Source Vedamu.Org : KalpaSutra : “Vedic religion involves complex ritualistic Karmakaanda (system of prescribed acts and sacrifices). A detailed understanding of this Karmakaanda became necessary in due course of time, and this gave rise to a vast literature of Kalpasutra. Kalpa means that which is understood or justified in respect of sacrifices and other prescribed acts and rituals. Karmakaanda is three-fold: Srauta-sutras, which are connected with sacrifices laid down in Sruti or Veda; Grhya-sutras, which are related to various rituals connected with the life of the householder, and various Samskaaras which are laid down for important occasions of life starting from birth up to death; and Dharma-sutras which are related to social, political and other benevolent duties. The entire Kalpa literature is Sutra literature, since it is composed aphoristically. There is also the fourth category of Kalpa-sutra, which is known as Shulba-sutra, and which is related to the science of geometry and architecture connected with the construction of sacrificial altars, fire-vessels and other related structures.
Corresponding to each Veda there are various Srauta-sutras. Saankhyaayana and Aaswalaayana pertain to the Rig-Veda; Arsheya (or Maashaka), Laahyaayana and Draahyaayana belong to the Sama-Veda; Aapastamba, Hiranyakeshi, Baudhaayana, Bhaaradwaja and Vaikaanasa are related to the Taittiriya sakha of the Krishna Yajur-Veda; Maanava Srauta-sutra is related to Maitrayani sakha of Krishna Yajur-Veda (this Sutra is believed to be the basis of the famous Manu Smrti); Kaatyaayana Srauta-sutra is related to the Sukla yajur-Veda; Vaitaana Sutra is related to the Atharva-Veda, and this Sutra is also related to Gopatha Brahamana and Kaatyaayana Srauta-sutra of Yajur-Veda.”
For more details click for Online Reference, or read B Datta, The science of the Sulba (Calcutta, 1932).
Vedic altars had to be built very precisely. The sutras contain formulae without derivations. (My thinking is that the derivations must have been taught ‘guru-mukhena’ by the guru, directly.)
- The method of constructing a square of area equal to a given rectangle is exact.
- Constructing a square of area equal to that of a given circle, is an approximation.
Baudhayana, Apastamba, Katyayana, and Manava are some of the authors of these sutras. (I have heard my father say that we traditionally belong to the Apastamba Sutra school, this has to be stated in the pravara.)
Western historians date Baudhayana at a 800 BCE, Pythagoras around 500 BCE and Katyayana at 200 BCE. (kAtyAyana the author of SuklaYajurVidhanaSastra, is the grand disciple of Saunaka as per the SaDgurusiSyA. So my date for him is around 3000 BCE.)
Baudhyana : The rope which is stretched across the diagonal of a square produces an area double the size of the original square.
Katyayana : The rope which is stretched along the length of the diagonal of a rectangle produces an area which the vertical and horizontal sides make together.
(Sutras can mean the rope for measuring an altar.)
Pythagoras : The square on the hypotenuse is equal to the sum of the squares on the other two sides, in a right angled triangle.
Apastamba : gave a sutra for computing the square root of 2 : Increase a unit length by its third and this third by its own fourth less the thirty-fourth part of that fourth.
√2 = 1 + 1/3 + 1/(3 4) – 1/(3 4 34) = 577/408 = 1.414215686 when computed to 9 decimal places.
Compare this with the present value of √2 = 1.414213562, and you can see that the value agrees to 5 decimal places.
The different constructions in the Sulabha Sutras, lead to different approximations for Pi.
Baudhayana’s : methods of constructions lead to the following approximations for Pi : 676/225, 900/289and 1156/361
Manava : 25/8 (Western date given for Manava is 750 BCE)
Others : 2.99, 3.00, 3.004, 3.029, 3.047, 3.088, 3.1141, 3.16049 and 3.2022
In schools we are now taught 22/7.
Interestingly, in sanskrit sutra means both thread and principle!
For more details click for Online Reference, or read B Datta, The science of the Sulba (Calcutta, 1932).
While I don’t agree with the western version of the Aryan Theory or their chronology, I think, you might find these links useful.
The Sacred Laws of the Âryas, Part I (SBE 2) George Bühler translator  (Sacred Books of the East, Vol. 2) (Apastamba, Gautama)
The Sacred Laws of the Âryas, Part II (SBE 14) George Bühler translator  (Sacred Books of the East, Vol. 14) (Vasistha, Baudhayana)
Also see: Photographs of Vedic Rituals.
In modern Indian languages the word yajna is used to signify a great focussed and dedicated effort. The word yajna is derived from the verb root yaj which means ‘to worship’. It’s synonym is yaga.
Vedic Rituals have not completely disappeared and yajnas have been performed even in the 21st century in India.
A proper study of Vedic Yajnas, helps to understand the Vedas, because the mantras are arranged to suit the needs of the Yajna.
The sulabha (sulba) sutras are concerned with the constructional and engineering aspects of the ‘Vedi’. The Vedi is loosely translated as altar in English, but the altars of the church are different. For us the Vedi is the place where the sacred fire will be placed and around which all the brahmans sit.
The following srauta sastras describe the method of performing the vedic rites.
A yajna is defined as the tyaga (giving up) of a dravya (material) unto a devata (luminary). Homa is the act of pouring ajya (ghee) into the gryhya or domestic fire. This act continues in the later adaptation of deeparadhana using a ghee lamp, which must not go out during the puja.
We learn from the Bhagavad Gita that Manavas and Devas sustain each other through yajnas. We offer them ‘havis’ and they bless us with rain and other good things. We take care of nature and nature takes care of us. Who can carry our offerings to the luminaries? Only one of them, someone who knows the way. So whatever we want to give the devatas we offer to agni and agni takes the offerings to the devas. (see Agnim Ile).
The Yajamana is the person performing the Yajna is performed. He meets the expenses and claims the fruit. All the rtvkiks and other brahmans are their to help him perform the yajna and for this they collect a fee called the dakshina.
Only grhastas (house holders – married men) of the brahmana, kshatriya and vaisya varnas, were eligible to establish the sacred agni and perform vedic rites. Since it was an expensive process (two cows had to be maintained for all the cow dung cakes and fuel sticks) and restricted travelling, grhastas usually waited till they were middle aged. The ahitagni, a man who had established such a sacred fire, had to maintain it thoughout his life and if any such fire went out, he would have to re-kindle it ceremoniously. Generally 3 fires were established, and when he died, these 3 fires and implements used in maintaining them would be cremated along with him according to the scriptures. If he took sanyasa, the fire would have to be discarded ceremoniously.
In common parlance today.. the word yajamana is used in the sense of ‘the master or boss’, by the wife and servants, even if he has never performed a single yajnam in his life.
The Yajamana selected the Rtviks. The Rtviks were preferably young men, well-versed in the Vedas, in perfect physical shape, from a good lineage and leading pure lives.
The hotr representing the rg veda had 3 assistants: maitravaruna, acchavaka, gravastut. (Agastya and Vasishtha have been called maitravarunis.)
The adhvaryu representing the yajurveda had 3 assistants: pratipasthata, nesta, unneta.
The udgatr representing the sama veda had the 3 assitants: prastota, pratiharta, subrahmanya (Naradawas an Udgata in some yajnas listed in the Harivamsa).
The Brahma represented the Atharva Veda and his 3 assistants were brahmanacchamsi, agnidhra and pota.
The 3 assistant were called dvitiyi or ardhi, tritiyi and padi and received a half, a third and a fourth of the fees paid to the mahartvijas or great rtviks.
Not all the 16 brahmans are needed in all the yagas.
A group of yajnas is called a samstha.
As per the Bodhayana grhyasutras (188.8.131.52) yajnas can be classified into 21 samsthas. They are performed with the mantras from 3 vedas Rk, Yajur and Sama. Domesticated Animals, Wild Animals and Tree-plant products are offered in the sacred fire. The brahmans are paid to keep the alive. Yajnas can also be classified as svadhyaya (self-study), japa (repetition), karma (performing) and manasa (meditation). Manasa yajnas are considered the best.
The first samstha are the Pakayajnas and they are 7 in number: Huta, Prahuta, Ahuta, Sulagava, Baliharana, Pratyavarohana and Ashtakahoma. They are meant for worldly gain and properity. Cooked offerings such as boiled grains mixed with butter are offered into the aupasanagni or the grhyagni.
The Seven Haviryajnas are Agnyadheya, Agnihotra, Darasa-purnamasa, Caturmasya, Agrayana,Nirudhapasubandha and Sautramani. The havis is uncooked offerings like barley, rice, milk or clarified butter offered into the srautagnis namely the garhapatya, dakshina and ahavaniya.
The seven Somayagas are Agnistoma, Atyagnistoma, Ukthya, Sodasi, Vajapeya, Atiratra andAptoryama. here the main offering is the SomaRasa (an extract of the soma plant).
The yajnas may be classified in other ways also. A model yajna like the darsapurnamasa is called a Prakrtiyajna. This yajna may be modified into vikrti yajnas like the kamyesti yajna. (We know that Dasaratha performed the Putra Kamyesti Yajna to get sons.) Kamyesti Yajnas are for getting some Kamas or wishes fulfilled. When Vikrti Yajnas are described only the modifications are described. The rest is as per the prakriti yajna.
Another classification is as follows: The Agnihotra is an example of a nitya yajna that must be performed everyday. The Ksamavatsiti yaga is a Naimittika (special cause) yajna that must be performed if one’s house is destroyed by fire. The Aindragnesti yajna is a kamya (wish) yajna which is performed to win a competitive venture.
Alternately: In a saumika yaga, the havis is Somarasa, in a pasuka yaga, the havis is an animal, and in anaistika yaga the havis is purodasa (rice cake), ajya (ghee) or caru (a porridge of 4 kinds of grains and/or lentils).
- Vedic Sacrifices, An Outline, By Swami Harshananda, Ramakrishna Math, Bangalore -19 (Rs 10/-)
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