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Dr Hansraj Joshi Department of Mathematics York U., Toronto, Canada A talk at the History of Math. Conference, Dec, 20 2007 Pantnagar, India. YAGN KUND : THE ORIGIN OF GEOMETRY. ABSTRACT & INTRODUCTION.

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Dr Hansraj JoshiDepartment of MathematicsYork U., Toronto, CanadaA talk at the History of Math. Conference, Dec, 20 2007 Pantnagar, India.


abstract introduction
  • It is well known that Vedic rituals required geometry for determination of the East – West direction before construction / layout of main Yagn Vedi and secondary Vedi in shapes of Rectangle, squares, and circles.
  • Some of the finds from Mohanjo-daro are testimonials to this.
  • We find description by various Mathematics historians, western as well as in Bhaarat, that during Vedic times they used bricks to rearrange square to circles to squares and one square to two squares.
  • I do not think that bricks was the only medium they used, because there may not have been bricks in the beginning.
  • Even today for construction of main Yagn Vedi and secondary Vedi we use mixture of soil and Gobar etc. Using certain volume of this mix, and requiring prescribed height, they created any shape of different areas and thereby actual squaring of a circle or splitting area c*2=a*2+b*2.

Secondary Vedi representing Brahma is Square where as those representing Soory (the Sun) and Prithavi (the Earth) are circles of area same as that of the square

  • Almost every writer on the subject or in reference to the origin of the Geometry, makes a statement to convey the sense that “ In Vedic era, our ancestors needed to construct Geometrical figures to perform various sacrifices” By this statement they mean performing a Yagn.
  • We know well what is a Yagn. It is a divine worship, social cohesion and creation, environmental replenishment and thankful giving. Associating any sense of sacrifice in such an act is unthinkable or rather criminal offence.
Yajurved -19-48 (Appendix item 8) gives one of the most appropriate descriptions of what Yagn is, and its purpose

Yajurved -19-48 (Appendix item 8) gives one of the most appropriate

descriptions of what Yagn is, and its purpose

why ritual of yagn became known as a sacrifice
  • Translators of our scriptures or writers on Hinduism in English; western as well as those from Bhaarat, they all use Sanskrit – English and English – Sanskrit dictionaries by Sir Monier Monier-Williams.
  • For example the books (i) The Shulba Sootras, a Text on Vedic Geometry by Satya Prakash and Usha Jyotishmati (ii) Ancient Hindu Geometry; The Science of Sulba by Bibhutibhusan Datta and (iii) The Shulbasootras by S N Sen and A K Bag, they all use “sacrifice” in relation to Yagn because they all used M-W dictionaries.
  • Only Subhas Kak in his book; The Astronomical Code of the Rig-veda, writes “… geometric constructions of fire altar represent the earliest mathematics and geometry”
  • The choice of the meaning in a translation (or in a write up) reflects the faith, integrity, honesty and motive of the person and the purpose.
  • Sir Monier was not at all academically honest.
  • His purpose then was to “meet the needs of the present day” and the need of the day was to convert learned and uneducated “natives” to Christianity.

The following passages from the Preface to the New Edition (1899) and the Preface of English – Sanskrit Dictionary (1852) proves my contention “Sir Monier was not at all academically honest” beyond any doubt.

  • In explanation I must draw attention to the fact I am only the second occupant of the Boden Chair, and that its Founder Colonel Boden, stated most explicitly in his will (dated August 15, 1811) that the special object of his munificent bequest was to promote translation of the (Christian) scriptures into Sanskrit, so as to enable his countrymen to proceed in conversion of natives of India to Christian Religion.
  • It was on this account that, when my distinguished predecessor and teacher Prof. H. H. Wilson, was a candidate for the Chair in 1832, his lexicographical labours were put forward as his principal claim to election.
  • My very first public lecture delivered after my election in 1860 was on “The Study of Sanskrit in Relation to Missionary Work in India” (Published 1861).
  • The Rev. J. Parsons of Benares, who has been engaged for years past in preparing a new Hindee version of the New Testament, has likewise derived material assistance from M. W’s work. Indian missionaries generally own him a large debt of gratitude.
Here is a quote from the introductory remarks for Devichan’s translation of Yajurved, by Prof. M C Joshi, which supports my opinion:
  • Yet all the scholars from the west could not remain free of prejudices and could not always maintain objectivity in their writings. Some of them it appears, aimed at perpetuating colonial rule in India while others expected to convert Indians to Christianity through their writings on Oriental subjects.
  • Thus it is clear that the motive behind the establishment of the professorship of Sanskrit in the University of Oxford was something else than the promotion of Sanskrit learning.

……The Great Max Muller was no exception.

  • In a letter to his wife he exposed the purpose with which he translated the Ved,

(he writes) “ …. This edition of mine and the translation of the Vedas will hereafter tell to a great extent on the fate of India and on the growth of millions of souls in that country. It ( he means the Ved) is the root of their religion and to show them what the root is, I feel sure, is the only way of uprooting all that has sprung from it during the last three thousand years.”

  • Further in a letter dated the 16th December 1868, he (Max Mullar) wrote to the Secretary of state for India, “ the ancient religion of India is doomed and if Christianity does not step in, whose fault will it be?
facts according to our ved
  • Please refer the Appendix for full text and Hindee translation (by Raam Kirshn Shastree of the Shukl Yajurved Samhita, Chaukhamba Vidya Bhawan, Varanasi, 2003) for following examples of Vedic Rucha.
  • This selection is mostly based on yet unpublished work of late Shree Satynand Shastri, edited by Dr Tulasi Ram Sharma. Dr Sharma; who now lives in Toronto, a retired Prof. of English, does not agree with MM-W dictionaries, and has undertaken monumental task of doing his own translation of all four Ved. I hope soon his translation will appear in print. I have good fortune of reading some his works. He taught English, for several years in UK, and India. He retired as Professor and Chairman of the English Department of Maharshi Dyanand University in Rohatak.
the very first rucha of yajurved forbids killing
The very first Rucha of Yajurved forbids killing.

Here the word ‘Aghynya’ is for

a cattle which must not be killed.


For me just one more Vedic Rucha

is enough; namely Yajurved-40-6 states:

Yastu Sarvaani Bhoota-nyaa-tmanne-vaanu-pashayti,

Sarv Bhooteshu Chaatmanm, Tato Na Vichi-kitsati.

This means “ He who sees all beings in the self and the self in all beings,

feels no hatred against any creature in the world, for,

he realizes the similarity (Aekyata=oneness) of all souls and sees himself in them”


2. Yajurved -13-47: “Imam Maa Hinseeh Dvi-paad Pashum”

meaning ‘do not destroy the biped living beings’


3. Yajurved -13-48:

“Imam Maa Himseerekashaphalm Pashu Kanikradm Vaajinm Vaajineshu”

meaning “do not destroy the one-hoofed animal the horse”


4. Yajurved -13-49 ”Ghritm Duhaanaan-maditim Janaayaagne Maa Himseeh”

Meaning “Do not destroy Aditi (the cow),

giver of milk for mankind and innocent in nature”

other references are listed below
Other references are listed below:
  • Yajurved -12-32

7. Rig-ved-8-56-17

8. Rig-ved-10-87-16

9. Atharv-ved-6-70-1

examples of yagn
  • Understanding of some Yagn, their purposes and how they were performed, will clarify my point further (cf: Satyaarth Prakaash by Swaamee Dayaanand Saraswati).
  • Three forms of Yagn namely Asw-medh, Go-medh and Nar-medh, should suffice to make the point.
  • The word ‘Medh’ according to Shatapath Braahman (13-2-6-2) is “Aajy” meaning Ghee
  • Medh was also used to convey the sense of fleshy parts of fruits etc.
  • Even today, Kaddu, the most flashy vegetable, we do not use or eat in our family, because some people in Rajasthan cut a Kaddu, during a Yagn. At what period and why animal killing crept in rituals is another subject.
asw medh yagn
  • Performed by a king, comprises of dispensation of justice to his subjects and propagation of education in his kingdom and is performed with Ghee Aahutee.
  • Any thing which runs very fast to high achievement is Asw (i.e. horse).
  • According to Satapath Braahman (13-1-6) Raastr ( i.e. nation or the national organization) is also called Asw.
  • Therefore all measures (or acts) conducive to high progress and development of a nation are acts of Asw-medh Yagn. The fire in a Yagn, looks like a galloping white horse, Ghee Aahutee in Yagn inflames it further and purifies the atmosphere.
nar medh yagn
  • Is the cremation of human corpse in a proper form.
  • In Satapath Braahman we have this description:
  • Dig a pit about 7 feet by 5.5 feet wide at the top and 4.5 feet deep. The pit should taper down so as to be about 3 feet wide at the bottom. Place about 50 pounds of Sandal wood and some Palash wood in the pit. Take Ghee equal in weight to the dead body and mix it with Kasturi (musk), little Kesar and Kapoor. Sprinkle mixture, all over body and set the fire to the corpse, and that is Nar-medh. Thus there will be no foul smell if a body is cremated in this (Vedic) way and there is no ‘sacrifice’ here.
go medh yagn
  • Is performed to keep pollution free; all edibles, sense organs, atmosphere and the earth.
  • In Sanskrit language the word GAU, conveys several connotations (i.e. meanings and usage). According to Paanini’s Unadi Kosh, Nighantu, Aachaary Yask, Aachaary Halaayudh and Abheedhaan Ratn-maala.
some of them are
Some of Them Are


Cow ( the animal) Earth (the land)

Ray (of light) Arrow (Baan)

Milk (of a cow) Sense organs (Indree)

Happiness Direction (Disha)

Rain Sun

Speech Vajr

Water Butter (from cow milk)

Moon Celestial region (Dwau)

Sight (Drishtee) Heaven (Swarg)

  • I think some of the reasons for various misinterpretations of Yang are ‘home grown’ and the fact that Christian missionaries in their zeal for conversion worked hard to degrade the Vedic culture and rituals.
  • The Western linguist did not understand the fact that Vedic language has a genius of using object name in place of a part of the object, for example we find usage of Gau where it is meant Ghee or any of the above.
  • As remarked before, other reason is ‘what suites the needs of the interpreter / translator’
  • Word Maas also means a type of grain (i.e.Udad) seed.
  • Yagn Saamagri is also called ‘Purodaas’ and is mixture of barley, rice, maas and ghee, Kesar etc.
  • Over the ages maas became maans mixed with ghee and then ghee and maas together became Gau-maans as part of a Yagn.
  • Thus there are such clear tenets directly decrying killing.
  • Therefore to call any Yagn, a ritual of sacrifice and Yagn Kund a place for sacrifice, or to say that Hindoo needed geometry in construction of sacrificial alters is the gross misrepresentation of the fact and demeaning our heritage.
  • Therefore I say do not translate, just write or say Yagn.
  • More of us will use word Yagn without translating it, this will become known just as now Yog (misspelled Yoga) so Yoga is a word in all English dictionaries.
I am forever grateful to my teacher, (now retired) Prof. Pramila Srivastav for encouragement and continued guidance.

Jay Seeya Raam

Dr Hansraj P Joshi

Department of Mathematics and Statistics

York University

TORONTO, Ont. Canada, M3J 1P3

  • (Appendix Item 1 Yajurved-1-1)
  • (Appendix Item 2 Yajurved-40-6)
  • (Appendix Item 3 Yajurve-16-3)
  • (Appendix Item 4 Yajurved-13-47)
  • (Appendix Item 5 Yajurved-13-48)
  • (Appendix Item 6 Yajurved-13-48)
  • (Appendix Item 7 Yajurved-13-50)
  • (Appendix Item 8 Yajurved-19-48)