Shad Vedangas (षड्वेदाङ्गानि)

Vedangas (Samskrit : वेदाङ्गम्) literally meaning 'limbs of the Veda' are the six angas or explanatory limbs to the Vedas. They include Shiksha (authored by various rishis), Vyakarana of Panini, the Chandas of Pingalacharya, the Nirukta of Maharshi Yaska, the Jyotish of Lagadha and the Kalpas (Shrauta, Grhya, Dharma and Shulba) belonging to the authorship of various Rishis.

It is said that Bhagavan Vishnu incarnated as Maharshi Veda Vyasa in Dvapara yuga and organized the Vedas in their present form. Maharshi Vyasa's efforts brought about uniformity in the religious observances thereby performance of rites and rituals, religious ceremonies, yajnas (sacrifices) and vratas (vows) continued without any flaw. As Vedas have different aspects of understanding to them, various types of expositions on Vedas came into existence and each became a subject to be learnt for a comprehensive understanding of the Vedas to be achieved. Maharshi Yaska, who gave Nirukta to the world, also expounded vedic terminology on the basis of legends and ancient lore. Manu, the Law giver of ancient Bharatavarsha, laid down certain instructions as to how the teaching of Vedas should be conducted.

Etymology

Vedangas (वेदाङ्गानि) help us construct, chant and understand Veda mantras. These are called Angas (अङ्गानि | ancillaries) to Vedas. The word 'अङ्गम्' is used in the sense of "उपकारक' - 'अंग्यन्ते ज्ञायन्ते अमीभिरिति अङ्गानि' meaning Angas are those by using which one understands the nature of an object/subject (here Vedas). Vedas are by themselves profound both in language and concept.

शिक्षा कल्पो व्याकरणं निरुक्तं छन्दसां चयः । ज्योतिषामयनं चैव वेदाङ्गानि षडेव तु ॥

śikṣā kalpo vyākaraṇaṃ niruktaṃ chandasāṃ cayaḥ । jyotiṣāmayanaṃ caiva vedāṅgāni ṣaḍeva tu ॥

According to the above shloka, Vedangas are six in number namely Shiksa (शिक्षा), Kalpa (कल्पः), Vyakarana (व्याकरणम्), Nirukta (निरुक्तम्), Chandas (छन्दस्) and Jyotish (ज्योतिष्).

वेदाङ्गानि ॥ Vedangas

Included in the Chaturdasha vidyas, Vedangas classified under the Smrti class of literature, are significant to gain complete knowledge of the Vedas. One becomes proficient in six aspects by adhyayana of Vedangas

• Shiksha - Pronunciation of the veda mantras
• Kalpa - Practice of the yajnas and yagas
• Vyakarana - Construction of words and knowing the primary meaning
• Nirukta - Meanings of words according to the vedic context
• Chandas - Metrical composition and patha-paddhati of mantras
• Jyotisha - Knowledge of appropriate time and place to perform yajnas and yagas.

शिक्षा ॥ Shiksha

Shiksha deals mainly with svarajnana (स्वरज्ञानम् | phonetics) and it is the science disciplining the efforts of ear, nose and vocal cords to utter the accurate sound as defined by Vedic mantras.

Shiksha deals with the origin of sound and teaches one about the production of accurate sound shuddhoccharana (शुध्दोच्चारणम्) with ease. In Vedic literature, accurate pronunciation of sound (vowels and consonants) is of great importance else the meaning is completely altered, hence Vedas have svarapradhanyatva (स्वरप्राधान्यत्वम्).

The earliest reference to Shiksha attached to Taittireeya Aranyaka (तैत्तिरीय-आरण्यकम्), extends the applicability as follows :

अथ शिक्षां व्याख्यास्यामः । वर्णः स्वरः । मात्रा बलम् । साम सन्तान। इत्युक्तः शिक्षाध्यायः ॥ (Tait. Aran. 7.2)

atha śikṣāṃ vyākhyāsyāmaḥ । varṇaḥ svaraḥ । mātrā balam । sāma santāna। ityuktaḥ śikṣādhyāyaḥ ॥ (Tait. Aran. 7.2)

Meaning : Let us comment about Shiksha. Shiksha study involves Varna, Svara, Matra, Bala, Sama, Santana.

Where,

1. वर्णः ॥ Varna - वर्णः अकारादिः । varṇaḥ akārādiḥ । - Varnas are the letters including Vowels and Consonants.
2. स्वरः ॥ Svara - स्वरस्तु उदात्तादिः । svarastu udāttādiḥ । - Svaras (Accents) are of three kinds udatta (उदात्तः | acute accent), anudatta (अनुदात्तः | accentless), svarita (स्वरितः | normal accent).
3. मात्रा ॥ Matra - मात्रा ह्रस्वादिकाः । mātrā hrasvādikāḥ । - Prosodically or metrically, hrsva (ह्रस्व | short), deergha (दीर्घ | long), pluta (प्लुत | prolated)
4. बलम् ॥ Bala - बलम् उच्चारणस्थानं ताल्वादिकम् । balam uccāraṇasthānaṃ tālvādikam । - Part of body from where sound is produced, such as talu (तालु:), kantha (कण्ठः), ostha (ओष्ठः) etc.
5. साम ॥ Sama - साम निषादादिः । sāma niṣādādiḥ । - 7 Musical notes enumerated as 1.Nishada (निषादः) 2.Riṣhabha (रिषभः) 3.Gandhara (गान्धारः) 4.Shadja (सड्जः) 5.Madhyama ( मध्यमः) 6.Dhaivata (धैवतः) 7.Pancama (पञ्चमः)
6. सन्तानः ॥ Santana - सन्तानो विकर्षणादि । santāno vikarṣaṇādi ।

Classical Sanskrit literature differs from Vedic literature, as it is not highly regulated by the uccharana (उच्चारणम् | utterance) which is important for the utterance of vedic mantras. Hence, Shiksha is of vital importance as an ancillary for vedas, because ashuddhoccharana (अशुध्दोच्चारणम् | wrong utterence) of mantras bring about a meaning change which can cause great harm to the yajamana (यजमानः | the performer of the yajna).

An example of such wrong utterance is typically explained by the legend of Vrttrasura's birth:

मन्त्रो हीनः स्वरतो वर्णतो वा मिथ्या प्रयुक्तो न तमर्थमाह । स वाग्वज्रो यजमानं हिनस्ति यथेन्द्रशत्रुः स्वरतोऽपराधात् ॥ (Pani. Shik. 42)

mantro hīnaḥ svarato varṇato vā mithyā prayukto na tamarthamāha । sa vāgvajro yajamānaṃ hinasti yathendraśatruḥ svarato'parādhāt ॥

If a mantra is devoid of a varna (letter), or has wrong utterances or svaras, then it does not the give the meaning it is intended to and produces a false meaning. This incorrectly and improperly uttered mantra becomes a vakvajra (वाक्वज्रः | word weapon) and is capable of destroying the yajamana (performer of the yajna). Example is the famous story of Indra's enemy, Vrtrasura (वृत्रासुरः) whose origin was due to svaraparadha (स्वरापराधः | wrong svara utterance) of a mantra.

वृत्रासुर-जननम् || Vrttrasura Janana

तत्त्वष्टाहवनीयमुप प्रावर्तयत्स्वाहेन्द्रशत्रुर्वर्धस्वेति यदवर्तयत्तद्वृत्रस्य वृत्रत्वं यदब्रवीत्स्वाहेन्द्रशत्रुर्वर्धस्वेति तस्मादस्येन्द्रः शत्रुरभवत् | (Tait. Samh. 2.5.2)

tattvaṣṭāhavanīyamupa prāvartayatsvāhendraśatrurvardhasveti yadavartayattadvṛtrasya vṛtratvaṃ yadabravītsvāhendraśatrurvardhasveti tasmādasyendraḥ śatrurabhavat | (Tait. Samh. 2.5.2)

Tvasta (त्वष्टा) angered by Indra's killing of his son Vishwaroopa, initiates an abhicharika yaga (अभिचारिक-यागः | a yaga performed to cause harm to an intended person) to procure a son to kill Indra. The rtvijas (ऋत्विज्-s) were to utter the mantra "इन्द्रशत्रुर्वर्धस्व" with Anta-Udatta (अन्त-उदात्तः) or Udatta svara in the end of the mantra (to mean, Prosper Oh ! Enemy of Indra). Instead, they used the Adya Udatta (आद्य-उदात्तः) or Udatta svara in the beginning of the mantra (meaning, Oh! Indra, one who has enemies, Prosper).So, instead of asking for the rise and prosperity of a son to take revenge on Indra, the Rtvijas asked for the prosperity and glory of Indra who destroyed Asuras. Thus, Vrtrasura, the son of Tvasta was born, an enemy of Indra, but eventually Indra was rewarded with glory in killing Vrtrasura.

Shiksha literature is very widely available based on the different shakhas (शाखा-s | divisions) of different vedas. They are Panineeya Shiksha (पाणिनीयशिक्षा), Vyasashiksha (व्यासशिक्षा), Bharadvaja shiksha (भारद्वाजशिक्षा), Yajnavalkya Shiksha (याज्ञवलक्यशिक्षा), Parashara shiksha (पराशरशिक्षा), Vasishtee shiksha (वासिष्टीशिक्षा), Katyayanee shiksha (कात्यायनीशिक्षा), Madhyandinee shiksha (माध्यन्दिनीशिक्षा), Keshavee shiksha (केशवीशिक्षा), Amoghanandinee shiksha (अमोघानन्दिनीशिक्षा), Mandavya shiksha (माण्डव्यशिक्षा), Mallasharma shiksha (मल्लशर्मशिक्षा), Svarakusha shiksha (स्वराकुशशिक्षा), Shodasha shiksha (षोडशशिक्षा), Naradeeya shiksha (नारदीयशिक्षा), Mandukeeya shiksha ( माण्डुकीयशिक्षा), Svarabhaktilakshana (स्वरभक्तिलक्षणशिक्षा), Avasananirnaya shiksha (अवसाननिर्णयशिक्षा), Varnaratna pradeepika shiksha (वर्णरत्नप्रदीपिकाशिक्षा) among many others.

कल्पः ॥ Kalpa

Kalpa (कल्पः) forms a set of texts which pertain to the different activities related to yajnas. Kalpa texts are composed in the famous Sutra format and have played a very significant role in the development of shastras such as Nyaya, Dharmas, Ganita (mathematics) in the subsequent times.

There are 4 types of Kalpa sutras

1. श्रौतसूत्राणि || Shrauta sutras - explain the दर्शपौर्णमासयज्ञः || Darshapournamasa Yajna and others as defined by Shruti
2. गृह्यसूत्राणि || Grhya sutras - explain the yajnas and samskaras (ceremonies) applicable to the domestic life a man and his family from birth to death and are to be followed by all people. The performance of Grhya yajnas requires only the laukikagni or domestic fire (aavasthya).
3. धर्मसूत्राणि || Dharma sutras - extensively give the dharmika rules for general people and the rulers. They are directly connected with the Grhyasutras which deal with dharma. Therefore, they deal with both secular and religious laws.
4. शुल्बसूत्राणि || Shulba sutras - Shastra for measurements, include the rekhaganita (रेखागणितम् | geometrical principles) laid down for vaidika constructions.

श्रौतसूत्राणि || Shrauta Sutras

The Shrauta Sutras vividly describe the procedures for the vaidika yajnas such as Darshapournamasa yajna (दर्शपौर्णमासयज्ञः), Agnihotra (अग्निहोत्रम्), Pashu yajna (पशुयज्ञः), and Soma yajna (सोमयज्ञः) among others as set forth in Shruti literature. Thus, it can be said that in Shrauta Sutras the explanations given in different Vaidika Brahamanas regarding Shrautagni yajnas (श्रौताग्नियज्ञाः) are dealt with in an orderly manner.

धर्मसूत्राणि || Dharma Sutras

Dharma Sutras expound the rules of Dharma and the actions (activities) to be performed by a person in general as well as the king or the ruler. A complete set of rules to be followed by the different people of different occupations and for those in the four ashramas (ब्रह्मचार्यः | brahmacharya, गृहस्थः | grhastha, वानप्रस्थः | vanaprastha and सन्यासः | sanyasa) are described in these sutras. Thus, it can be said that the topics related to the spiritual world, this material world, society and social activities, and all righteous activities are described in a holistic manner.

गृह्यसूत्राणि || Grhya Sutras

Grhya Sutras extensively discuss the yajnas (different from Shrauta Yajnas) to be performed by the brahmana, kshatriya and vaishya people. Most importantly, the षोडशसंस्काराः | Shodasa samskaras (from गर्भाधानम् | Garbhadhana to अन्त्येष्टिः | Antyeshti) that are performed for a person from birth till death are expounded vividly in these sutras. Thus, how a grhasta should lead his life and the procedure in which he has to conduct different dharmic activities are completely described here. The seven kinds of Grhya yajnas (गृह्ययज्ञाः) to be performed are:

1. पितृयज्ञः || Pitru Yajna
2. पार्वणयज्ञः || Parvana Yajna
3. अष्टकयज्ञः || Ashtaka Yajna
4. श्रावणीयज्ञः || Shravani yajna
5. आष्वेयुजीयज्ञः || Ashveyujee yajna
6. आग्रहायणीयज्ञः || Agrahayanee Yajna
7. चैत्रॆययज्ञः || Chaitreya Yajna

Apart from these seven, there are पञ्चमहायज्ञाः || Panchamahayajnas (five Yajnas) to be performed by all people which are

1. देवयज्ञः || Deva yajna
2. भूतयज्ञः || Bhuta yajna
3. पितृयज्ञः || Pitru yajna
4. ब्रह्मयज्ञः || Brahma yajna
5. मनुष्ययज्ञः || Manushya yajnas.

शुल्बसूत्राणि || Shulba Sutras

Shulba Sutras explain the different systems of measurements. Aspects of measurements of various vedinirmanavidhi (वेदिनिर्माणविधिः | altars and the procedure to construct them). For Example, homa shala (होमशाला), yajnashala (यज्ञशाला) are discussed. Thus, Vaidika Karmakanda (वैदिककर्मकाण्डः) is the topic for Shulbasutras, wherein geometry or the Rekhaganita (रेखागणितम्) is applied. Only those Shulbasutras associated with Yajurveda are available extensively indicating that Yajurveda is the main base for karmakanda.

Available Kalpasutra Literature

Shrautasutras	Grhyasutras	Dharmasutras	Shulbasutras
Ashvalayana (आश्वलायनः)	Ashvalayana (आश्वलायनः)	Vasishta (वासिष्ठः)	Varaha (वाराहः), Vadhula (वाधूलः)
Shankhayana (शाङ्खायनः)	Shankhayana (शाङ्खायनः)	Gautama (गौतमः)	Maitreyi (मैत्रेयी)
Katyayana (कात्यायनः)			Katyayana (कात्यायनः)
Hiranyakeshi (हिरण्यकेषी), Jaimineeya (जैमिनीयः), Vaitana (वैतानः), Latyayana (लाट्यायनः), Drahyayana Shrauta sutras (द्राह्यायनः)
Apastamba (आपस्तम्बः), Manava (मानवः), Baudhayana (बौधायनः) are commonly available Kalpa literature under all the four headings.

व्याकरणम् ॥ Vyakarana

Vyakarana is described as the Veda purusha's face.

व्याक्रियन्ते शब्दाः अनेन इति व्याकरणम् । vyākriyante śabdāḥ anena iti vyākaraṇam ।

व्याक्रियन्ते व्युत्पाद्यन्ते साधुशब्दा अस्मिन् अनेनेति वा . इति दुर्गादासः .. is the व्युत्पत्ति-अर्थः || vyutpatti artha or the subjective definition of word according to Durgadasa in Shabdakalpadruma

Shabdakalpadruma also gives deliberates on the content matter of Vyakarana as "तत्र साध्यसाधनकर्त्तृकर्म्मक्रिया-समासादिनिरूपणम् ." One where all grammatical aspects (vibhaktis, samasas etc are shown or derived)

This shastra only deliberates on the shuddhi-ashuddhi (accurate and inaccurate) usages of words in Sanskrita vangmaya (sanskrit literature). It is the grammar of sanskrit shlokas and it deals with the formation of words, different forms of the words and their combination, usage and semantic nuances. Although, Rigvedic references to grammar are available, it is only the Taittireeya samhita that outlines the story of origin of grammar. In Maharshi Yaska's Nirukta, different technical or conventional terms related to grammar are available in abundance.

It was Maharshi Panini who has given अष्टाध्यायी || Ashtadhyayi the most profound and brilliant treatise on grammar to the intellectual world, wherein he describes all the previous grammarians belonging to a time period before him. Also called Shabdanushasana (शब्दानुशासनम्), it was the Astadhyayi which brought about the regularization of grammatical rules of the vedic usages also.

Vyakarana is divided into Pracheena vyakarana (प्राचीनव्याकरणम्) and navya vyakarana (नव्यव्याकरणम्). Later age grammarians recognize the eight vyakarana shastra pravartakas (व्याकरणशास्त्रप्रवर्तकाः) as follows

इन्द्रश्चन्द्रः काशकृत्स्नापिशली शाकटायनः । पाणिन्यमरजैनेन्द्राः जयन्त्यष्टौ च शाब्दिकाः ॥

indraścandraḥ kāśakṛtsnāpiśalī śākaṭāyanaḥ । pāṇinyamarajainendrāḥ jayantyaṣṭau ca śābdikāḥ ॥

Indra (इन्द्रः), Chandra (चन्द्रः), Kasha (काशः), krtsnapishali (कृत्स्नापिशली), shakatayana (शाकटायनः), panini (पाणिनिः), amarajainendra (अमरजैनेन्द्रः), jayanti (जयन्तिः) are the eight preachers of shabda (word) or grammar.

निरुक्तम् ॥ Nirukta

Maharshi Yaska's Nirukta is another treasure that has been produced in Bharatavarsha and given to the world. It is an excellent treatise that deals with etymology or the objective definition of words. Nirukta is written in prose form while all other shastras are built in the sutra format. Sayanacharya (सायणाचार्यः) while giving the preface of Rigveda Bhashya (ऋग्वेदभाष्यम्) speaks thus about Nirukta :

अर्थावबोधे निरपेक्षतया पदजातं यत्रोक्तं तन्निरुक्तम् ।

arthāvabodhe nirapekṣatayā padajātaṃ yatroktaṃ tanniruktam ।

When other Vedangas extol the tattvas (तत्त्वानि | material aspects) of Vedas, Nirukta propounds the supernatural or the uncommon aspects or tattvas of the Vedas.

Yaskacharya has accepted 4 Jatis (जाति-s | types) called Bhedachatushtaya (भेदचतुष्टयम्) for words :

1. नामजातिः || Nama Jati : सत्वप्रधानम् || Satva pradhana - Significance attributed to existence of a thing as in Ghata (घटः | pot), Dhana (धनम् | Money)
2. आख्यातजातिः || Akhyata Jati : भावप्रधानम् || Bhava pradhana - Significance attributed to kriya (क्रिया | action) as in pathati (पठति | Read), karoti (करोति | Do).
3. उपसर्गजातिः || Upasarga Jati : नानाविधविशेष-अर्थप्रधानम् || Nanavidha vishesha artha pradhana - Significance attributed to a special meaning of one word as in Ahara (आहारः), samhara (संहारः), vihara (विहारः)
4. निपातजातिः || Nipata Jaati : उपमार्थे पदपूरणार्थम् || Upamarthe pada puranartha - Significance of comparison and for appropriate chandas as in eva (एव), na (न), cha (च).

Without the existence of Nirukta, understanding the Vedic terminology is extremely difficult. Yaskacharya in his preface to Nirukta says,

समाम्नायः समाम्नातः स व्याख्यातव्यः । इदमन्तरेण मन्त्रेष्वर्थप्रत्ययो न विद्यते इति ।

samāmnāyaḥ samāmnātaḥ sa vyākhyātavyaḥ । idamantareṇa mantreṣvarthapratyayo na vidyate iti ।

Meaning : Collection of the texts handed down by tradition are to be commented upon. Without this reference (nirukta), the meaning of mantras cannot be obtained.

Thus, it can be inferred that Nirukta determines the meanings of various vaidika mantras and comments on them. Knowledge about the various divine beings is given by Nirukta. Hence, its use in various yajna karmas is indispensable. Thus, only Nirukta experts can understand the different characteristics or identifying marks of various devatas praised in vedas.

Difference between व्याकरणम् and निरुक्तम् 

व्याकरणम् ।	निरुक्तम् ।
Vyakarana (Grammar) discusses the origin of the word.	Nirukta (etymology) determines the meaning. Thus, it completes the study of vyakarana.
Vyakarana is lakshana pradhana (लक्षणप्रधानम् | defines the attributes of a word).	Nirukta is artha pradhana (अर्थप्रधानम् | independently explains the meaning).
Grammar talks about rules for splitting the word.	Etymology defines how to split a word. With out Nirukta, splitting of the word is not possible.

Difference between निघण्टुः and निरुक्तम् 

निघण्टुः ।	निरुक्तम् ।
Nighantu (Dictionary) is a compilation of usages of Vedic literature.	Nirukta extensively discusses the different Vedic words and their applications. Derivation of meaning of vedic terms is achieved in Nirukta.
Nighantu, A dictionary, consists of Panchadhyayas (पञ्चाध्यायाः | 5 components)	Nirukta deals with Dvadashadhyayas (द्वादशाध्यायाः | 12 components).

छन्दस् ॥ Chandas

Chandas is a word derived from the dhatu चदि in the meaning of ahlade (आह्लादे | joy or delight) - as given in Shabdakalpadruma. It is regarded as the feet of the Vedapurusha.

Vedas are bound in chandas (metre). Since vedas are highly dependent on the sound or the way they are uttered, chandas is very important for their accurate utterance. It is the science for determination of metrical forms and qualities of mantras.

The Rigveda and Samaveda mantras are totally constructed with chandas. Yajurveda has both prose and shloka forms of mantras, and the shlokas are all built with appropriate chandas.

Vaidika chandas is different from chandas and meters of poems in classical sanskrit. Vaidika chandas is Akshara pradhana (अक्षरप्रधानम्). So, the number of letters is significant to understand the chandas and not the matras (मात्राः | Morae). In classical sanskrit, the number of syllables as well as quality (Laghu and Guru) are taken into account . The general sutras as applicable to classical sanskrit are not applicable to Vaidika chandas.

Pingalacharya’s Chandassutra (छन्दस्सूत्रम्) is a work which gives information about vaidika chandas. The number of letters range from 1 to 104. Based on the number of letters, each chandas has a different name. There are seven principle chandas in Vedas

Chandas Name	पादाः ॥ Padas and Syllables	Total number of Syllables
गायत्री || Gayatri	3 padas of 8 syllables	24
उष्णिक् || Ushnik	4 padas of 7 syllables	28
अनुष्टुप् || Anushtup	4 padas of 8 syllables	32
बृहती || Brhati	4 padas of 9 syllables	36
पङ्क्तिः || Pankti	4 padas of 10 syllables	40
त्रिष्टुप् || Trishtup	4 padas of 11 syllables	44
जगती || Jagati	4 padas of 12 syllables	48

Ashti (अष्टिः | 64), Prakrti (प्रकृतिः | 84), Vikrti (विकृतिः | 92), Abhikrti (अभिकृतिः | 100), Utkrti (उत्कृतिः | 104) are a few other Vedic chandas according to other classifications. Other texts dealing with Chandas include Rkpratishakhya, Shankhayana Shrauta sutras and Nidana Sutra of Samaveda. Devotional works are constructed in other meters mostly different from vedic meters. The first Rig veda Sukta - Agni sukta is in the Gayatri meter.

ज्योतिष् ॥ Jyotisha

Vedanga Jyotisha ((Samskrit : वेदाङ्गज्योतिषम्) is term given to astronomical studies which occupies a very important place in the Shad Vedangas. Lagadha is regarded as the author of ancient Jyotisha and his text is named as Vedanga Jyotisha. It deals with the study of the Universe i.e., astronomy to determine the configuration and position of stars and planets, stellar objects, distances between the stars, zodiac configurations among many things in order to fix the Shruti defined times for performing Yajnas and samskaras. Vedanga Jyotisha is significantly different from the Phalita Jyotisha developed in the more recent times.

Jyotish shastra is like the eye to the veda purusha. Without the knowledge of this shastra, kala (कालः | time) cannot be determined. For example - Determination of the Day, night, fortnight, month, season, and year for the performance of yajnas and travel is by the knowledge of this shastra. Vaidika samhitas explicitly deal with the kala (time) as in जीवेम शरदं शतम् || jīvema śaradaṃ śatam.

Ancient treatises on Jyotish available are Suryasiddhanta (सूर्यसिद्धन्तः), Brihat Parasharahora (बृहत्पराशरहोरः) by Parashara rishi (पराशर-ऋषिः), Brihat Jataka (बृहज्जातकम्) by Varahamihira (वराहमिहिरः) among others. Aryabhata and Brahmagupta, the Kerala school of Astronomy which are of the more recent centuries have given Bharatavarsha an important place in the world through their astronomical and mathematical contributions.

Notes

Vyakarana and Nirukta are unique to each Veda. Whereas Shiksha, Chandas, Kalpa and Jyotish are common for all Vedas.

Commentaries by Medhatiti (मेधातितिः), Govindaraja (गोविन्दराजः), Kallukabhatta (कल्लुकभट्टः) are available to read Manu Smriti.