter singular नपुंसकलिङ्गी.
Roman numerals are alphabetical, starting from I, II, III, IV, V, ….. L (=50) C (=100) D (=500) and M (= 1000). There is no symbol of zero.
When writing numbers, using numerals 1, 2, 3, we have use of commas for every 3 zero’s. The names for large numbers are also in steps of 3 zero’s – after ‘Thousand’ (3 zero’s), next name is ‘Million’ (6 zero’s) then ‘Billion’ (9 zeros). Numbernames in Sanskrit are for every extra zero i.e. for every power of 10 !
There is a shloka in अथर्ववेद wherein value of π (the ratio of circumference to diameter of a circle) is composed up to 32 digits. It reads –
गोपीभाग्यमधुव्रातश्रुङ्गिशोदधिसंधिग 
खलजीवितखाताव गलहालारसंधर 
For deciphering the value of π from this shloka, one needs to apply कटपयादि सूत्र –
कादिनव टादिनव पादिपञ्चक याद्यष्टक क्षः शून्यम् 
Method of using the कटपयादि सूत्र is –
कादिनव = nine letters starting from क would stand for numbers from 1 to 9
टादिनव = nine letters starting from ट would stand for numbers from 1 to 9
पादिपञ्चक = five letters starting from प would stand for numbers from 1 to 5
याद्यष्टक = eight letters starting from य would stand for numbers from 1 to 8
क्षः शून्यम् = क्ष for zero
Table 74
Alphabetical options for numerals as per कटपयादि सूत्र

1

2

3

4

5

6

7

8

9

0

कादिनव

क

ख

ग

घ

ङ

च

छ

ज

झ


टादिनव

ट

ठ

ड

ढ

ण

त

थ

द

ध


पादिपञ्चक

प

फ

ब

भ

म






याद्यष्टक

य

र

ल

व

श

ष

स

ह



शून्यम्










क्ष

Table 74 is similar to composing a sms on a mobile having only number keys. The concept of alphabetical coding of numerals is that old !! And how intelligently it is used for value of π up to 32 digits ! Isn’t it easy to remember a shloka than all the 32 digits correctly ? How intelligently the shloka is composed ! It has three interpretations – one, as a eulogy to Lord Krishna, secondly, as eulogy to Lord Shiva and thirdly as the value of π !! The scientific mode of calculator available on computers have a key for π. Once when exploring this key for π. I got value of π to 32 digits. When I checked the value with that by the above shloka, I found a difference only in the last 32nd digit. In the above shloka the 32nd digit is र = 2. In calculator of that computer I got 32nd digit to be 5.
When wondering why Rishi’s would have needed value of π to 32 digits, it comes to mind that the Rishi’s did indulge deeply in understanding movements of planets and their orbits, i.e. understanding astronomy in depth. Calculations in the realm of astronomy would certainly need value of π to be as accurate as possible. In astrology, it seems, they link up an astronomical combination of planets to the occurrence of an event in lives of people. This could be by some theory of probability, such as, if astronomical combination of planetpositions is working out to be so and so, likelihood of occurrence of a particular type of event is so much. For such analysis to be as accurate and in turn as reliable, the calculation of astronomical combination of planetpositions has to be accurate in the first place. That can be accurate only if value of π is used as accurate as possible.
In Sanskrit the concept of coding has been employed quite charmingly. There are codes derived from mythological concepts associated with different numbers.
Table 74
Mythological concepts associated with numbers and their use for coding
Number

Codeword

Mythological concept

Reference

1

ब्रह्म

ब्रह्म is only one


2

नेत्र, कर्ण

नेत्र and कर्ण are two


3

गुण

Implying the त्रिगुणs सत्त्वरजतम

सत्त्वं रजस्तम इति गुणाः प्रकृतिसंभवाः (गीता १४५)

4

वेद

वेदs are four


5

भूत

implying the पञ्चमहाभूतs – पृथ्वी, अप्, तेजस्, वायु, आकाश


6

दर्शन, शास्त्र

दर्शनs or शास्त्रs are six : सांख्य योग न्याय वैशेषिक मीमांसा वेदान्त


7

स्वर्ग, महर्षयः

स्वर्गs are seven भूः भुवः स्वः महः जनः तपः सत्यम्

महर्षयः सप्त पूर्वे (गीता, १०६)

8

वसु, करि

वसुs and करिs are eight


9

ग्रह

Planets are nine


ग्रहवसुकरिचंद्रमिते वर्षे = In the year 1889
There are many more concepts associated with different numbers, e.g.
मनु – They are said to be fourteen. However there is this quotation also चत्वारो मनवस्तथा (गीता, १०६)
Numbers are important not just for counting and arithmetic. Numbers are important in daytoday life for all metrological needs, for measuring distances, volumes, weights, time, etc. Systems of measurement have been various at different places at different times for different situations. In Mahabharata system of measurement is detailed to denote strength of armies. Strength of army on side of Pandavas was 7 अक्षौहिणी and on side of Kauravas was 11 अक्षौहिणी. There is a long sequence of calculations defining what one अक्षौहिणी is.
Coming to measurement of time, there is a quotation in GeetA, where it is said, one day of Brahma is equivalent to 1000 eras on earth and so is one night of Brahma.
सहस्रयुगपर्यन्तं अहर्यद्ब्रह्मणो विदुः 
रात्रिं युगसहस्राणां तेऽहोरात्रविदो जनाः  ८१७ 
Measurement of Time has occupied the minds of scientists since time immemorial. In SI system of units 1 second is defined as – The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
The smallest unit of time in Sanskrit is possibly निमिष or निमेष, which is time taken by eyelids to make one wink. But there is also क्षण translated as ‘moment’. In Apte’s dictionary क्षण is defined as measure of time equal to ⅘ of a second.
Then there is घटिका or घटी a measure of 24 minutes (Ref. – Apte’s dictionary) Also, मुहूर्त or मुहूर्तक a period of 48 minutes (Ref. – Apte’s dictionary)
Some detailed definition is available in मनुस्मृति There it is said –
निमेषे दश चाष्टौ च काष्ठा त्रिंशत्तु ताः कलाः 
त्रिंशत्कला मुहूर्तः स्यात् अहोरात्रं तु तावतः  (१६८)
निमेष is time taken by eyelids to make one wink
18 निमेषs = 1 काष्ठा; 30 काष्ठाs = 1 कला; 30 कलाs = 1 मुहूर्त; 30 मुहूर्तs = 1 daynight (average 24 hours) That makes 1 daynight = 306,000 निमेषs At 3600 seconds to an hour, 24 hours become 86,400 seconds. By that 1 second = 3.541666666666667 निमेषs
Most common unit of measurement of time is ‘day’. But if ‘day’ is to be understood as duration from one sunrise to the next, geographically its duration varies widely. They say, on the North pole there is sunlight for 6 months ! ‘Day’ as distinct from night is often considered to be the duration from sunrise to sunset. In अमरकोश one finds five synonyms for ‘day’ as घस्रो दिनाऽहनी वा तु क्लीबे दिवसवासरौ ।।१४२।। (इति पञ्च “दिनस्य” नामानि)
That makes one think how we shall tell time by the clock in Sanskrit. Since there are no exact words in Sanskrit for second, minute or hour, it has become an accepted practice to speak as follows –
Table 75
Time by the clock
Time In words

Time by clock

In Sanskrit

5 O’clock

5:00

पञ्चवादनसमयः

Quarter past 3

3:15

सपादत्रिवादनम्

Half past 7

7:30

सार्धसप्तवादनम्

Quarter to one

12:45

पादोनैकवादनम्

8 minutes past 9

9:08

अष्टाधिकनववादनम्

12 minutes to 12

11:48

द्वादशोनद्वादशवादनम्

am


माध्याह्नपूर्वम्

pm


माध्याह्नपश्चात्

12 noon

12:00

माध्याह्न:

12 midnight

0:00 am

मध्यरात्रिः

Units of measurement of distance, mass/weight have all changed over time. In the context of mass and weight one finds the concepts of even atom and molecule mentioned in अणोरणीयान् समनुस्मरेद्यः (गीता ८९)
However it would be appropriate to adopt into Sanskrit, names of units, as they are in common usage. It should be alright to speak of 2 kg of sugar as किलोद्वयशर्करा or of 5 litres of oil as पञ्च लिटरतावत् तैलम् (Note तावत् = that much).
शुभमस्तु 
oOo