Analytic Insight Net - FREE Online Tipiṭaka Research and Practice University and related NEWS through 
Paṭisambhidā Jāla-Abaddha Paripanti Tipiṭaka Anvesanā ca Paricaya Nikhilavijjālaya ca ñātibhūta Pavatti Nissāya anto 105 Seṭṭhaganthāyatta Bhāsā

January 2011
« Dec   Feb »
143 LESSON 20 01 2011 Ajita manava puccha Ajitas Questions FREE ONLINE eNālandā Research and Practice UNIVERSITY to VOTE for BSP ELEPHANT for Social Transformation and Economic Emancipation to attain Ultimate Bliss-Jambudvipa, i.e, PraBuddha Bharath scientific thought in Mathematics, Astronomy-GOOD GOVERNANCE-Cabinet Minister Mr. Ashok Kumar Dohre relieved from his ministerial post-BSP shortlists 200 candidates for 2012 polls
Filed under: General
Posted by: @ 2:10 am

143 LESSON 20 01 2011 Ajita manava puccha Ajitas Questions FREE ONLINE eNālandā Research and Practice UNIVERSITY to VOTE for BSP ELEPHANT for Social Transformation and Economic Emancipation to attain Ultimate Bliss


Awakeness Practices

All 84,000 Khandas As Found in the Pali Suttas

Traditionally the are 84,000 Dharma Doors - 84,000 ways to get Awakeness. Maybe so; certainly the Buddha taught a large number of practices that lead to Awakeness. This web page attempts to catalogue those found in the Pali Suttas (DN, MN, SN, AN, Ud & Sn 1). There are 3 sections:

The discourses of Buddha are divided into 84,000, as to separate addresses. The division includes all that was spoken by Buddha.”I received from Buddha,” said Ananda, “82,000 Khandas, and  from the priests 2000; these are 84,000 Khandas maintained by me.” They are divided into 275,250, as to the stanzas of the original text, and into 361,550, as to the stanzas of the commentary. All the discourses including both those of Buddha and those of the commentator, are divided  into 2,547 banawaras, containing 737,000 stanzas, and 29,368,000 separate letters.

Course Programs:


Snp 5.1 

PTS: Sn 1032-1039

Ajita-manava-puccha: Ajita’s Questions

translated from the Pali by

John D. Ireland

© 1994–2011

Alternate translation: Thanissaro

[The Venerable Ajita:]

“By what is the world enveloped? Because of what is it not known? With what do you say it is soiled? What is its great fear?”

[The Lord:]

“The world is enveloped by ignorance, Ajita. Because of wrongly directed desire and heedlessness it is not known (as it really is). It is soiled by longings and its great fear is suffering.”


“Everywhere flow the streams.[1] What is the obstruction for the streams, tell me the restricting of them, by what are they cut off?”

[The Lord:]

“Whatever streams are in the world, it is mindfulness that obstructs them and restricts them, and by wisdom they are cut off.”


“It is just wisdom and mindfulness. Now mind-and-body, sir, explain this: where does it cease?”

[The Lord:]

“This question you have asked, Ajita, I will answer for you: where mind-and-body completely cease. By the cessation of consciousness they cease.”[2]


“Those who have fully understood the Dhamma, those who are training and the other individuals here,[3] explain their (rule of) conduct.”

[The Lord:]

“Not craving for sensual pleasures and with a mind that is pure and tranquil[4] a bhikkhu should mindfully go forth, skillful in all situations.”



“The streams” are cravings flowing out towards pleasurable and desirable objects in the world.


This question and answer refers to the doctrine of dependent-arising (paticca-samuppada). Where rebirth-consciousness (pati-sandhi-vinnana) does not arise there is no establishment of an individual (mind-and-body, namarupa) in a realm of existence, nor the consequent appearance of old age and death and the other sufferings inherent in life.


“Those who have fully understood” are arahants (perfected ones) who have reached the highest goal. “Those who are training” are those noble beings (ariya) who are working towards and are assured of that goal. The other individuals are ordinary beings (puthujjana) who have not yet reached assurance.


The word anavilo means pure, clear, tranquil, unagitated, unmuddied, etc. In theDhammapada v. 82, the wise are compared to a deep lake with this quality.



Awakened One Shows the Path to Attain Eternal Bliss

Using such an instrument

The Free ONLINE e-Nālandā Research and Practice University has been re-organized to function through the following Schools of Learning :

Buddha’s Sangha Practiced His Dhamma Free of cost, hence the Free- e-Nālandā Research and Practice University follows suit

As the Original Nālandā University did not offer any Degree, so also the Free  e-Nālandā Research and Practice University.

The teachings of Buddha are eternal, but even then Buddha did not proclaim them to be infallible. The religion of Buddha has the capacity to change according to times, a quality which no other religion can claim to have…Now what is the basis of Buddhism? If you study carefully, you will see that Buddhism is based on reason. There is an element of flexibility inherent in it, which is not found in any other religion.

Bhimrao Ramji Ambedkar , Indian scholar, philosopher and architect of Constitution of India, in his writing and speeches



Level I: Introduction to Buddhism,Level II: Buddhist Studies,


Level III: Stream-Enterer,Level IV: Once – Returner,Level V: Non-Returner,Level VI: Arhat

Jambudvipa, i.e, PraBuddha Bharath scientific thought in


Philosophy and Comparative Religions;Historical Studies;International Relations and Peace Studies;Business Management in relation to Public Policy and Development Studies;Languages and Literature;and Ecology and Environmental Studies

Jambudvipa, i.e, PraBuddha Bharath scientific thought in






Jambudvipa, i.e, PraBuddha Bharath scientific thought in< ?xml:namespace prefix = o ns = “urn:schemas-microsoft-com:office:office” />

Mathematics, Astronomy


Pali literature has innumerable references to the maritime activity of Jambudvipans in ancient times.

Since ancient times Jambudvipa philosophers believed that except Akash (ether), all other elements were physically palpable and hence comprised miniscule particles of matter. The last miniscule particle of matter which could not be subdivided further was termed Parmanu. The word Parmanu is a combination of Param, meaning beyond, and anu meaning atom. Thus the term Parmanu is suggestive of the possibility that, at least at an abstract level Jambudvipa philosophers in ancient times had conceived the possibility of splitting an atom which, as we know today, is the source of atomic energy. This Jambudvipa concept of the atom was developed independently and prior to the development of the idea in the Greco-Roman world. The first Jambudvipa philosopher who formulated ideas about the atom in a systematic manner was Kanada who lived in the 6th century B.C. Another Jambudvipa philosopher, Pakudha Katyayana who also lived in the 6th century B.C. and was a contemporary of Gautama Buddha, had also propounded ideas about the atomic constitution of the material world.

These philosophers considered the Atom to be indestructible and hence eternal. The Buddhists believed atoms to be minute objects invisible to the naked eye and which come into being and vanish in an instant. The Vaisheshika school of philosophers believed that an atom was a mere point in space. Jambudvipan theories about the atom are greatly abstract and enmeshed in philosophy as they were based on logic and not on personal experience or experimentation.

Jambudvipans had classified the material world into four elements viz. Earth (Prithvi), fire (Agni), air (Maya) and water (Apa).

The Buddhist philosophers who came later, rejected ether as an element and replaced it with life, joy and sorrow.

Since ancient times Jambudvipan philosophers believed that except Akash (ether), all other elements were physically palpable and hence comprised miniscule particles of matter. The last miniscule particle of matter which could not be subdivided further was termed Parmanu. The word Parmanu is a combination of Param, meaning beyond, and any meaning atom. Thus the term Parmanu is suggestive of the possibility that, at least at an abstract level Indian philosophers in ancient times had conceived the possibility of splitting an atom which, as we know today, is the source of atomic energy. This Jambudvipans concept of the atom

was developed independently and prior to the development of the idea in the Greco-Roman world. The first Indian philosopher who formulated ideas about the atom in a systematic manner was Kanada who lived in the 6th century B.C. Another Indian philosopher, Pakudha Katyayana who also lived in the 6th century B.C. and was a contemporary of Gautama Buddha, had also propounded ideas about the atomic constitution of the material world.

These philosophers considered the Atom to be indestructible and hence eternal. The Buddhists believed atoms to be minute objects invisible to the naked eye and which come into being and vanish in an instant. The Vaisheshika school of philosophers believed that an atom was a mere point in space. Jambudvipan theories about the atom are greatly abstract and enmeshed in philosophy as they were based on logic and not on personal experience or experimentation. Thus the Jambudvipan theories lacked an empirical base, but in the words of A.L. Basham, the veteran Australian Indologist “they were brilliant imaginative explanations of the physical structure of the world, and in a large measure, agreed with the discoveries of modern physics.”

The Story of Kanada

The school of philosophy which contributed to the development of ideas about the atom was the Vaisheshika school. A brilliant philosopher by the name Kashyapa (later called Kanada) is credited with having propounded the concept of atom for the first time. According to legend, Kashyapa lived in the 6th century B.C. He was the son of a phi losopher named Ulka. From his child days Kashyapa displayed a keen sense of observation. Minute things attracted his attention. The story goes that once when young boy he had accompanied his father a pilgrimage to Prayaga, he noticed that thousands of pilgrims who were flocking the town littered its roads with flowers grains of rice which they offered at the temples by the river Ganges. While everybody else was busy offering prayers, or bathing the Ganges, the young Kashyapa started collecting the grains (Kana) of rice that littered the streets.

Looking at this strange behaviour coming from a boy who seemingly belonged to do family, many of the passers-by curious and started wondering who he could be and why was he acting in strange manner. Soon a crowd collected around the young Kashyapa who continued collecting the grains, oblivious of the attention he was attracting. Passing by that was Muni Somasharma a learned Sage, wondered why the crowd had gathered time when everybody should have been the bathing ghats for the morning’s ritual bath. On going near he saw for himself reason and heard the derogatory remarks being made about the young Kashyapa. Muni Somasharma knew who Kashyapa was, he silenced the crowd and said that, knew who the boy was.

Being himself curious to know the reason for Kashyapa’s strange behaviour, Somasharma asked him why he was counting discarded grains which even a beggar would not care to collect. Somewhat hurt at question, Kashyapa replied that howsoever miniscule an object might be, it nevertheless was a part of the universe. Individual grains in themselves may seem worthless, but a collection of some hundred grains make up a person’s meal, the collection many meals would feed an entire family and ultimately the entire mankind was made of many families, thus even a single grain of rice was as important as all the valuable riches in this world.

This reply of the young Kashyapa deeply impressed Muni Somasharma who said that one day Kashyapa would grow into a celebrated philosopher and said that in recognition of Kayshapa’s unusual sense of perceiving miniscule objects he would henceforth be Kanada, from Kana which means a grain.

This was how Kashyapa came to acquire the Kanada, which was made immortal in history of Indian science due to the path-breaking conception of atom and relativity which Kanada was to put forth. He propounded the Vaisheshika-Sutra (Peculiarity Aphorisms). These Sutras were a of science and philosophy. Their subject was the atomic theory of matter. On reading these Sutras we find that Kanada’s atomic theory was far more advanced than formulated later by the Greek philosophers, Democritus and Leucippus.

Anu and Parmanu

It was Kanada who first propounded the that the Parmanu (atom) was an indestrutible particle of matter. According to the material universe is made up of Kana. When matter is divided and sudivided, we reach a stage beyond which no division is possible, the undivisible element of matter is Parmanu. Kanada explained that this indivisible, indestructible y cannot be sensed through any human organ.

In saying that there are different types of Parmanu for the five Pancha Mahabhootas, Earth, water, fire, air and ether. Each Parmanu has a peculiar property which depends, on the substance to which it belongs . It was because of this conception of peculiarity of Parmanu (atoms) that this theory unded by Kanada came to be known Vaisheshika-Sutra (Peculiarity Aphorisms). In this context Kanada seems to arrived at conclusions which were surpassed only many centuries after him.

According to Kanada, an object appears to be heavy under water than it does in air because the density of atoms in water is more than in air. The additional density of , in water, Kanada said, takes on part of the weight of an object, hence we feel only a part of its total weight, while in air, the lesser density of atoms results in a lesser part of an object’s weight being picked by air, hence we feel the object to be heavier in air than what is was when under the water. In saying this, in a very elementary but important way, Kanada foreshadowed Archimedes’ theory that a body immersed in a fluid is subject to an upward force equal in magnitude to the weight of the fluid it displaces. Kanada’s idea also had shades of relativity in it which was propounded by Einstien in our times.

About his ideas on atom, Kanada observed that an inherent urge made one Parmanu combine with another. When two Parmanu belonging to one class of substance combined, a dwinuka (binary molecule) was the result. This dwinuka had properties similar to the two parent Parmanu. In the material universe, according to him, Parmanu be longing to different classes of substances combine in different combinations giving us a variety of dwinuka, which in other words means different types of substances. Apart from such combination of different Parmanu, Kanada also put forth the idea of chemical changes occuring because of various factors. He claimed that variation in temperature could bring about such changes.

He cited the examples of blackening of a new earthen pot and the ripening of fruit to illustrate the chemical change in substances brought about by the heat. Thus according to Kanada all substances, all matter that existed in the universe was formed of Parmanu (atoms). The variations in the matter reflected the peculiarity of the Parmanu which constituted that particular matter, the variety of combinations between different types of Parmanu and the effect on them of variation in temperature.

These Indian ideas about atom and atomic physics could have been transmitted to the west during the contacts created between India and the west by the invasion of Alexander. The Greeks invaded north-western India in around 330 B C. Alongwith Alexander, came Greek philosophers like Aristotle who is reported to have been Alexander’s mentor. Scholars like Aristotle would surely have keenly studied the sciences of the lands which the Greek armies overran. Even after Alexander’s departure, massive trade and diplomatic relations existed between Indians and Greeks (who had settled in Asia) This way perhaps, Indian ideas could have travelled westwards where they were developed further.

Some scholars even go to the extent of saying that in Kanada’s lifetime itself some Greek scholars had visited India and through a debate with the great philosopher had been exposed to Indian ideas about atom. the possibility of such a meeting is remote as Kanada lived in the 6th century B.C. and the Greeks came into India only in the 4th century B.C. But nevertheless it remains a fact that Indian ideas about atom are the oldest. It is only after the 4th century B.C., after the Greeks had come in contact with India do we find references to the idea of an atom in Greek science. Thus it is quite possible that the Greeks borrowed the ideas about atom from Indian philosophers in the 4th century B.C. But the credit of developing these ideas further, goes to the Greeks and other western philosophers.

Q.      Who invented Nuclear Physics?

Buddhist teacher Pakudha Katyayana taught atomic theory. Maharshi Kanaada of 3rd century,B.C. wrote atomic theory in Vaiseshika Suttas


The Jambudvipa Emperor Ashoka started a “Secret Society of the Nine Unknown Men”: great Jambudvipa scientists who were supposed to catalogue the many sciences. Ashoka kept their work secret because he was afraid that the advanced science catalogued by these men, culled from ancient Jambudvipa sources, would be used for the evil purpose of war, which Ashoka was strongly against, having been converted to Buddhism after defeating a rival army in a bloody battle.

The “Nine Unknown Men” wrote a total of nine books, presumably one each. Book number was “The Secrets of Gravitation!” This book, known to historians, but not actually seen by them dealt chiefly with “gravity control.” It is presumably still around somewhere, kept in a secret library in India, Tibet or elsewhere (perhaps even in North America somewhere). One can certainly understand Ashoka’s reasoning for wanting to keep such knowledge a secret, assuming it exists. if the Nazis had such weapons at their disposal during World War II. Ashoka was also aware devastating wars using such advanced vehicles and other “futuristic weapons” that had destroyed the ancient Jambudvipa “Rama Empire” several thousand years before.

Only a few years ago, the Chinese discovered some documents in Lhasa, Tibet and sent them to the University of Chandrigarh to be translated. Dr. Ruth Reyna of the University said recently that the documents contain directions for building interstellar spaceships! 

Their method of propulsion, she said, was “anti-gravitational” and was based upon a system analogous to that of “laghima,” the unknown power of the ego existing in man’s physiological makeup, “a centrifugal force strong enough to counteract all gravitational pull.” According to Yogis, it is this “laghima” which enables a person to levitate. 

Dr. Reyna said that on board these machines, which were called “Astras” by the text, the ancient Indians could have sent a detachment of men onto any planet, according to the document, which is thought to be thousands of years old. The manuscripts were also said to reveal the secret of “antima”; “the cap of invisibility” and “garima”; “how to become as heavy as a mountain of lead.” 

Naturally, Jambudviapan scientists did not take the texts very seriously, but then became more positive about the value of them when the Chinese announced that they were including certain parts of the data for study in their space program! This was one of the first instances of a government admitting to be researching anti-gravity. 

The manuscripts did not say definitely that interplanetary travel was ever made but did mention, of all things, a planned trip to the Moon, though it is not clear whether this trip was actually carried out.

This is but a small bit of recent evidence of anti-gravity and aerospace technology used by Indians. To really understand the technology, we must go much further back in time. 

The so-called “Rama Empire” of Northern Jambudvipa and Pakistan developed at least fifteen thousand years ago on the Jambudvipa sub-continent and was a nation of many large, sophisticated cities, many of which are still to be found in the deserts of Pakistan, northern, and western Jambudvipa. Rama existed, apparently, parallel to the Atlantean civilization in the mid-Atlantic Ocean, and was ruled by “awakened Priest-Kings” who governed the cities, The seven greatest capital cities of Rama were known in classical Hindu texts as “The Seven Rishi Cities.” 

According to ancient Jambudvipa texts, the people had flying machines which were called “Vimanas.” The ancient Jambudvipan epic describes a Vimana as a double-deck, circular aircraft with portholes and a dome, much as we would imagine a flying saucer. 

It flew with the “speed of the wind” and gave forth a “melodious sound.” There were at least four different types of Vimanas; some saucer shaped, others like long cylinders (”cigar shaped airships”). The ancient Indian texts on Vimanas are so numerous, it  would take volumes to relate what they had to say. The ancient Indians, who manufactured these ships themselves, wrote entire flight manuals on the control of the various types of Vimanas, many of which are still in existence, and some have even been translated into English. 

The Samara Sutradhara is a scientific treatise dealing with every possible angle of air travel in a Vimana. There are 230 stanzas dealing with the construction, take-off, cruising for thousand of miles, normal and forced landings, and even possible collisions with birds. In 1875, the Vaimanika Sastra, a fourth century B.C. text written by Bharadvajy the Wise, using even older texts as his source, was rediscovered in a temple in India. It dealt with the operation of Vimanas and included information on the steering, precautions for long flights, protection of the airships from storms and lightening and how to switch the drive to “solar energy” from a free energy source which sounds like “anti-gravity.” 

The Vaimanika Sastra (or Vymaanika-Shaastra) has eight chapters with diagrams, describing three types of aircraft, including apparatuses that could neither catch on fire nor break. It also mentions 31 essential parts of these vehicles and 16 materials from which they are constructed, which absorb light and heat; for which reason they were considered suitable for the construction of Vimanas. This document has been translated into English and is available by writing the publisher: VYMAANIDASHAASTRA AERONAUTICS by Maharishi Bharadwaaja, translated into English and edited, printed and published by Mr. G. R. Josyer, Mysore, India, 1979 (sorry, no street address).

There seems to be no doubt that Vimanas were powered by some sort of “anti-gravity.” Vimanas took off vertically, and were capable of hovering in the sky, like a modern helicopter or dirigible. Bharadvajy the Wise refers to no less than 70 authorities and 10 experts of air travel in antiquity. These sources are now lost. 

Vimanas were kept in a Vimana Griha, a kind of hanger, and were sometimes said to be propelled by a yellowish-white liquid, and sometimes by some sort of mercury compound, though writers seem confused in this matter. It is most likely that the later writers on Vimanas, wrote as observers and from earlier texts, and were understandably confused on the principle of their propulsion. The “yellowish-white liquid” sounds suspiciously like gasoline, and perhaps Vimanas had a number of different propulsion sources, including combustion engines and even “pulse-jet” engines. It is interesting to note, that the Nazis developed the first practical pulse-jet engines for their V-8 rocket “buzz bombs.” Hitler and the Nazi staff were exceptionally interested in ancient Jambudvipa and Tibet and sent expeditions to both these places yearly, starting in the 30’s, in order to gather esoteric evidence that they did so, and perhaps it was from these people that the Nazis gained some of their scientific information! 

One Vimana described was shaped like a sphere and born along at great speed on a mighty wind generated by mercury. It moved like a UFO, going up, down, backwards and forewards as the pilot desired. In another Jambudvipa source, the Samar, Vimanas were “iron machines, well-knit and smooth, with a charge of mercury that shot out of the back in the form of a roaring flame.” Another work called the Samaranganasutradhara describes how the vehicles were constructed. It is possible that mercury did have something to do with the propulsion, or more possibly, with the guidance system. Curiously, Soviet scientists have discovered what they call “age-old instruments used in navigating cosmic vehicles” in caves in Turkestan and the Gobi Desert. The “devices” are hemispherical objects of glass or porcelain, ending in a cone with a drop of mercury inside. 

It is evident that ancient Jambudvipa flew around in these vehicles, all over Asia, to Atlantis presumably; and even, apparently, to South America. Writing found at Mohenjodaro in Pakistan (presumed to be one of the “Seven Rishi Cities of the Rama Empire”) and still undeciphered, has also been found in one other place in the world: Easter Island! Writing on Easter Island, called Rongo-Rongo writing, is also undeciphered, and is uncannily similar to the Mohenjodaro script. Was Easter Island an air base for the Rama Empire’s Vimana route? (At the Mohenjo-Daro Vimana-drome, as the passenger walks down the concourse, he hears the sweet, melodic sound of the announcer over the loudspeaker,

Pali literature has innumerable references to the maritime activity of Jambudvipans in ancient times.

This gives a technocratic exposition on the technique of
shipbuilding. It sets forth minute details about the various types of ships, their sizes, the materials from which they were built. The Yukti Kappa Taru sums up in a condensed form all the available information 

The Yukti Kappa Taru gives sufficient information and date to prove that in ancient times, Jambudvipa shipbuilders had a good knowledge of the materials which were used in building ships. Apart from describing the qualities of the different types of wood and their suitablility in shipbuilding, the Yukti Kalpa Taru also gives an elaborate classification of ships based on their size. 

The primary division is into 2 classes viz. Samanya (ordinary) and Vishesha (Special). The ordinary type for sea voyages. Ships that undertook sea voyages were classified into, Dirgha type of ships which had a long and narrow hull and the Unnata type of ships which had a higher hull. 

This gives elaborate directions for decorating and furnishing the ships with a view to making them comfortable for passengers. Also mentioned are details about the internal seating and accommodation to be provided on the ships. Three classes of ships are distinguished according to their length and the position of cabins. The ships having cabins extending from one end of the deck to the other are called Sarvamandira vessels. These ships are recommended for the transport of royal treasure and horses. The next are the Madhyamarnandira vessels which have cabins only in the middle part of their deck. these vessels are recommended for pleasure trips. And finally there is a category of Agramandira vessels, these ships were used mainly in warfare. 


Interestingly there were terms for many parts of a ship. The ship’s anchor was known as Nava-Bandhan-Kilaha which literally means ‘A Nail to tie up a ship’ . The sail was called Vata Vastra a which means ‘wind-cloth’. The hull was termed StulaBhaga i.e. an’expanded area’. The rudder was called Keni-Pata, Pata means blade; the rudder was also known as Karna which literally means a ‘ear’ and was so called because it used to be a hollow curved blade, as is found today in exhaust fans. The ship’s keel was called Nava-Tala which means ‘bottom of a ship’. The mast was known as Kupadanda, in which danda means a pole. 

Even a sextant was used for navigation and was called Vruttashanga-Bhaga. But what is more surprising is that even a contrived mariner’s compass was used by Jambudvipan navigators nearly 1500 to 2000 years ago. This claim is not being made in an overzealous nationalistic spirit. This has in fact been the suggestion of an European expert, Mr. J.L. Reid, who was a member of the Institute of Naval Architects and Shipbuilders in England at around the beginning of the present century.


In ancient Jambudvipa conventional mathematics termed Ganitam was known before the development of algebra. This is borne out by the name - Bijaganitam, which was given to the algebraic form of computation. Bijaganitam means ‘the other mathematics’ (Bija means ‘another’ or ’second’ and Ganitam means mathematics). The fact that this name was chosen for this system of computation implies that it was recognised as a parallel system of computation, different from the conventional one which was used since the past and was till then the only one. Some have interpreted the term Bija to mean seed, symbolizing origin or beginning. And the inference that Bijaganitam was the original form of computation is derived. Credence is lent to this view by the existence of mathematics in the Vedic literature which was also shorthand method of computation. But whatever the origin of algebra, it is certain that this technique of computation Originated in Jambudvipa and was current around 1500 years back. Aryabhatta and Jambudvipa mathematican who lived in the Jambudvipa 5th century A.D. has referred to Bijaganitam in his treatise on Mathematics, Aryabhattiya. An mathematician - astronomer, Bhaskaracharya has also authored a treatise on this subject. the treatise which is dated around the 12th century A.D. is entitled ‘Siddhanta-Shiromani’ of which one section is entitled Bijaganitam. 


But even in the area of Geometry, Jambudvipan mathematicians had their contribution. There was an area of mathematical applications called Rekha Ganita (Line Computation). The Sulva Suttas, which literally mean ‘Rule of the Chord’ give geometrical methods of constructing altars and temples. The temples layouts were called Mandalas. Some of important works in this field are by Apastamba, Baudhayana, Hiranyakesin, Manava, Varaha and Vadhula. 

The Arab scholar Mohammed Ibn Jubair al Battani studied Jambudvipan use of ratios from Retha Ganita and introduced them among the Arab scholars like Al Khwarazmi, Washiya and Abe Mashar who incorporated the newly acquired knowledge of algebra and other branches of Indian mathema into the Arab ideas about the subject. 

The chief exponent of this Indo-Arab amalgam in mathematics was Al Khwarazmi who evolved a technique of calculation from Indian sources. This technique which was named by westerners after Al Khwarazmi as “Algorismi” gave us the modern term Algorithm, which is used in computer software. 

Algorithm which is a process of calculation based on decimal notation numbers. This method was deduced by Khwarazmi from the Indian techniques geometric computation which he had st ied. Al Khwarazmi’s work was translated into Latin under the title “De Numero Indico” which means ‘of Indian Numerals’ thus betraying its Indian origin. This translation which belong to the 12th century A.D credited to one Adelard who lived in a town called Bath in Britian. 

Thus Al Khwarazmi and Adelard could looked upon as pioneers who transmit Jambudvipan numerals to the west. Incidents according to the Oxford Dictionary, word algorithm which we use in the English language is a corruption of the name Khwarazmi which literally means ‘(a person) from Khawarizm’, which was the name of the town where Al Khwarazmi lived. To day unfortunately’, the original Indian texts that Al Khwarazmi studied arelost to us, only the translations are avail able . 

The Arabs borrowed so much from Jambudvipa the field of mathematics that even the subject of mathematics in Arabic came to known as Hindsa which means ‘from India and a mathematician or engineer in Arabic is called Muhandis which means ‘an expert in Mathematics’. The word Muhandis possibly derived from the Arabic term mathematics viz. Hindsa.

The Concept of Zero 

The concept of zero also originated in ancient Jambudvipa. This concept may seem to be a very ordinary one and a claim to its discovery may be viewed as queer. But if one gives a hard thought to this concept it would be seen that zero is not just a numeral. Apart from being a numeral, it is also a concept, and a fundamental one at that. It is fundamental because, terms to identify visible or perceptible objects do not require much ingenuity. 

But a concept and symbol that connotes nullity represents a qualitative advancement of the human capacity of abstraction. In absence of a concept of zero there could have been only positive numerals in computation, the inclusion of zero in mathematics opened up a new dimension of negative numerals and gave a cut off point and a standard in the measurability of qualities whose extremes are as yet unknown to human beings, such as temperature.

In ancient Jambudvipa this numeral was used in computation, it was indicated by a dot and was termed Pujyam. Even today we use this term for zero along with the more current term Shunyam meaning a blank. But queerly the term Pujyam also means holy. Param-Pujya is a prefix used in written communication with elders. In this case it means respected or esteemed. The reason why the term Pujya - meaning blank - came to be sanctified can only be guessed.” 

The ancient Jambudvipa astronomer Brahmagupta is credited with having put forth the concept of zero for the first time: Brahmagupta is said to have been born the year 598 A.D. at Bhillamala (today’s Bhinmal ) in Gujarat, Western Jambudvipa much is known about Brahmagupta’s early life. We are told that his name as a mathematician was well established when K Vyaghramukha of the Chapa dyansty m him the court astronomer. Of his two treatises, Brahma-sputa siddhanta and Karanakhandakhadyaka, first is more famous. It was a corrected version of the old Astronomical text, Brahma siddhanta. It was in his Brahma-sphu siddhanta, for the first time ever had be formulated the rules of the operation zero, foreshadowing the decimal system numeration. With the integration of zero into the numerals it became possible to note higher numerals with limited charecters. 

In the earlier Roman and Babylonian systems of numeration, a large number of chara acters were required to denote higher numerals. Thus enumeration and computation became unwieldy. For instance, as E the Roman system of numeration, the number thirty would have to be written as X: while as per the decimal system it would 30, further the number thirty three would be XXXIII as per the Roman system, would be 33 as per the decimal system. Thus it is clear how the introduction of the decimal system made possible the writing of numerals having a high value with limited characters. This also made computation easier. 

Apart from developing the decimal system based on the incorporation of zero in enumeration, Brahmagupta also arrived at solutions for indeterminate equations of 1 type ax2+1=y2 and thus can be called the founder of higher branch of mathematics called numerical analysis. Brahmagupta’s treatise Brahma-sputa-siddhanta was translated into Arabic under the title Sind Hind).


made of five metals

In ancient Jambudvipa, chemistry was caled Rasayan Shastra, Rasa-Vidya, Rasatantra and Rasakriya all of which roughly mean ‘Science of liquids’. There also existed chemical laboratories and chemicals works, which were called Rasakriya-nagaram and Rasakriya-shala which literally mean ‘School where liquids are activated’. A chemist was referred to as a Rasadnya and Rasa-tantra-vid which mean ‘Person having knowledge about liquids. Apart from the term Rasa which means liquid, another word, Dravya which means slurry, was also used to refer to chemicals. Thus, in ancient India, chemistry was evidently developed to a significant level. 

Metallurgy was an important activity the world over. In fact the discovery of smelting of metals made possible the progress of society from the Stone Age to the Bronze and Iron Ages. In the area of smelting metals, Indians had acquired proficiency in the extraction of metals from ore, and also in the casting of metals. In very early times: around 2000 B.C. the idea of smelting metals was known in Mesopotemia and the Near East. It is possible that Jambudvipans could have borrowed the idea from an outside source. It is generally agreed that the Aryan tribes who are said to have destroyed the Indus Valley civilization had bronze weapons which helped them to overcome the otherwise more advanced people of the Indus cities. 

Though  Jambudvipa could have had borrowed the idea of smelting metals from an outside source, they seem to have had used metals in warfare from around 1500 B.C when the Aryans are said to have invaded the Indus Valley cities. The next definite reference to the use of metals by Jambudvipan soldiers is by the Greeks. The Greek historian Herodotus has observed in the 5th century that “Jambudvipas in the Persian army used arrows tipped with iron”. Jambudvipan steel and iron were reportedly being used by the Romans for manufacturing armour as well as cutlery. But these references apart, it is in India itself that we find actual objects that reflect the advancement of the technique of smelting.

physics and chemistry

In Jambudvipan languages, the science of Astronomy is today called Khagola-shastra. The word Khagola perhaps is derived from the famous astronomical observatory at the University of Nalanda which was called Khagola. It was at Khagola that the famous 5th century Indian Astronomer Aryabhatta studied and extended the subject. 

Aryabhatta is said to have been born in 476 A.D. at a town called Ashmaka in today’s Jambudvipan state of Kerala. When he was still a young boy he had been sent to the University of Nalanda to study astronomy. He made significant contributions to the field of astronomy. He also propounded the Heliocentric theory of gravitation, thus predating Copernicus by almost one thousand years.

Aryabhatta’s Magnum Opus, the Aryabhattiya was translated into Latin in the 13th century. Through this translation, European mathematicians got to know methods for calculating the areas of triangles, volumes of spheres as well as square and cube root. Aryabhatta’s ideas about eclipses and the sun being the source of moonlight may not have caused much of an impression on European astronomers as by then they had come to know of these facts throught the observations of Copernicus and Galileo. 

But considering that Aryabhatta discovered these facts 1500 years ago, and 1000 years before Copernicus and Galileo makes him a pioneer in this area too. Aryabhatta’s methods of astronomical calculations expounded in his Aryabhatta-siddhanta were reliable for practical purposes of fixing the Panchanga. Thus in ancient Jambudvipa, eclipses were also forecast and their true nature was perceived at least by the astronomers. 

The lack of a telescope hindered further advancement of ancient Jambudvipan astronomy. Though it should be admitted that with their unaided observations with crude instruments, the astronomers in ancient  Jambudvipa were able to arrive at near perfect measurement of astronomical movements and predict eclipses. 

Jambudvipan astronomers also propounded the theory that the earth was a sphere. Aryabhatta was the first one to have propounded this theory in the 5th century. Another Jambudvipan astronomer, Brahmagupta estimated in the 7th century that the circumference of the earth was 5000 yojanas. A yojana is around 7.2 kms. Calculating on this basis we see that the estimate of 36,000 kms as the earth’s circumference comes quite close to the actual circumference known today.


From Wikipedia, the free encyclopedia

Baudhāyana, (fl. c. 800 BCE)[1] was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sutra—appendices to the Vedas giving rules for the construction of altars—called theBaudhāyana Śulbasûtra, which contained several important mathematical results. He is older than other famous mathematician Apastambha. He belongs to Yajurveda school.

He is accredited with calculating the value of pi to some degree of precision, and with DISCOVERING what is now known as the Pythagorean theorem.[2]

The suttas of Baudhayana

The Shrautasutta

His shrauta sutras related to performing to Vedic sacrifices has followers in some Smartha brahmins (Iyers)And some Iyengars of Tamil Nadu, Yajurvedis or Namboothiris of Kerala, Gurukkal brahmins, among others. The followers of this sutra follow a different method and do 24 Tilatarpana, as Lord Krishna had done tarpana on the day before Amavasaya; they call themselves Baudhayana Amavasya.

The Dhammasutta

The Vivarana of Govindasvami is an important commentary on the Dharmasûtra.

The mathematics in Shulbasutta

Pythagorean theorem

The most notable of the rules (the Sulbasutras do not contain any proofs of the rules which they describe) in the Baudhāyana Sulba Sutta says:

dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī,
cha yatpṛthagbhUte kurutastadubhayāṅ karoti.

A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.

This appears to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.

If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.

Baudhayana also provides a non-axiomatic demonstration using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle:

The cord which is stretched across a square produces an area double the size of the original square.

Circling the Square

Another problem tackled by Baudhayana is that of finding a circle whose area is the same as that of a square (the reverse of squaring the circle). His sutra i.58 gives this construction:

Draw half its diagonal about the centre towards the East-West line; then describe a circle together with a third part of that which lies outside the square.


  • Draw the half-diagonal of the square, which is larger than the half-side by x = {a \over 2}\sqrt{2}- {a \over 2}.
  • Then draw a circle with radius {a \over 2} + {x \over 3}, or {a \over 2} + {a \over 6}(\sqrt{2}-1), which equals {a \over 6}(2 + \sqrt{2}).
  • Now (2+\sqrt{2})^2 \approx 11.66 \approx {36.6\over \pi}, so the area {\pi}r^2 \approx \pi \times {a^2 \over 6^2} \times {36.6\over \pi} \approx a^2.

Square root of 2

Baudhayana i.61-2 (elaborated in Apastamba Sulbasutra i.6) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2:

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet
tac caturthenātmacatustriṃśonena saviśeṣaḥ
The diagonal [lit. “doubler”] of a square. The measure is to be increased by a third and by a fourth decreased by the thirty-fourth. That is its diagonal approximately.

\sqrt{2} = 1 + \frac{1}{3} + \frac{1}{3 \cdot 4} - \frac{1}{3 \cdot4 \cdot 34} = \frac{577}{408} \approx 1.414216

which is correct to five decimals.

Other theorems include: diagonals of rectangle bisect each other, diagonals of rhombus bisect at right angles, area of a square formed by joining the middle points of a square is half of original, the midpoints of a rectangle joined forms a rhombus whose area is half the rectangle, etc.

Note the emphasis on rectangles and squares; this arises from the need to specify yajña bhūmikās—i.e. the altar on which a rituals were conducted, including fire offerings (yajña).

Apastamba (c. 600 BC) and Katyayana (c. 200 BC), authors of other sulba sutras, extend some of Baudhayana’s ideas. Apastamba provides a more general proof[citation needed] of the Pythagorean theorem.



Press Information Bureau

(Chief Minister Information Campus)

Information & Public Relations Department, U.P.

Cabinet Minister Mr. Ashok Kumar Dohre relieved from his ministerial post

Lucknow : 19 January 2011

The Governor Mr. B.L. Joshi has relieved t

he U.P.

Minister for land development and water resources Mr. Ashok

Kumar Dohre from his ministerial post on the recommendation

of the Hon’ble Chief Minister of U.P. Ms. Mayawati ji for his

behaviour and conduct which were adverse to the dignity of

ministerial post.


BSP shortlists 200 candidates for 2012 polls< ?xml:namespace prefix = o ns = “urn:schemas-microsoft-com:office:office” />

LUCKNOW: With an eye on the coming 2012 assembly elections in the state,

 Bahujan Samaj Party has already shortlisted candidates in around 200 seats out of total 403 in the state assembly. It is likely to finalise all its candidates for the polls within next two months. 

Going by the formula `jiski jitani bhagedari, uski utani hissedari’ (share according to contribution), backward classes besides SC/STs might get large share of tickets in comparison to other castes. The reason being party’s success in the backward dominated constituencies in assembly by-election since 2007 and in 2009 Lok Sabha elections. 

Chief minister and BSP supremo Mayawati wants to complete all ticket distribution `formalities’ one year in advance, so that her candidates get enough time to groom their constituencies. PWD minister and Muslim face of the BSP, Naseemuddin Siddiqui, has been assigned the task of overseeing work in 89 reserved assembly constituencies. Siddiqui’s main task would be to build a strong Muslim-SC/ST alliance in the reserved seats. SC Mishra, Maya’s close confidant and Brahmin face of the party, will continue to focus on Brahmins, while state BSP president Swami Prasad Maurya will work among backward classes 

The state has been divided into nine zones for better management. Maya has also issued instructions that only committed party workers should get the important positions from booth to the district level in the party hierarchy. She has directed functionaries to focus on the rural areas, BSP’s traditional base in comparison to the urban. She has also asked party MLAs to conduct scrutiny of the government welfare schemes in their respective areas and ensure that the benefit reaches the people, particularly SC/STs. 

The BSP cadre will also publicise the work done by the state government for SC/STs through a door-to-door campaign. 

Other backward and most backward classes (OBCs/MBCs) played important role besides Brahmin-SC/ST-Muslim combination in Maya’s 2007 success. Over 50 OBC/MBC candidates fielded by BSP had won in 2007. And, in 2009 Lok Sabha elections, five OBCs/MBCs, of 20 fielded, won. In by-elections held after 2009 general elections, BSP has won 10 backward dominated seats, making foray into backward dominated areas and Samajwadi Party strongholds like Etawah and Barthana. 

Party sources said that Maya plans to compensate for the losses due to any `anti-incumbency’ and `Brahmin disenchantment’ factors by roping in non-Yadav OBCs and MBCs. 

Not surprisingly, at present, Babu Singh Kushwaha is the second most powerful leader in the BSP. Kushwaha and BSP state president Swami Prasad Maurya are party’s OBC face. Sukhdev Rajbhar, another OBC, has been made Vidhan Sabha speaker. Mayawati had sent Ganga Charan Rajput, a Lodh (who lost to Varun Gandhi in 2009 Lok Sabha elections) to Rajya Sabha. Similarly, Vinay Shakya, who lost to Mulayam in Lok Sabha polls from Mainpuri has been to legislative council. The SC/STs constitute 30% of UP’s population and OBC/MBC around 35%. While keeping her dalit vote intact, Mayawati wants to win over MBCs for 2012. 

“Though MBCs are 5-10% in a constituency, they can tilt the results in over 150 assembly seats. A prospective winning combination will automatically attract Muslims, who vote tactically for the party in a better position to defeat BJP and form a government,” said a BSP functionary. “Behenji has also decided to drop all sitting MLAs with criminal background and those caught in controversies like Purshottam Naresh Dwivedi of Nareni (Banda), who has been accused of rape,” he added. “Only those sitting MLAs will get tickets again, whose image is good in their constituency and have potential to win the election,” he said. 

comments (0)