Vedic Literature and the Amazing Sciences and Knowledge that was Already Known


This is the basis of vedic literature. After this list and explanation there is a list of scientific discoveries of the vedic era. Your gonna be surprised at what was already know that has been just rediscovered by modern science.

The Four Veda

The following four Vedas are the most important and the ancient Vedic Granth:-

  1. Rig Veda (Rig; Rik; Rg; Rug; Rk; Richah Veda)
  2. Yajur Veda (Yajur; Yaju; Yajuh; Veda)
  3. Sam Veda (Sam; Saam; Saamaani Veda)
  4. Atharva Veda (Atharva; Atharv; Athrv; Chanddashi; Aangirash Veda)

The word Veda means knowledge, derived from the root “vid” from which four meanings can be described ‘knowledge’, ‘existing’, ‘beneficial’ and ‘thought’. They were revealed to four Rishis (Rsis) named ‘Agni’, ‘Vaayu’, ‘Aaditya’ and ‘Angiraa’ by the God at the onset of the God’s best creation – the Mankind. Patanjali, the author of Yoga-Darshana declares that God is the original teacher for the mankind – “sa purvesamapi guruh kalenanavacchedat”. Badarayana says “tattu samanvayat”; that is to say, Vedas must be God’s revelations because all they contain tally well with the creation. Vedas are also called Shruti or Samhita. The Vedas are composed of Mantras. The mantra, composed in a metre, bears a concept and teaching worth contemplation and adoption. It contains true knowledge, and inspires noble thought and action.

 

There is nothing in the Vedas that is contrary to what is seen in nature. Over and beyond what we know today, the Vedas may contain many more revelations that we might not be even aware of today. Vedas contain knowledge about both matter and spirit. The knowledge about matter is in seed form leaving ample room for man to discover further and create his own body of literature. On the other hand, the knowledge pertaining to spirit is at its pinnacle that man will never be able to add anything to that body of knowledge.

 

Vedas contain knowledge of all disciplines that man may ever get interested in, such as humanities and economics, political and social sciences, earth sciences and astronomy, chemistry and biology, physics and mathematics, technology and engineering sciences, etc and the spiritual sciences about the individual soul and the infinite soul called God. A list of such sciences with examples is given in RigVedaDiBhasyaBhumika authored in 18xx by Maharshi Dayanand Saraswati.

 

Downfall of the Vedas and then again Back to the Vedas:-

Till about more than 5000 years ago, Sanskrit was the most prominent language. Learned people like Lord Krishna and Ved Vyaas contributed to literature that contained the essence of the Vedas. However, the downfall of the Brahmin (faculty) community had already started then. With the war of Mahabharat and other events, Lord Krishna was able to unite India and uplift the Khstriya (administration) community, which lasted well for next 3000 years; till whence India saw its first invasion with Alexander. But for 3000 years the downfall of the Brahmin community continued to impact all other communities, viz; Khstriya (administration), Vaishya (commerce) and Sudra (service). Sanskrit started to become the propriety of the Brahmins. The communities started to become by birth and not by action, which they follow. The brahmins had started to undermean the Vedas for there personal benefits and supremacy and in the process the true essence of the Vedas was lost. Sanskrit started being replaced with local languages like Tamil, Pali, Prakrit, etc.

 

To compete with the advent / invasion of various faiths there after like Buddhism, Jainism, Christianity, Islam, Sikhism, Sufism, etc.; the Brahmins in the last 2000 years further worked out various literature like Puranas, Bhaagvat (not Bhagvat Gita), etc. on containing stories on things that looked great and out of the world but were opposed to the natural and spiritual sciences. The meaning of Vedas were further lost to these scriptures. Then, everything in Sanskrit became as sacred as the Vedas and anything said by the Brahmin became as sacred as Vedas even if the Brahmin knew absolutely nothing of the Vedas. In the last 1000 years, Muslims killed the learned people, burnt the sacred books and plundered the places of learning and temples. The Missionary propagandists in their zeal for conversion, in their anxiety to show the superiority of the Christian Bible, condemned the Vedas in the most positive language at their command. For this purpose they even transgressed the rules of fair honest controversy by quoting the conclusions of European Scholars on Vedic Religion and Vedic Culture without accompanying qualifications, and without giving the reader any idea of the unsatisfactory character of the translations on which these conclusions were based, though well known to and acknowledged by themselves.

 

During this period (last 2000 years), we lost many scriptures that were based on the Vedas. With the grace of God, Vedas in its Sanskrit form were not lost. Many noble people including the Brahmins over thousand of years had laid their lives to keep the original texts intact. Also, during this period came great people like Shankaracharya, Madhavacharya and Maharshi Dayanand (though with some differences of opinion) whose learned efforts helped restoring the true meaning of the Vedas.

 

Today, meaning and translations (not necessarily good translations) of the Vedas are available in almost all Indian and many foreign languages.

 

Vedas are beyond History and Geography:-

The Vedas were revealed to the earliest noble rishis and traditionally handed down to posterity. Since they were revealed in the beginning of creation, that is, prior to human history, no historical or geographical references can be sought for in the Vedic texts. As such the question of historical or geographical references to any particular country or the people inhabiting it does not arise. The Vedas were given to us when there were neither any territorial or political divisions and nor any proper names were given to particular lands, mountains, rivers or seas. All men belonged to a common world, and they stood for universal fraternity for whom the whole world was one family – “Vasudhaiva Kutumbkam”. It was centuries, or may be, millennia afterwards that the lands, rivers and mountains etc were given names, borrowed from the Vedic texts.

 

Examples:-

1) The Vedas speak of the universal and eternal conflict that goes on in man even today – an eternal conflict between good and evil, between noble and baser instincts, a conflict between knowledge and ignorance. If we come across in the Vedas a conflict between Arya and Dasyu, it is not between two particular races or tribes, but between the law abider (Arya) and the law breaker (Dasyu).

 

2) Atharva Ved 1.23.1 says “Naktam Jaatasyovadhe Rame Krishne Aasakti ch”. Now, Ram of Ramayan and Krishna of the Mahabharat belonged to quite different ages; and both long after the Vedas. These have to be interpreted etymologically in the context in which they occur in the Atharva Veda, which is as a treatise on medicine here. The verse under consideration deals the treatment of leucoderma (kilaas) and suggests a particular herb which is duskly (rama), dark (krishna) and black (asikni) in hue. This medicine recolors the ashy spots.

 

 

 

 

 

 

Upaveda

The Up-Vedas are the texts on the auxillary themes of the Vedas. The Upaveda of RigVeda, YajurVeda, SamaVeda and Atharv Veda are Economics, Military Science, Music and Dance and Medical Sciences respectively. There are 5 Upaveda that can be traced in some meaningful form, they are as follows:-
  1. Ayurveda (Sciences relating to LIFE and MEDICINE):- Ayurveda is related to the secret of life and the science of long life. The originator of Ayurveda is supposed to be Lord Dhanwantari. Apart from him, other prominent names are Aitareya, Kashyapa, Harit, Agnivesha, and Bhedamuni. At present, three important books of Ayurveda are: Charaka Samhita, Sushruta Samhita and Vagbhatta Samhita. These three books are collectively called Brihat-trayi. Patanjali has also authored text on Ayurveda.
  2. Dhanurveda: This Upaveda explains Spiritual sciences like PURUSHARTHA, DUTIES, DEEDS, etc and also Material sciences like CIVIL and MILITARY defense, war and politics. The Ramayana and Mahabharata a good deal of light is thrown upon this science and art, particularly in the descriptions of battles. The most ancient books of Dhanurveda are not available, but some of the known books are Dhanurvidhi, Drauna Vidya, Kodanda Mandana and Dhanurveda Samhita.
  3. Gandharva Veda: Gandharvaveda is the science of music, derived from the Sama-Veda, and we have already dealt with this subject briefly, while dealing with the Vedanga of Chhandas. Apart from Devotional Music it also deals with some subjects of Spiritual Sciences.
  4. Shilpa Veda (Sthapatya Veda): It deals with architecture and various arts. According to Shukra-niti there are a number of arts but 64 are considered to be more prominent.
  5. Artha Veda: Artha-Veda is the Upaveda of the Atharva-Veda, which deals with social, economic, and political systems. In the early medieval times Artha Shashtra was also authored by Chanakya

 

 

 

 

Vedanga

Vedanga are the auxiliary to the four Vedas essential for the correct interpretation of the Vedas.

Mundaka Upanishad mentions that there are six Vedanga (anga is limb) which are as follows: (i) Siksha (Education), (ii) Kalpa (Creation), (iii) Vyakarana (Grammer), (iv) Nirukta (Etymology), (v) Chhanda (Metres), and (vi) Jyotisha (Mathematics & Astronomy).

  1. Shikshaa: Science of Articulation and Pronunciation:-Siksha is related to sound, letters, pronunciation, the method of teaching and learning of these basic elements. Every Veda has its own peculiar pronunciation of certain letters, and each one of them has its specific modes and speed of recitation. A book called Siksha Sangraha contains a collection of 32 systems of siksha. These systems relate to different sakhas of the four Vedas. The most important among the books relating to siksha is the famous Paniniya Siksha. Another important book is Yaajnavalkya Siksha. In Vasishthi Siksha we have a detailed account of the differences between the mantras of the Rig-Veda and Yajur-Veda. Both Yaajnavalkya siksha and Vasishthi siksa are related to the Vajasaneyi Samhita. The other important works are: Katyaayani siksha, Paaraashari siksha, Maadhyandini Siksha, Keshavi Siksha and Manduki Siksha. In Naaradiya Siksha, which is related to the Sama-Veda, there is supposed to be the knowledge of the secret of different sounds.

The development of Siksha as a Vedaanga and as a science demonstrates the profundity and vast scope of research that was undertaken in respect of pronunciation in ancient India. It is because of this Vedaanga that the system of Vedic recitation has remained intact right from the ancient times to the present day. A given sakha is recited in the same way all over the country, and Vedapaathis of the same sakha, belonging to different parts of India, pronounce mantras with the same intonation, speed and strength and force and even the same hand movements. If the Vedaanga system of pronunciation has remained so uniform in the country, and if the tradition has remained so powerful, it is because of the degree of perfection that was achieved in respect of Siksha.

  1. Kalpa: Vedic system involves Karmakaanda (system of prescribed acts and rituals). 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 prescribed acts and rituals.
  2. Pratishakhya / Vyaakaran / Grammer:- Vyakarana is considered to be a principal part of the six Veda angas. Vyakarana is looked upon as the mouth among the Veda angas. The most celebrated author of vyakarana is Panini, who has himself mentioned several great names of the great grammarians. Panini’s famous book is Ashtadhyayi, in which he has discussed both Vedic and non-Vedic words. One of the greatest commentaries on vyakarana is that of Patanjali (the same Patanjali as in The Yoga Sutras). This is supposed to be the most authentic book on Panini’s Vyakarana. The authenticity of Patanjali’s commentary is so great that wherever there is a difference of opinion between Sutra, Vaarttika and Mahabhashya, the verdict of the Mahabhashya of Patanjali is regarded to be ultimately acceptable.

Closely connected with Siksha, Chhandas and Vyakarana, there is a body of literature known as Praatisaakhya. For each Veda and for each sakha there are certain specific rules, and these rules deal with various subjects connected with pronunciation, meters, and other grammatical matters. The meaning of the Veda is also indicated in the Praatisaakhya, and it is therefore considered to be an aid to the study of the concerned Veda. The Rik Praatisaakhya deals with the Saishiriya Upasaakha of the Saakala sakha of the Rig-Veda. Maharshi Shaunaka is the author. The great commentator Uvat has written a commentary on this Praatisaakhya.

Kaatyaayana who belonged to a period earlier than that of Panini composed Vajasaneyi Praatisaakhya. Uvat and Anantabhatta have written, respectively, Matriveda and Padaarthaprakashaka to elucidate the Praatisaakhya of Katyayana. Taittiriya Praatisaakhya is related to the Taittiriya Samhita of Krishna Yajur-Veda. The commentary has been written by Mahishi, which is known as Padakramasadana.

Pushpasutra and Riktantra are the two Praatisaakhyas on the Sama-Veda. The author of Pushpasutra is supposed to be Vararuchi, and the author of Riktantra is supposed to be Shaakatayaana.

The Chaturaadhyayika is the oldest Praatisaakhya of the Atharva-Veda. Kautsa is supposed to be the author of this Praatisaakhya, which is also known as Kautsa Vyakarana.

In sixteenth century AD, the method of the study of grammar propounded by Panini began to be replaced to some extent by the tradition of Kaatantra. In that tradition, Siddhanta Kaumudi of Bhattoji Dikshit and Prakriya Sarvasa of Narayana Bhatta are most prominent. Vyakarana developed also in the field of philosophy, and Bhartrihari who belonged to the sixth century AD initiated this.

  1. Nighantu / Nirukta (including Bhavprakash by Yashkaacharya):- Nirukta is a kind of commentary on Nighantu, which is a collection of difficult words of the Veda. Nighantu is supposed to have been one meaning, and in the fourth chapter, it gives a collection of those words, which have several meanings. In the fifth chapter, the names of Vedic gods have been collected. There have been many commentaries on Nighantu, but it is the commentary of Yaksha, which has found its place as one of the Vedaangas, and this Vedaanga is known as Nirukta. Nirukta is not confined only to meanings of words; it traces the words to their originals, and it indicates how different similar or dissimilar words arose from those origins. The principle that all names originated from verbs is an important principle of Nirukta, and even modern linguists accept this principle. Prior to Yaksha also, there were many methods and systems of Vedic interpretation, such as Aadhi-daivata, Aadhyaatma, Aakhyaana-Samaya, Aitihaasika, Naidaana, Paarivraaajaka, Yaajnika, etc.
  2. Chando Granth (prosody poetry):-
    The composition of the Vedas indicates consummate development of the knowledge of the poetic meter, chhandas. The first discussion on Vedic meters is to be found in the Saankhyaayana Srauta-sutra. But the classical work on meters is that of Maharshi Pingal. Meters or chhandas have been studied by Pingal in the eighth chapter of his book Chhandah-sutra. In this book, he has taken into account not only Vedic meters but also others. There are mainly seven Vedic meters, namely, Gayatri, Ushnik, Anushtubh, Brhati, Pankti, Trishtubh, and Jagati. According to Kaatyaayana, the highest number of mantras in the Rig-Veda is to be found in Trishtubh. This number is 4253. Gayatri has 24 67 mantras; Ushnik has 341 mantras; Pankti has 312 mantras, and Brahti has 181 mantras. Although there are numerous meters, we find only 50 meters in the Sanskrit literature.Prior to Pingalacharya, there were several great teachers of Chhanda Sastra, such as Koshtuki, Yaksha, Kaashyapa and Maandavya. There have been several commentaries on the Chhanda-sutra of Pingalacharya. In fact, there has been a continuous development of books on Chhanda Sastra.

The development of musical science also owed a great deal to Chhanda Sastra. It is well known that the Sama-Veda is to sing. Although the method of singing the Sama is different from that of classical music, the seven tunes, namely, shadja, rishabha, gandhara, madhyama, panchama, dhaivata, and nishaada are used in Sama in the same way as in classical music. In the Chhaandogya Upanisad which is based upon the Sama-Veda, five types of musical renderings of the Sama have been indicated, namely, Himkaara, Prastaava, Udgitha, Pratihaar and Nidhaan. It is noteworthy that Vedic literature refers also to several musical instruments, including the veena. In social life, too, because of the close connection between religious rites and music, various melodies developed, particularly six melodies corresponding to the six seasons. Closely connected with music was the development of dance and drama. Among the important works in Sanskrit regarding music, dance and drama the most important one is Naatya Sastra of Bharat Muni. There are two Samhitas on Natya Sastra, namely, Dwaadasha Sahasri and Shat Sahasri. The traditions established by Bharat Muni remained prevalent for more than a thousand years, and even in the book Sangeet Ratnaakar or Sharangadeva of thirteenth century AD, the authority of Bharat Muni has been acknowledged. Thereafter also there has been a vast literature on music, dance and drama. In fact, music, dance, and drama received royal patronage throughout the ages, and some of the great kings of the north and south were themselves great musicians.

Jyotish / Astronomy and Astrophysics:-The sixth Vedaanga relates to Jyotisa – astronomy and astrology. Jyotisa is considered to be the science of light, and it is looked upon as the eyes among the Vedaangas. Vedic knowledge had discovered an inner rhythm cosmic movement, and this rhythm seems to correspond with periodic developments and seasons of human life. The transit of planets, calculation of days and nights and the determination of various seasons were closely studied. The science of Jyotisa described planets, constellations, comets and also the rotations and revolutions of various luminous objects of the heavens.

Rig-Veda Jyotisa Vedaanga has been attributed to Lagadhaacharya. It consists of 36 verses. There is also a Jyotisa related to the Yajur-Veda and another related to Atharva-Veda. Yajur-Veda Jyotisa consists of 34 verses, and it has been attributed to Shoshaacharya. Atharva-Veda Jyotisa has 14 chapters and 102 verses. It is supposed to be a dialogue between Pitaamaha who was the speaker and Kashyapa who was the listener.

In due course, Jyotisa inspired the development of various sciences including arithmetic, algebra, geometry, astronomy, and astrology. Bhaskaraacharya of twelfth century AD is regarded as the first among the mathematicians and astrologers of the middle ages. Jyotisa is even today prevalent all over India, and it is even now a developing science. The Panchaanga, which gives detailed information regarding the tithi, vaara, nakshatra, yoga and karana, is commonly used in most Indian homes; and astronomers, astrologers and many individuals in day-to-day life constantly consult the annuals of the Panchaanga.

 

 

 

 

 

 

Shaakha

The Shaakhas of the Vedas are explanations and / or editions of the original Samhitas (Vedas); and thus not the original Vedas. They may be even mixed up with the Brahmanas. So they are the creation of later Vedic Seers. In the past there where 1127 Shakhas of the Vedas including 20 of the RigVeda, 100 of the Yajurveda, 1000 of the SamVeda and 7 of the AtharvaVeda.

But at present only a few (8-10) Shakhas are available.

 

 

 

 

 

Brahman

Vedas in its pure form though can be understood by the Rishis (who had that acquired intellect), such rishis authored Brahmans that can be stated to be the first interpretations of the Vedas. Some scholars have mistaken Brahmanas to be a part of the original Vedas. Brihal Parashar Smriti defines thus “A Brahman is a book which tells the meaning of Vedic Mantras and its use”. Similarly in Vaishaishik Darshan, Maharshi Kannaaad says, “Brahmanas defines words of the Vedas and its meanings. In ancient times there where many Brahmanas, but currently only six are to be found:-

  1. Aitareya Brahman Granth based on Rig Veda authored by Rishi Aitareya Mahidaas.
  2. Shankhyayan Brahman Granth based on Rig Veda
  3. Kaushtiki Brahman based on Rig Veda
  4. Shatapath Brahman Granth based on Yajurveda
  5. Maha-Tandya Brahman Granth based on Sam Veda
  6. Gopath Brahman Granth based on Atharva Veda

 

 

 

 

 

Aranyak

Aranyak Granth contains the extracts from Brahman Granths.

 

 

 

 

 

 

 

 

Sutra Granth

The following are the nine Vedic Sutra Granth that can be found:-

  1. Grihay Sutra
  2. Dharma Sutra
  3. Shrota Sutra
  4. Ashvalayana
  5. Gobhil
  6. Paraskar
  7. Koshitaki
  8. Katyayana
  9. Bodhayana

 

 

 

 

 

 

Smriti

Smriti(s) are the books of social, economic and political laws, which are changeable with time and have been composed by scholars from time to time as the need was. Amongst 250 Smrities (known to have been mentioned in different texts) only some 57 are traceable now, the most prominent ones being Manu Smriti.

 

After the last plavan, the learned King Vaivaswat Manu took the pledge of re establishing the displaced human society. He authored Manu Smriti in which he laid the basic natural, civil and criminal laws required to run a society. There are 12 chapters in ManuSmriti.

 

YajyaValka Smriti is another valuable one. It consists of 3 Chapters: Aachaar, Vyavahaar, & Praayashchita. Some twenty other Smritis are: –

  •                                                               i.            Atri
  •                                                             ii.            Vishnu
  •                                                           iii.            Haareeta
  •                                                           iv.            Aushanasi
  •                                                             v.            AAngirasa
  •                                                           vi.            Yama
  •                                                         vii.            AApastamba
  •                                                       viii.            Samvarta
  •                                                           ix.            Kaatyaayana
  •                                                             x.            Brihaspati
  •                                                           xi.            Paaraashara
  •                                                         xii.            Vyaasa
  •                                                       xiii.            Shankha
  •                                                       xiv.            Likhita
  •                                                         xv.            Daksha
  •                                                       xvi.            Gautama
  •                                                     xvii.            Shaataatapa
  •                                                   xviii.            Vashishtha
  •                                                       xix.            Bhrigu
  •                                                         xx.            Naarada

 

 

 

 

 

 

Darshan Shashtra

There are six Darshan Shashtras  – also known as Upaang or Shat Darshan (The Six Philosophies); they are:-
  1. Purva Mimaansa / Mimaansa Shashtra by Rishi Jaimini:- The author of this Darshan is Rishi Jaimini ji. The science of morals is discussed in detail. The concept of this darshan is Dharma, Dharmi (the thing which possess dharma) & Yagya (Sacrifice) & the duties & non-duties of the mankind which range from family life to national service are described, through which the extreme development of the entire nation is possible. Infect the great form of the Dharma is the Yagya (Sacrifice).
  2. Vaisheshika Shashtra by Rishi Kannaada:- The author of this Darshan is Rishi Kanaad ji. He has described the true form of the Dharma. The mean that is helpful in achieving worldly & spiritual success is Dharma. Moksha (Supreme Bliss) is obtained by living as truly righteous life & thereby getting the soul purified & exalted, and gaining a true conception of the six entities, viz., Noumenom, Attribute, Action, Commonness, Dissimilitude & Inherent relation, (as of cause & effect, of whole with its parts). Its main themes are “Nothing can be created without any material’, “Absence of the cause is absence of the effect”, etc.
  3. Nyaaya Shashtra by Rishi Gautama:- The author of this Darshan is Rishi Gautama ji. The subject of this darshan is to attain Moksha (Salvation) by getting the philosophical knowledge of 16 (sixteen) objects like Proof/Evidence, Proposition, Logic etc., The order in which the above 16 objects explained is as follows (i) Name (ii) Features & (iii) Detailed examination of the objects. Its main theme is ” To examine the things through the proofs & evidences is Nyaaya”. God is the creator of the universe, formless, omnipresent, Soul is different from the body, mind etc., & material nature is unintellectual & raw material of the universe are clearly explained & proving the Traitavaad. An ancient & authentic commentary on this darshan by Maharishi Vaatsyayan ji is available.
  4. Yoga Shashtra by Rishi Patanjali:- The author of this Darshan is Maharishi Patanjali ji & it deals with the Saadhana, Dhyan, Samaadhi etc., & gives a clear-cut idea about the God, Soul & Material world, true form of the God, Vedic worship (Upaasanaa) & Means of obtaining the Moksha (Salvation). Further subtle topics are also explained like, (i) what is yoga?, (ii) What is the reason of soul’s bondage ?, (iii) what are the different stages & attainments of the yoga practitioner (Saadhak) ?, (iv) what are the fluctuations of the mind & how to completely stop it ?, (v) Till what time the connection of the soul & mind exists? Etc., An ancient & authentic commentary on this darshan by Maharishi Vyaasa ji’s is very familiar in yoga.
  5. Sankhya Shashtra by Rishi Kapila:- The author of this Darshan is Rishi Kapil ji & its subject is about the Prakriti & its products & Purusha. It is absorbed that the word “Purusha” is denoted for both the God & the Soul. The basis of this darshan is Sat Kaarya Vaad “Nothing can ever become something, nor can something ever become nothing”. The order of Creation & Dissolution of the universe from the Prakriti is exclusively explained in this darshan. Only through discrimination obtained by knowing the true form of the material world & purusha, Moksha/Salvation is obtained. It is also explained that the universe is not false, True in existence by having the material world as the subtle cause & further 24 (Twenty Four) intermediate entities.
  6. Uttar Mimaansa  / Vedaant Shashtra by Rishi Veda Vyaas / Baadaraayana:- The author of this Darshan is Rishi Vyaasa ji & the subject is about the Brahmaa (Iswhar) & attainment of Brahmaa / Moksha (Salvation). Its other names are Brahmasootra & Uttar Meemaamsaa. Brahmaa (God) is an entity, which is omnipotent, omnipresent, blissful. He is free from sorrows of birth & death. Jeevaatmaa (Soul) is also a different entity having little intellect & subtle. He wants to get rid out of sorrows. God creates the universe from the Prakriti. The meaning of the Vedaanta is – “The essence of the Vedas”.

In short some few common principles of the six Darshans :

  • By the freedom, from the three types of sorrows, Moksha (Salvation) is obtained.
  • God, Soul & Prakriti are the eternal causes of the creation of the universe.
  • Nonexistence of Existent objects & existence of nonexistent objects is extremely impossible.
  • Vedas are self-proven, because it is gospel-word of the God.
  • Soul is different from the body, mind etc., & inconsequential.
  • God is different from the soul, omnipresent, infinite intellect, omnipotent etc.,
  • According to the God’s discipline & deeds done by the soul, the soul repeal the results of the deeds.
  • The visible universe is the product of the Prakriti.
  • The reason of the bondage of the soul is its ignorance.
  • Each & Every body has its own unique soul.
  • Soul can never become a God, it has its own unique existence.

 

 

 

 

 

Upanishad

The Upanishads mostly explain in details Vedic Theology including metaphysics, spiritual and mystical powers and concepts of the God. The literal meaning of Upanishad itself is “the knowledge of realizing and visualizing God”. In some Upanishads, some of the Vedic hymns are produced as such. These texts mostly deal with the concepts, characteristics and manifestations of powers of the God, nature and properties of the soul, its relationship with the God; sometimes in figurative manner or in symbolic stories. in these books, most complex philosophical concepts and spiritual experiences have been presented through lucid dialogues. Upanishad is also called Shruti.

 

References in mythological literature indicate the existence of 1000 Upanishads in ancient times. It is said that in ancient times each Shaakha of a Veda had its own Upanishad. But like Shakaas, Upanishads are also untraceable now. The major 11 ones are as noted below (with the Veda they belong to):-

  1. Isha (Yajur): – Ishopanishad provides the basic tenants of the Vedas in brief. Important Vedic Concepts relating to the God, soul and nature, moral duties, monotheism, life after death, and other complex philosophical concepts are clearly dealt therein. Except one mantra, the entire Ishopanishad is the last chapter of YajurVed and is the gist of Vedic Religion.
  2. Kena (Sam)
  3. Kantha (Atharv)
  4. Prashna (Atharv)
  5. Mundaka (Atharv)
  6. Maandukya (Atharv)
  7. Aitareya (Rig)
  8. Taittreya (Yaju)
  9. Chaandogya (Sam)
  10. Brihadaarannyak (Yaju)
  11. Shwetashwatar (Atharv)

 

 

 

 

 

Purana

The Puraanas are the books of ancient Indian History, culture and civilization along with mythology of Hindu Religion and its several sects. Along with some description of creation of Universe, moral education, and history of Kings, they emphasize on incarnation of God in different gods and goddesses as Brahma, Vishnu, Shiva and their incarnations. Each Purana is devoted to the main deity of a particular sect, i.e. Vaishnav, Shaiva or Shakti showing supremacy of one over other – reflecting the sectarian approach.

 

 

The Pauranics (the believers of the Puraanas) are not unanimous about the number and source of the Puranas. Given below is one of the counts available:-

 

Eighteen (18) Maha Puranas:

Brahm

Padma

Vishnu

Shiva (or Vayu)

Shrimadbhaagvata

Narada

Markandeya

Agni

Bhavishya

Brhmvaivarta

Linga

Varaaha

Skanda

Vamana

Koorma

Matsya

Garurha

Brahmaanda

 

 

In addition, there are eighteen (18) Upa-Puranas, and eighteen (18) Upa-Puranas which are also called Ati-Puranas as follows:

Eighteen (18) Upa- Puranas:

Bhaagvat

Maaheshvara

Brahmaand

Aaditya

Saura

Nandakeshvara

Saamba

Kaalikaa

Varuna

Ushanas

Maanava

Kaapila

Durvaasas

Shivadharma

Vrehannaaradiya

Naarasinha

Sanatkumaara

 

 

Eighteen (18) Upa-Puranas or Ati-Puranas:

Kaartava

Riju

Aadi

Mudgala

Pashupati

Ganesha

Surya

Paramaananda

Brehaddharma

Mahaabhagavata

Devi

Kalki

Bhargava

Vaashishtha

Kaurma

Garga

Chandi

Lakshmi

 

 

 

 

 

Itihaas

Out of the various historical stories authored in Sanskrit, two of them find a special place in Vedic Literature as contain valuable study, reading and following of the Veda. These are also called the great epics of Hinduism, they are: –

  1. Ramayan (The history of Sri Ram of liberating India from Raavan rajya and establishing Ram rajya) by Maharshi Valmiki
  2. Mahabharat (The history of Sri Krishna of uniting the Indian Sub Continent) by Maharshi Ved Vyaas. Mahabharat includes the famous dialogue “Bhagvad Gita” between Sri Krishna and his disciple Arjun.

 

 

 

 

 

Neeti

At various times, sages have authored literature on their primary set of beliefs and ethics. These are called Neeti. There are various Neeti, of which authored the following are worth mentioning: –

  1. Vidur Neeti
  2. Chaanakyaa Neeti
  3. Bhartrihari Neeti
  4. Shikra Neeti

 

 

This is just a small list of some of the scientific knowledge that comes from the Vedic literature.

 

 

 

MOTION OF EARTH

Rig Veda 10.22.14
“This earth is devoid of hands and legs, yet it moves ahead. All the objects over the earth also move with it. It moves around the sun.

In this mantra,
Kshaa = Earth (refer Nigantu 1.1)
Ahastaa = without hands
Apadee = without legs
Vardhat = moves ahead
Shushnam Pari = around the sun
Pradakshinit = revolves

Rig Veda 10.149.1
“The sun has tied Earth and other planets through attraction and moves them around itself as if a trainer moves newly trained horses around itself holding their reins.”

In this mantra,
Savita = Sun
Yantraih = through reins
Prithiveem = Earth
Aramnaat = Ties
Dyaam Andahat = other planets in sky as well
Atoorte = Unbreakable
Baddham = Holds
Ashwam Iv Adhukshat = Like horses

 

 

GRAVITATIONAL FORCE

Rig Veda 8.12.28
“O Indra! by putting forth your mighty rays, which possess the qualities of gravitation and attraction-illumination and motion – keep up the entire universe in order through the Power of your attraction.”

Rig Veda 1.6.5, Rig Veda 8.12.30
“O God, You have created this Sun. You possess infinite power. You are upholding the sun and other spheres and render them steadfast by your power of attraction.

Yajur Veda 33.43
“The sun moves in its own orbit in space taking along with itself the mortal bodies like earth through force of attraction.”

Rig Veda 1.35.9
“The sun moves in its own orbit but holding earth and other heavenly bodies in a manner that they do not collide with each other through force of attraction.

Rig Veda 1.164.13

“Sun moves in its orbit which itself is moving. Earth and other bodies move around sun due to force of attraction, because sun is heavier than them.

Atharva Veda 4.11.1
“The sun has held the earth and other planets”

 

 



LIGHT OF MOON

Rig Veda 1.84.15
“The moving moon always receives a ray of light from sun”

Rig Veda 10.85.9
“Moon decided to marry. Day and Night attended its wedding. And sun gifted his daughter “Sun ray” to Moon.”

 

 
ECLIPSE

Rig Veda 5.40.5
“O Sun! When you are blocked by the one whom you gifted your own light (moon), then earth gets scared by sudden darkness.”

 

 



“SCIENCE OF BUILDING SHIPS AND AIRPLANES”
Swami Dayanand has detailed Mantras regarding these in his Vedic commentary and Introduction to Vedas” (1876). The scientists of IISc concluded that the mechanism of airplane as suggested by Dayanand is feasible. The first manned plane was built 20 years after death of Swami Dayanand.

The verses are difficult to translate in English here, but readers are advised to review “Introduction to Vedas” by Swami Dayanand or interpretations of following mantras: Rig Veda 1.116.3, 1.116.4, 10.62.1, 1.116.5, 1.116.6, 1.34.2, 1.34.7, 1.48.8 etc.

 

 

 

SCIENCE OF TELEGRAPHY

Rig Veda 1.119.10
“With the help of bipolar forces (Asvins), you should employ telegraphic apparatus made of good conductor of electricity. It is necessary for efficient military operations but should be used with caution.”

 

 

DISCOVERY AND USE OF ZERO

Gaayathre shadsankhyaamardhe apaneethe dvayanke avasishtasthrayastheshu roopamapaneeya dvayankaadha: soonyam sthaapyam In gayatri chandas, one pada has six letters. When this number is made half, it becomes three (i.e the pada can be divided into two). Remove one from three and make it half to get one. Remove one from it, thus gets the zero (Soonya). PINGALACHARYA IN CHANDA SASTRA 200 B.C. 

 

 

CALCULATIONS WITH ZERO

Vikaaramaayaanthi dhanarunakhaani na soonya samyoga viyogathasthu soonyaaddhi suddham swamrunam kshayam swam vadhaadinaa kham khaharam vibhakthaa: Nothing happens (to the number) when a positive or negative number is added with 0. When +ve and -ve numbers are subtracted from 0, the +ve number becomes negative and -ve number becomes +ve. When multiplied with 0, the values of both +ve and -ve numbers become 0, when divided by 0, it becomes infinity (khahara). SRIPATI IN SIDDHANTHA SEKHARA 1039 AD Yathaa ekarekhaa sathasthaane satham dasasthane dasaiam chaikasthaane yathaa cha ekathvepi sthree mathaa cha uchyathe duhithaa svasaa cha ithi In the unit place the digit has the same value, in 10th place, 10 times the value and in 100th place 100 times the value, is given.

VYASA BHASHAYA TO YOGA SUTRA 650 AD

 

 

 

DISCOVERY OF PLACE VALUES – II 

Yathaachaikaapi rekha sthaananyathvena nivisamaanaika dasa satha sahasraadi sabda prathyaya bhedhamanubhavathi 

One and the same numerical sign when occupying different places is conceived as measuring 1, 10, 100, 1000 etc.

SANKARACHARYA VEDANTA SUTRA BHASHAYA 

 

 

 

KNOWLEDGE ON INFINITY 

Asmin vikara khahare na raasaavapi praveshteshvapi ni: srutheshu bahushvapi syaallaya srushtikaalenanthe chyuthe bhoothaganeshu yaddhath 

Nothing happens to the (huge number) infinity, when any number enters (added) or leaves (subtrated) the infinity. During pralaya many things get dissolved in Mahavishnu and after pralaya, during srushti all those things get out of him. This happens without affecting the lord himself. Like that, whatever number is added to infinity or whatever is subtracted from it, the infinity remains unchanged.

BRAHMAGUPTHA IN BRAHMASPHUTA SIDDHANTA 600 AD, BHAKARACHARYA II – BEEJAGANITA 1148 AD 

 

 

 

USE OF AVERAGE VALUES 

Ganayithva visthaaram bahushusthaneshu thadyuthirbhaayyaa sthaanakamithyaa samamithirevam dairgye cha vedhe cha 

(For length, breadth and depth) the measurements should be taken at many places and the sum should be divided by the number of times (places) the measurement is taken. BHASKARACHARYA II IN LILAVATI 1150 AD 

 

 

 

USE OF FRACTIONS

Drammaardha thrilavadvayasya sumathe paadathrayam yadbhaveth that panchaamsaka shoda saamsa charana: sampraarthithenaa- rthinaa datto yenavaraatakaa: kathi kadaryenarpithastena me broohithvam yadi vetsi vatsaganitha jaathim prabhagaabhidhaam 

One man has given to a beggar fraction of 1 dramma (a unit of money). That fraction is one fourth of the one sixth of one fifth of the three fourth of the two third of the half of a dramma. Then tell how much kowdi (a unit fraction of the amount dramma) was given to the beggar?

BHASKARACHARYA I – ARYABHATEEYA BHASHAYA 628 AD 

 

 

 

USE OF RATIO AND PROPORTION 

Ashtow daanthaa sthryo damyaa ithi gaava: prakeerthi thaa: ekaagrasya sahasrasya kathi daanthaa: katheetharai: 

(Out of 11 cattle) Eight are tamed and 3 are to be tamed and (how many are) to be tamed) if the number of cows is 1001?

BHASKARACHARYA I – ARYABHATEEYA BHASHAYA 628 AD 

 

 

 

PERMUTATIONS AND COMBINATION – I 

Katukathiktha kashaayaamla lavana madhurai: sakhe rasai: shadbhi: vidadhaathi soopakaaro vyanchanamaachakshva kathibhedam 

Friend, a cook prepared varieties of food with 6 savours: pungent, bitter, astringent, acid, saline and sweet. Say what is the possible number of varieties of food that can be made with these savours.

SRIDHARACHARYA IN PATIGANITA 990 AD 

 

 

 

PERMUTATIONS AND COMBINATION – II

Paasankusaahi damarooka kapaala soolai: khadvangasakthi sara chaapayuthairbhavanthi anyonya hastha kalithai: kathi moorthibhedaa: sambho haririva gadaari saroja sankachakrai: 

Pasa, ankusa, serpant, damaru, kapala, soola, khatvanga, sakti, chapa, sara with these (ten) items how many permutations and combinations are possible for Lord Siva. Similarly with the four items, sanku, chakra, gadha and padma holding in the hands, how many combinations are possible for Lord Vishnu?

BHASKARACHARYA II IN LILAVATI 1114 AD 

 

 

 

PARTNERSHIP AND SHARES 

Samavaayakaasthu vanija: panchaikaikottharaadhi mooladhanaa: laabha: sahasra sankhyo vada kasmai thathra kim deyam 

Five partners collaborate in a business. The capital invested by them are (in the ratio) one and the same number increasing successively by one (i.e 1,2,3,4, & 5) respectively. Profit that accrued amounts to 1000. Say what should be given to whom.

BHASKARACHARYA I – IN ARYABHATEEYA BHASHYA 628 AD 

 

 

 

LOANS AND INTERESTS 

Kutumbaarthamasakthena gruheetham vyaadhithena vaa upaplava nimittham cha vidyaathaapalkrutham thath kanyaavaivahikam chaiva prethakaaryeshu yathkrutham ethath sarvam pradaathavyam kutumbena krutham prabho 

Loans are taken for meeting the expenditure connected with economic problems due to family burden, health problems, treatment, education, expenditure during accident, marriage of daughter, for performing rituals connected with the demise of the family members, etc.

VISHNUSMRUTHI 100 BC 

 

 

 

INTEREST CALCULATION

Maasena sathasya phalam panchaiko bhavyakerdhamaya vruttho lekhakapaado varshe panchaadika navasatheemisram 

The rate of interest being 5% per month, the commission of surety 1% per month, fee for accountant .% and charges of the scribe 1/4% per month, certain sum amounts to 905 a year. Find the capital, the interest and the shares of the surety?

SRIDHARACHARYA IN PATIGANITA 990 AD 

 

 

 

RULES OF CHARGING INTEREST 

Atha utthamarna: adhamarnaadyathaa datthamartham gruhneeyaath dvikam thrikam chathushkam panchakam cha satham prathimaasam 

The loans can be given and taken between borrower and lender. Generally charged interest rates are 2, 3, 4, or 5% per month.

Sa paadapanaa dharmyaa maasavruddhi: panassathasya panchapanaa vyaavaharikee 

Reasonable (dharmic) rate of interest is 1.25% per month (i.e 15% per annum) on the transactions with common man for non commercial purposes. But for commercial purposes (for making profit out of it) interest rate can be 5% per month.

VISHNU SMRUTHI 100 B.C 

 

 

 

RULES OF BODIES IN MOTION 

Bhakthe vilomavivare gathiyogenaanulomavivare dvow gathyantharena labdow dviyogakaalaavatheethaishyow 

Whenever two bodies are travelling in the opposite directions, the distance between them is to be divided by the sum of their speeds. If they move in the same direction, the distance is to be divided by the difference of their speeds. This gives the time required for meeting of the bodies or the time elapsed after meeting of the moving bodies.

ARYABHATA I – ARYABHATEEYA 499 AD 

Ekow naa yojananyashtow yaathyanyo yojanadvayam yojanaanaan satham panthaa: sangama: kva gamaagame

One man travels at 8 yojana speed per day. Another travels at 2 yojana per day, starting simultaneously from the same place. After reaching the destination, the first man comes back. If the length of the track is 100 yojana. Say where is the meeting place of the two? (One going forward and the other traveller returning).

SREEDHARACHARYA PATIGANITHA 990 AD 

 

 

 

PROGRESSION OF THE TYPE 

12 + 22 + 32 + 42 + …. 

Sapthaanaam ashtaanaam saptadasaanaam chathurbhu jaaschithaya: ekavidyaanaam vaachyam padastharaasthaa hi vargaakhyaa: 

There are (three pyramidal) piles on square bases having 7, 8 and 17 layers which are also squares. Say the number of units there in.

BHASKARACHARYA I – ARYABHATEEYA BHASHYA 628 AD 

 

 

 

PROGRESSION OF THE TYPE 13 + 23 + 33 + 43 + 

Chathurasraghanaschithaya: panchachathurnavastharaa vinirdesyaa: ekaavaghatithaasthaa: samachathura sreshtakaa: kramasa: 

There are three pyramidal piles having 5, 4 and 9 cuboidal layers. They are cuboidal bricks (of unit dimension) with one brick in the topmost layer. Find the number of bricks used in them.

BHASKARACHARYA I – ARYABHATEEYA BHASHYA 628 AD 

 

 

 

PROGRESSION OF THE TYPE 

n + n2 + n3 + n 4 

Sankalithakruthighanaanaam sankalithasamaasamaanaam me kathaya shannaam sakhe padaanaam ganayithvaa yadivijaanaasi

Friend, if you know, then say after calculation (i) the sum of successive sum of 6 natural numbers (ii) the sum of the squares of the first 6 natural numbers and (iii) the sum of the cubes of first 6 natural numbers.

SREEDHARACHARYA – IN PATIGANITHA 900 AD 

 

 

 

FIRST DEGREE INDETERMINATE EQUATION 

Mudgaanaam kudavaa: saptha labhyanthe navabhi: pane: panena kudavasyaardham thandulaanaamavaapyathe thatha: panathrayam saardham gruheethvaaasu vaningmama thandulaanaam prayacchaamsa mudgaanaam cha dvisangunam 

7 kudavas (unit of measurement) of mudga are obtained for 9 panas and . kudava of rice is obtained for one pana. Then O! merchant take 3. panas and quickly give me one part of rice and two parts of mudga.

SREEDHARACHARYA – IN PATIGANITHA 900 AD 

 

 

 

FIRST ORDER EQUATION – I 

Ye nirjaraa dinadinaardha thrutheeya shashtai: sampoorayanthi pruthak pruthakeva mukthaa: vaapeem yadaa yugapadeva sakhe vimukthaasthe kenavaasaralavena thadaa vadaasu 

By opening 4 inlets separately, one pond gets filled respectively within 1, ., 1/3, and 1/6 days. If all the four inlets are opened together, how much time (in fraction of the day) is required to fill the pond ?

BHASKARACHARYA II – IN LILVATI 1114 AD 

 

 

 

FIRST ORDER EQUATION – II 

Nava gulikaa saptha (cha) roopakasamaasthrayaanaam (thu) gulikaanaam thrayodasaanaam cha roopakaanaam thadaa kim gulikaa moolyam 

If 9 gulika and 7 rupaka are equal to 3 gulika and 13 rupaka, what is the price of one gulika? (the answer can be determined through the same method followed above)

SREEDHARACHARYA PATIGANITHA 990 AD 

 

 

 

EQUATIONS OF HIGHER ORDER- I 

Vaanarakulathribhaga: svathryamsa samanvi1tha: sara: prayayow moolam cha pipaasathi dvow choothathale sthithow seshow 

One third of a troop of monkey with one third of itself has gone to the tank; the square root of the whole troop is afflicted with thirst, and the remaining 2 monkeys are sitting under the mango tree. What is the total number of monkeys? 1/3 a + 1/9 a + a + 2 = a

REEDHARACHARYA – PATIGANITHA 990 AD 

 

 

 

EQUATIONS OF HIGHER ORDER- II 

Bale maralakula mooladalaani saptha theere vilaasabhara manthara gaanyapasyam kurvancha keleekalaham kalahamsayugmam sesham jale vada maraalakula pramaanam 

I saw that one half of 7 times of the square root of the total number of swans were slowly moving away in the river. Remaining 2 are playing in water. What is the number of total swans? (equation: 7/2 a+2=a)

BHASKARACHARYA – LILAVATI 1114 AD 

 

 

 

PYTHAGORUS THEOREM DISCOVERED BY BOUDHAYANA 

Samachathurasrasyakshnayaa rajju dvishtavathim bhoomim karothi 

The diagonal of a square produces double the area of the square.

Deerghachathurasrasyakshnayaarajju: paarsvamaani thiryanmaani cha yatpruthakbhoothe kuruthasthadubhayam karoti 

Areas produced separately by the length and breadth of rectangle together equal to the area of the (square) produced by the diagonal.

BOUDHAYANA BOUDHAYANA SULBASUTRA 700 BC 

 

 

 

EXPLANATION OF BINOMIAL THEOREM 

If a three syllablic Madhya Chanda based on guru and lakhu sounds were followed, then variation of guru and lakhu sound will be on the following pattern: 3 guru sound occur once, 2 guru and 1 lakhu occur thrice, 1 guru and 2 lakhu sounds occur thrice, 3 lakhu occur once. The equation can be derived easily. If guru is g and lakhu is 1 then,

(g+1)3 = g3+3g21+3g12+l3. This equation is the same as (x+y)3. Similarly for finding the pratishta Chanda, in the Chanda sastra of Pingalacharya, the following equation can be indirectly applied in this form: (g+1)4 which is expanded as g4+4g31+4g212+4g13+14 I.e 4 guru sound occur once, 3 guru and 1 lakhu occur four times, 2 guru and 2 lakhu occur four times, 1 guru and 3 lakhu occur four times and 4 lakhu occur once.

PINGALACHARYA – CHANDASASTRA 200 BC 

 

 

 

GEOMETRY IN SULBASUTRA-II 

Thaasaam trika chathushkayordvaadasikapanchikayo: panchadasikaashti kayo: saaptikachathurimsathikayo: dvaadasika panchathrimsathikayo: panchadasikashad- thrimsikayo: ithyethaasoopalabdhi: 

Hypotenuse in rectangles having sides 3 and 4 (= 5), 12 and 5 (= 13), 15 and 8 (= 17), 7 and 24 (= 25), 12 and 35 (= 37) and 15 and 36 (= 39) (I.49).

BOUDHAYANA BOUDHAYANA SULBASUTRA 700 BC

 

 

 

ANGULAR DIMENSIONS 

Angagunavedahuthaasaa: kalikaa vikalaa: samudrajaladhaya: svalpajalakhaashtasasi dhruthisasina: kalikaa: saraagnayo vikalaa: thrijyaakruthivarashta navathribhuvo visve jinaamsajyaa. 

Thribhujasya phalasareeram samadalakoti bhujaardha samvarga: 

The area of a triangle is the product of the prependicular and half the base.

ARYABHATTA I ARYABHATEEYA 499 AD 

Karnasthrayodasa syaath panchadasaanyo mahee drisapthaiva vishamasthri bhujasya sakhe phalasankhyaa kaa bhavedasya 

What is the area of a scalene traingle in which one lateral side is 13 units, other 15 unit and the base is 14 units.

Ashtaadasakocchrayovamso vaathena paathithomoolaath shadgathvaavasow pathithaasthribhujam kruthvaa kva bhaghna: syaath 

A bamboo of beight 18 cubits fell by the wind, it falls at a distance of 6 cubits from the root, thus forming a right triangle, where is the break?

BHASKARA I COMMENTARY TO ARYABHATEEYA 628 AD 

 

 

 

POLYGONAL 

Thribdhyankaagninabha schandraisthri bhaanaa shtayugaashtabhi: vedaagni baanakhaaschaicha khakhaabhraa bhrarasai: kramaath baaneshu nakha baanai schadvidvi nandeshu saagarai: kuraamadasavedaischa vruthhavyaase samaahathe khakhakhaabhraarka sambhakthe labhyanthe kramasobhujaa: vrutthaantha sthraya poorvaanaam navaasraantham pruthak pruthak 

For cyclic equilateral triangle, cyclic square, cyclic equilateral pentagon,…. to cyclic equilateral nonagon, (cyclic figures having 3 to 9 sides with equal side measurements) their sides can be calculated respectively when diameter is multiplied separetely with 103923 (triangle) 84854 (quadrilateral) 70534 (pentagon), 60000 (hexagon) 52055 (septagon) 45922 (octagon) and 41031 (nonagon) and divided by 120000, the value will be the measurements of the sides of cyclic equilateral triangles to cyclic equilateral nonagon. Bhaskaracharya has given the example: If 2000 is the diameter of circle, equilateral geometrical figures inscribed inside that circle will have sides as follows:

Geometrical figure Bhaskara’s value Modern value

Triangle 1732 + .05 1732.043

Square 1414 + .021 1414.211

Pentagon 1175 + .056 1175.5619

Hexagon 1000 + .00 999.996

Septagon 867 + .58 867.5799

Octagon 765 + .36 765.3636

Nonagon 683 + .85 683.85

BHASKARA II – LILAVATI 1114 AD 

 

 

 

CIRCLE – VALUE OF Π 

Chathuradhikam sathatmashtagunam dvaashashtisthathaa sahasraanaam ayuthadvya vishkambasyaasannoo vruthhaparinaaha: 

When 100 increased by 4 multiplied by 8 and added to 62,000 gives an approximate value for the circumference of a circle having diameter 20,000 units.

ARYABHATA I ARYABHATEEYA 499 AD 

Ashtadvaadasa shadkaa: vishkambhasthathvatho mayaa drushtaa: theshaam samavrutthaanaam parithiphalam me pruthak broohi 

Diameter of 3 circles are correctly seen by me to be 8, 12 and 6 units respectively. Tell me separately the circumference and areas of the circles.

BHASKARACHARYA I – 628 AD

 

 

 

SOMAYAJI’S THEOREMS 

Vyaasaath vanasangunithaath pruthagaaptam thryaadyayugvimoola ghanai: thrigunavygaase svamrunam kramasa: kruthvaapi paridhiraaneyu: 

Multiply the diameter of a circle with 4 and keep it at different places and divide each with the odd numbers beginning from 3, 5, 7,… as their cubes subtracted by the same value. Repeat this and add/subtract alternatively the results to three times the diameter of the circle to get the circumference with the highest degree of accuracy. This theorem can be mathematically represented as follows:

Circumference = 3D+4D/(33-3)-4D/(53-5)+4D/73 7)-..

Vargairyujaam vaa dvigunairnirekair vargeekruthair varji thayugma vargai: vyaasam cha chadghnam vibhajeth phalam svam vyaase thrinighne paridhi sthadaasyaath 

Six times the diameter is divided separetely by the square of twice the square of even integers 2,4,6…. minus one, diminished by the squares of even integers themselves. The sum of the resulting quotient by thrice the diameter is the circumference.

This can be mathematically written as follows:Circumference =

3D+6D([1/2×22-1]2-22) + ([1/2×42-1]2-42)+[(1/2×62-1)2-62])+….

PUTHUMANA SOMAYAJI – KARANAPADDHATI 1450 AD 

 

 

 

AREA OF CIRCLE AND SPHERE 

Vrutthakshethre paridhigunitha vyaasapaada: phalam thath kshunnam vedairupari paritha:kandukasyeva jaalam golasyaivam thadapi cha phalam prushtajam vyaasanighnam shadbhirbhaktham bhavathi niyatham golagarbhe ghanaakhyam 

When circumference is multiplied with diameter and that result divided by 4, that will give the area of a circle. This when multiplied with 4 gives the surface area of the globe which is like surface of a ball. This when multiplied with diameter and divided by 6 gives the volume of the sphere of globe.

Mathematically it can be written as 2r x 2r/4 =r2

BHASKARACHARYA II – LILAVATI – 1114 A.D 

 

 

 

NEWTON GAUSS (1670AD) BACKWARD INTERPOLATION DISCOVERED BY VATESWARACHARYA 

Dhanushaaptha bhuktha jeevaghaathe labdham saroopakam dalitham labdaghna vivarahatham cha samsodhya niyogya vikalajyaa 

In modern mathematical form this interpolation formula can be written as f(x) = f(xi)+ (x-xi)1/h Df(xi-h) + (x-xi)1/h. (x-xi+h)1/h. D2f(xi-h)..

VATESWARA VATESWARA SIDDHANTA 904 AD 

 

 

 

ARC AND CHORD 

Svalpachaapaacchaghanashashta bhaagatho vistaraardhakruthir- bhaktha varjitham sishtachaapamihasinjanee bhaveth thadyuth oalpaka gunoasakruthdhanu: 

The chord of an arc of a circle is obtained from the result of the cube of the length of the arc divided by six times the cube of radius and subtracted from the arc. This can be mathematically presented as follows: Chord (R Sine ) = s – (s3 / 6r3). Here length of the arc s is in angular dimensions, r is the radius and  is the angle of the arc.

PUTHUMANA SOMAYAJI – KARANA PADDHATHI – 1450 AD 

Paridhe: shadbhaagajyaa vishkambhaardhena saa thulyaa 

The chord of one sixth of circumference is equal to the radius of that circle.

ARYABHATTA I – ARYABHATEEYA 499 AD 

 

 

 

LENGTH OF ARC – CHORD 

Vyaasaabdhighaathayuthamourvikayaa vibhaktho jeevangghri panchagunitha: paridhesthuvarga: labdhonithaath paridhivarga chathurtha bhaagaadaapte pade vruthidalaath pathithedhanu: syaath. 

One fourth of five times the chord multiplied with square of circumference divided by four times the diameter added with the chord. This value is subtracted from one fourth of the square of circumference. Square root of this is taken and subtracted from half of the circumference to get the arc.

BHASKARA II – LILAVATI 1114 AD 

 

 

 

ARC AND ARROW 

Jyaavyaasayogaanthara ghaathamoolam vyaasasthadoono dalitha: sara: syaath vyaasaaccharonaacchara sangunaa cha moolam dvinighnam bhavatheeha geevaa yeevaardhavarge sarabhaktha yukthe vyaasapramaanam pravadanthi vrutthe 

When the sum and differences of diameter and the chord are multiplied, and their square root is taken and if half of that is subtracted from the diameter, the arrow is obtained. The difference of diameter and the arrow multiplied with the arrow, twice the square root of that value gives the chord. The square of half the chord divided by arrow and added with arrow gives the diameter of the circle.

BHASKARA II – LILAVATI 1114 AD 

 

 

 

NEWTON’S INFINITE GP CONVERGENT SERIES DISCOVERED BY NILAKANTA SOMAYAJI 

Evam yasthuthya ccheda paramabhaaga paramaparyayaa ananthaayaa api samyoga: thasya ananthaanaam api kalpyamaanasya

yogasyaaddhyaavayavina: parasparama cchedaad ekonacchedaa mamsa saadhyam sarvathraapi samaanam eva… 

Thus the sum of an infinite series, whose later terms (after the first) are got by diminishing the preceding or by the same divisor, is always equal to the first term divided by one less than the common mutual divisor.

NILKANTA ARYABHATEEYA BHASHAYA 1444 

 

 

 

SINE, COSINE, RADIUS AND ARC 

Anyonya kotihathayorabhimatha gunayosthrijeejavayaa hathayo: yogaviyogow syaathaamabhimathagunachaapa yogavivaragunow 

The sum of the products of Sin A and Cos B and when angles are exchanged, Sin B and Cos A, gives the Sin of the sum of the angles. Similarly the difference of the above gives the value of the sin of angular difference. Sin (A+B) = Sin A Cos B+Cos A Sin B And Sin (A-B) = Sin A Cos B – Cos A Sin B. 

Yadveshta chaapagunatha ccharavargayoga moolaardhamishta dhanurardhaguna: pradishta: jyaanaam nijathriguna vargaviseshamoolam kotisthadoona sahithow thrigunow svabhaanow 

Square root, of the square of a chord (R sin ) diminished from squares of radius gives the koti (R cos ). This subtracted from radius gives the (small) arrow of arc. This added to radius is big arrow of the arc…..

PUTHUMANA SOMAYAJI – KARANA PADDHATI 1450 

 

 

 

TAYLOR (1685 AD) SERIES OF SINE AND COSINE DISCOVERED BY NILAKANTA 

ista-dohkotidhanushoh svasamipasamirate jye dve saavayave nyasya kuryaad unaadhikam dhanuh dvighna talliptikaptaikasarasailasikhindavah nyasyacchedaaya cha mithastatsamskaaravidhitsaya anyasyam atha taam dvighnaam tathaa syam iti samskriti: santha te krtasamskare svagunau dhanusas tayo: 

Placing the sine and cosine chords nearest to the arc, whose sine and cosine chords are required, get the arc difference to be subtracted or added. For making the correction, 13,751 should be divided by twice the arc difference in minutes and the quotient is to be placed as the divisor, divide the one (sine or cosine) by this divisor and add to or subtract from the other (cosine or sine) according as the arc difference is to be added or subtracted. Double this result and do as before. Add or subtract the result to or from the first sine or cosine to get the desired sine or cosine chords.

NILAKANTA – TANTRA SANGRAHA 1444 AD 

 

 

 

NEWTON GAUSS (1670) INTERPOLATION FORMULA DISCOVERED BY GOVINDASWAMI 

gacchad-yata-gunantharavapuryathaishya-disvasanaa cchedaabhyaasa-samuha-kaarmukakrti-praapthath tribhisthaadithah vedaihi sadbhir avaaptam antyagunaje rasyo: kramad antyabhe ganthavaahata-varthamaana-gunajaaccha paatham ekaadibhi:antyad utkramatah kramena vishamai: sankhyaviseshai: khsipedbhankthvaptam, yadi maurvikavidhir ayam makhyah kramad vartate sodhyam vyutkramathaa stathakrthaphlam….. 

Mathematicaly this formula is summarised as follows: F(x+nh)=f(x)+nf(x)+.n(n-1)(f(x)-f(x-h) Multiply the difference of the last and the current sine differences by the square of the elemental arc and further mutiply by three. Now divide the result so obtained by four in the first rasi, or by six in the second rasi. The final result thus obtained should be added to the portion of the current sine difference (got by linear proportion). In the last rasi, multiply the linearly promotional part of the current sine differences by the remaining part of the elemental arc and divide by the elemental arc. Now, divide the result by the odd numbers according to the current sine difference, when counted from the end in the reverse order. Add the final result thus obtained to the portion of the current sine difference. These are the rules for computing true sine differences for sines. In the case of versed sines, apply the rules in the reverse order and the above corrections are to be subtracted from the respective differences.

GOVINDASWAMI – COMMENTARY FOR MAHABHASKAREEYA 800 AD

 

 

 

NEWTON’S (1660 AD) POWER SERIES DISCOVERED BY SOMAYAJI 

nihatya chapavargena chapam tatthathphalani cha haret samulayugvargaistrijyavargahatai: kramaat chapam phlani chadhodhonyasyoparyupari tyajet jivaptyai, sangraho syaiva vidvan-ityadina krtha: nihathya chapavargena rupam tattatphalani cha hared vimulayugvargaistrijyavargahatai: kramat kintu vyasadalenaiva dvighnenadyam vibhajyataam phalanyadhodha: kramaso nyasyoparyupari tyajet saraptyai, sangraho asyaiva stenastri-tyadinaa krta: 

Multiply repeatedly the arc by its square and divide by the square of even numbers increased by that number and then multiplied by the square of radius. Place the arc and result one below the other and subtract each from what is above it. To derive the arc, which are collected, beginning with the expression Vidvan (katapayadi number). Multiply repeatedly, the unit measurement which is the radius, by the square of the arc and divide by the square of even numbers decreased by that number and then multiplied by the square of radius; the first is, however, to be divided by twice the radius. Place the results one below the other and subtract each from the one above it. That is the method to derive the saras, which are collected in the beginning with stena. (This equation is now known as Newton power series.)

PUTHUMANA SOMAYAJI – KARANAPADDHATI (1450 AD) 

 

 

 

VOLUMES OF CONES 

Samakhaatha phalathryamasai: soochikhathe phalam bhavathi

The one third of the volume of the uniform cylinder is the volume of the cone.

Pardhirbhitthilagrasya raasesthrimsathkara: kila anthakonasthithasyaapi thithithulyakara: sakhe bahishkona sthithasyaapi panchaghnanava sammitha: theshaa ma chakshva me kshipram ghanahasthaath pruthak pruthak 

Friend, the food grains are kept at a circumference of 30 cubit in the floor, outside corner of the room, inside corner and side of the wall. Find out the volume of the grain if the height is 45 cubit.

BHASKARA II LILAVATI 1114 AD 

 

 

 

LHUILER’S (1782 AD) FORMULA DISCOVERED BY SOMAYAJI 

Doshnamdvayordvayor ghaatayutaanaam tisraanaam vadhaat ekaikonetarattraikyam catushkavadhabhajitam Iabdha mulena yadvrttam vishkambhaardhena nirmitam sarvam caturbhujakshetram tasminneva tisthtahathe 

The three sums of the product of sides, taken two at a time are to be multiplied together and divided by the product of the sums of the sides taken three at a time and diminished by the fourth. If a circle is drawn with the square root of this quantity as radius, the whole quadrilateral will be situated inside it.

PARAMESWARA COMMENTARY FOR LILAVATI (1360 AD) 

 

 

 

GREGORY’S (1632 AD) SERIES FOR INVERSE TANGENT DISCOVERED BY MADHAVA CHARYA 

istajya-trijyayorghathath kotyaptam prathamam phalam jyavargam gunakam kritva kotivargam cha haarakam pratha maadiphalebhyo atha neya phalakrtir muhu: eka-tryaady-ojasankhyabhirabhakteshveteshv anukramaat ojanam samyutesthyaktva

yugmayogam dhanur bhavet doh-kotyor alpameveha kalpaniyam iha smrtam labdhinam avasanam syanna thathaapi muhu: krte 

Obtain the first result of multiplying the jya (R sine ) by the trijya (radius) and dividing the product by koti (R cos ). Multiply this result by the square of the jya and divide the square by the koti. Thus we obtain a second result a sequence of the further results by repeatedly multiply by the square of the jya and dividing by the square of the koti. Divide the terms of the sequence in order by the odd numbers 1,3,5,…; after this, add all the odd terms and subtract from them all the even terms (without disturbing the order of the terms). Thus is obtained the dhanus whose two elements are the given jya and koti. (Here the smaller of the two elements should be taken as the jya, since other wise the series obtained will be non finite) (use of Tangent)

MADHAVA YUKTI BHASHA? (1350 AD) 

 

 

 

DE MOIVRE’S (1650 AD) APPROXIMATION DISCOVERED BY MADHAVA CHARYA 

Asmat sukshmataroanyo vilikhyate kashcanapi samskara: ante samasankhyadalavarga saiko guna:, sa eva puna: yugagunito rupayuta: samasankhyadalahato bhaved haara: trisaradivisa mashankhyaharanat param etad eve va karyam 

A correction for cirumference still more precise is being stated here. The multiplier is the square of half the even integer increased by unity. This multiplier multiplied by 4, then increased by unity and then multiplied by half the even integer is the divisor. This correction may be applied after the division by odd integers,3, 5, etc. i.e Circumference = 4D (1-1/3+1/5-1/7….. + ..-1/n(.(n+1)2+1((.(n+1)2 x 4 +1) (.(n+1))

MADHAVA KRIYA KRAMAKARI (1350 AD) 

 

 

 

DE MOIVRE’S (1650 AD) APPROXIMATION

yatsankhyaaatra harane krte nivrtta hrtis tu jamitaya tasya urdhvagatasyas samasankhya taddalam guno ante syat tadvargai rupahato haaro vyasabdhighatata: pragvat tasyam aptam svamrne krte dhane sodhanan cha karaniyam sukhma: paridhi: sa syat bahukrtvo haranato atisukshmas cha 

………. Let the process stop at a certain stage, giving rise to a finite sum, multiply four times the diameter by half the even integer subsequent to the last odd integer used as divisor and then divide by the square of the integer increased by unity. The result is the correction to be added to or subtracted from finite sum. The choice of addition or subtraction is depending on sign of the last term in the sum. The final result is the circumference determined more accurately than by taking a large number of terms:

MADHAVA YUKTIBHASHA? (1350 AD) 

 

 

 

HORIZON

Aaveshtamaanamatha thaani dalapravruthyaa yadvrutthamathra harijam kshithijam thadaahu: yasmin bhaveth samudayasthamayo akhilaanaam praachyaam kramaadaparadisyudu khecharaanaam 

The great circle which goes round them, dividing each of them into two equal parts, is called harija or kshitija. This in modern astronomy is horizon. This is the circle on which rising and setting of stars and planets take place towards east and west respectively.

VATESWARA SIDDHANTA 880 AD 

 

 

 

ASTRONOMICAL DEFINITIONS 

Urdhvamadho apara poorvamihaadyam praahuridam samamandala manyath thadvadihotthara dakshinadikstham vrutthayugam vidisorapi thadvath 

Vertical circle passing through the west and east cardinal points is the first circle: this is called the samamandala. (This circle is the prime vertical. Another similar vertical circle (called the yaamyottara-vrutta) which passes through the north and south cardinal points is called the meridian.

VATESWARA – VATESWARA SIDDHANTA 880 AD 

 

 

 

TYCHO BRAHE REDUCTION OF ECLIPTIC DISCOVERED BY ACHYUTA PISHAROTI 

Patonasya vidhostu kotibhujayorjive mithastadayet antyakshepasarahatam vadhamamum vikshepakotyaharet labdham vyasadaloddhrtam himakare svarnam, vipate vidhau yugmaayugmapadopage; vidhurayam spashto bhagole bhavet 

Multiply the tabular cosine and sine of the moon minus node and the product by the tabular versine of the maximum latitude of the moon. Divide this by the tabular cosine of the latitude at the particular moment and the quotient is to be divided again by the tabular radius. The result is to be added to or subtracted from the moon’s longitude, as the moon minus node is in an even or an odd quadrant, respectively. The true moon measured on the ecliptic is thus obtained.

ACHYUTA PISHAROTI SPHUTANIRNAYA 

 

 

 

EQUATOR 

Khasvasthikaad dakshinatho akshabhaagow paathaa (la) samjnachha thathottharena naadyankitham vaishuvatham thaduktham vruttham bhagolasya khagolamadhye 

The sphere of the asterisms lie within the sphere of the sky. Great circle of the sphere of asterisms which lies towoards the south of the zenith by an amount equal to the degrees of local latitude and towards the north of nadir by the same amount and which is graduated with the division of nadis is the vishuvathvrutta. This circle is called the equator.

VATESWARA SIDDHANTA 880 AD 

 

 

 

6 O’CLOCK CIRCLE

Poorvaaparakshithija sangamayorgathamcha yaamyaadadha: palalavai:

kshithijaadvi lagnam soumyaadathopari samadruvamarga samstham unmandalam dinaniso: kshayavruddhikruthaath. 

Passing through the two points of intersection of prime vertical and horizon, lying below the south cardinal point by the degrees of local latitude, fastened to the horizon, and lying above the north cardinal point, passing through the north celestial pole, is the Unmandala, the cause of decrease and increase of the day and night. (This in modern astronomy is known as the 6’o clock circle.)

VATESWARA SIDDHANTA 880 AD 

 

 

 

CIRCLE OF DIURNAL MOTION 

Harije parapoorva mandala dyujaavruthha visesha sinjinee udayaagraguno dyumandale bhoojyothavruttha kujaan tharaamsajeevaa: 

R sine of the arc of the horizon lying between the prime vertical and the diurnal circle of the planet is the R sine of agra (now known as the rising point of the planet) and the R sine of the degrees of diurnal circle lying between six o’ clock circle and the horizon is bhoojya (bhujya) which is termed as Earthsine.

VATESWARA SIDDHANTA 880 AD 

 

 

 

DAY RADIUS 

Kraanthijyaa vargonaath thrijyaavargaath padam dyujeevaa syaath thrijyaakraanthi yaanthara samaasa ghaathasya moolam vaa 

Day radius is equal to the square root of the difference obtained by subtracting the squares of R sine of the declination from the square of the radius or the square root of the product of the difference and the sum of the radius and the R sine of the declination.

VATESWARA SIDDHANTA 880 AD 

 

 

 

ECLIPTIC

Naaddyaahvavrutthaajathulaadilagnam jinaamsakairadakshinatho mrugaadow soumye seetha mandiraadaav apakramaakhyam thadusanthi vruttham 

Fastened to the so called nadivrutta or the equator at the points of Aries and Libra and lying 24 degrees of the south (of equator) at the first point of Capricon and 24 degrees to the north (of equator) at the first point of Cancer, there is a great circle called the apakrama vrutta (now known as the ecliptic)

VATESWARA SIDDHANTA 880 AD 

 

 

 

DAY DIAMETER 

Vishuvajyaa aayaa mardha varga vislesha moolamavalambaka: kranthithrijyaakruthyo rantharapadam dvigunam dinavyaasa 

Square the sine of latitude and deduct from the square of the radius. Its square root is the sine of the co-latitude (its arc being the co-latitude). Square the sine of the declination deduct from the square of the radius and find its root. Twice the result is the day diameter.

PANCHASIDDHANTIKA 4-23 – VARAHA MIHIRA 505 AD 

 

 

 

SETTING POINT OF ECLIPTIC 

Praachyaam kuja apakrama vrutthasanga praaglagnamaahu (paritho asthalagnam) (lagnaadbhaveth) sa (pta) ma (raa) si (ra) stha thasyaa (stha) kaalo abhyudayosya bhooyath 

Point of intersection of horoizon and the ecliptic in the eastern half of the celestial sphere is called praglagna. I.e. the rising point of ecliptic; the same in the western half is called astalagna, known as setting point of ecliptic.

VATESWARA SIDDHANTA 880 AD 

 

 

 

RISING – SETTING LINE

Vyaasaardha vrutthe antharam ethayo: syaaccharaardha jeevaa parapoorvayosthath agraagrayoryad harijenibaddham soothram grahaanaam udayaastha samjnam 

The arcual distance between the six o’clock circle and the horizon measure, along the R circle trijyavrutta known as great circle of the celestial sphere, supposed to be of radius 3438’ (minute of angle) is the charardhajya. It is called the R sine of the Ascensional difference. A thread tied to the extremities of the agra on the eastern and western halves of the horizon is called the udayaastasutra. (In moderen astronomy it is known as the rising – setting line of planets).

TESWARA SIDDHANTA 880 AD 

 

 

 

DAY RADIUS AND EARTHSINE 

Kraanti thribhaantharajyaa dyujyaa vaa charadalajeevayaa hruthaa thrijyaa kshithi jeevaghnaa svaahoraathraardhajeevaa vaa 

Rsine of the difference between the three signs and the declination is also equal to the day radius. Day radius multiplied by earthsine and divided by the R sine of the Ascensional difference gives the day radius.

VATESWARA SIDDHANTA 3(4)-3) – 880 AD 

 

 

 

SUN’S PRIME VERTICAL 

Urdhvamadho aparapoorvamihaadyam praahuridam samamandala manyath thadvathihottharadakshina dikstham vrutthayugam vidisorapi thadvath. 

Vertical circle passing through the west and east cardinal points is the first circle called samamandala or the prime vertical.

VATESWARA SIDDHANTA- GOLA. 3-1, 2 – 880 AD 

 

 

 

PARALLAX-I

Thithernathasya kramasinjanee hathaa khamadhya lagnaprabhavena sankunaa kshamaashadangkaabhi saraankanethrahrud vilambane syaad ghatikaadi vaa phalam. 

R sine of the hour angle at the amavasya multiplied by R sine of the altitude of the meridian ecliptic point and divided by 2954961 gives the parallax in ghatikas at mid eclipse (Sishyadhi vruddhi Tantra 6-8)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 

 

 

 

PARALLAX-II 

Thriraasijeevaa valanajyakaa hruthaa sileemukhai rankulathaam vrajanthi thaa: dvisankunaa drushtigathi: saraachalairvibhaajithaa lambana naadikaa phalam 

Radius and the valanajya when divided by 5, are converted into angulas. The R sine of driggati multiplied by 2 and divided by 75 gives ghatika of the parallax in longitude. (Sishyadhi vruddhi Tantra 13-11)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD 

 

 

 

PARALLAX-III 

Nathakramajyaambara sankunighnaa syaallambanam thathvarase shuhrudvaa drukshepabhukthyanthara yoscha ghaatha: khabaanayugmaa kshihrutho nathi: syaath 

R sine of the hour angle multiplied by Rsine of altitude of the merdian ecliptic point and divided by 5625 gives parallax in longitude. The Difference of true motions of the Sun and the moon multiplied by the Rsine of drikshepa and divided by 2250 gives the parallax in latitude. (Sishyadhi vruddhi Tantra 13-12)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD

 

 

 

APOGEE, PERIGEE AND ORBIT OF EARTH

Svochhaath shadbhaagaadhyadhiko yadaa thadaa bhavathi svaneechastha: doorenochhaga urvyaa: karnavasaannochhago nikate 

When a planet is at a distance of 6 signs from its apogee, it is said to be at the perigee or neecha. When a planet is at the apogee, it is farthest from the earth when at the perigee, it is nearest to the earth. This is so because of the length of the hypotenuse in each case (Sishyadhi vruddhi Tantra 14-10)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD 

 

 

 

VELOCITY OF PLANETS PER DAY 

Sun 59’ 8” 10’’’ 13’’’’ (gopaajnayaa dinadhaama) 

34” 51’’’ 36’’’’

(Chandikeso bharga snigdhosow) 

Mars 31’ 26” 29’’’ 42’’’’ (Prabhurdharaachakra paala) 

Mercury 245’ 32” 36’’’ 32’’’’

(Rageethumbururganeswara) 

Jupiter 4’ 59” 7’’’ 2’’’’

(Prajnaasanoo dharmavaan) 

: Venus 96’ 7” 37’’’ 51’’’’

(Kasi saambasanna chola:) 

Saturn 2’ 0” 23’’’ 32’’’’

(Prabhalapraajno nara:) 

The modern values of angular motions are Earth/Sun 59.14’, Mars 31.45’, Mercury 245.7’, Juptiter 4.99’ Venus 96.13’, and Saturn 2’.

PUTHUMANA SOMAYAJI KARANAPADHATI (1450 AD) 

 

 

 

SHAPE OF EARTH 

Gaganamarudaagni jalamrunmayo mahaabhootha gunayutha:khastha: kakshaabhiraavrutho ayam bhapan charaanthascha bhoogola 

Spherical earth, made of ether, fire, air, water and clay (Panchabhoothas) and thus have all the properties of the five elements, surrounded by the orbits and extending upto the sphere of stars, remain in the space (Sishyadhi vruddhi Tantra 17-1)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD 

Praguna paridhe: sathaamsako ganithajnaa: kathayanthi drusyathe prathi bhaathi thadaa samaa mahee vishaye yanthra thathaiva gamyathe 

Mathematicians say that one hundredth of the cirucumference of the earth appears to be plane. So, that portion of the earth appears to be plane to an observer (Sishyadhi vruddhi Tantra 20-35)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD 

 

 

 

ROTATION OF EARTH – I 

Pranenaithi kalaam bhooryadi tharhi kutho vrajeth kamadhyaanam aavarthana murvyaa schenna pathanthi samucchrayaa: kasmath 

If earth rotates at a speed of 1’ of an angle in 4 seconds, will not the things on the loft fall? Where does the earth go in this speed? (Brahmasphuta siddhanta 11-17).

BRAHMAGUPTA BRAHMASPHUTA SIDDHANTA 629 AD 

 

 

 

FOUR QUADRANTS OF EARTH 

Udayo yo lankaayaam soasthamayo: savithureva siddhapure madhyahno yavakotyaam romake vishaye ardharaathramsyaath

When it is Sunrise in Lanka, the same Sun sets in Siddhapura. (Gautimaala). It is noon in Yavakoti (Korea) and midnight in Romaka (Rome) (Aryabhateeyam 4-13).

ARYABHATA -I ARYABHATEEYA (499 AD) 

 

 

 

GLOBE 

Samavrutthaprushtamaanam sookshmam golam prasaadhya daarumayam sthagithaarka samaankitha kaala bhogarekaadvaye paridhov 

Perfectly circular throughout and spherical, made of wood, marked with degrees and minutes, incorporated with lines both longitude and latitude at ends, is the golayantra. (Panchasiddhantika 14-23)

VARAHAMIHIRA PANCHASIDDHANTIKA (505 AD) 

Kaashtamayam samavruthham samanthatha: samagurum laghum golam paaradathaila jalaistham bhramayeth svadhiyaa cha kaalasamam 

Made of wood, fully circular, uniform, equally dense throughout and spherical shaped golayantra, which rotates at a fixed rate of time as the earth does by the help of mercury, oil and water, by the application of our intelligent calculation, is the golayantra-Globe.

Nrushiyojanam, njilaa bhoovyaaso 

8000 Nr units is equal to one yojana. The diameter of earth is 1050 yojana.

ARYABHATA-I ARYABHATEEYA (499 AD) 

 

 

 

ROTATION OF EARTH – II 

Ku ngi si bu nlru shru khru praak

Eastward rotations of the earth in one Yuga is 1582237500

Anuulomagathirnoustha: pasyathyachalam vilomagam yadvath achalaani bhaani thadvath samapaschimagaani lankaayaam 

Just as a man in a boat moving forward sees the stationary objects as moving backward, so are the stationary stars and celestial bodies seen by the people at equator (Lanka) as moving exactly towards west.

Ku aavarthaaschaapi naakshathraa: 

The rotation of the earth is the cause of days (Aryabhateeyam 3-5).

ARYABHATA-I ARYABHATEEYA (499 AD) 

 

 

 

MERIDIAN 

Lankaayaamekam sankukeelam prathishtaapya thenaikam soothraagram baddhvaa punarmerorupari thadagramanyath baddhvaa yathaayathaa drusyatha….. thadvath bhoomaavapi kaachidrekha lankaatha: kharapuratha….. merumasthakaanavagaahya sthithaa saa punarathra desaanthara vidhaayini syaath 

Fix a pole in Lanka, tie thread on that, take the other end to the North pole, tie it there also, then one can see the line of the thread passing through Lanka, Kharapuri, Arctic point and so many other countries upto the top of Meru. This is international meridian line (Sankaranarayana on Laghubhaskareeya I-23)

SANKARANARAYANA I LAGHUBHASKAREEYA (950 AD) 

 

 

 

GRAVITY 

Aakrushti sakthischa mahee thayaa yath khastham guru svaabhimukham svasakthyaa aakrushyathe thathpathatheeva bhaathi same samanthaath kva pathathyayam khe:

This earth attracts whatever solid materials are in the space, by her own force of attraction towards her (earth). All those subjected to this attractional force fall, to the earth. Due to equal force of attraction among the celestial bodies, where can each among them fall? (Siddhanta siromani Bhuvanakosham 6)

BHASKARA II SIDDHANTA SIROMANY (1114 AD) 

 

 

 

MERIDIAN AND TIME 

Desaanthara ghatee kshunnah madhyaa bhukthir dyuchaarinaam shashtyaa bhaktham runam praachyaam rekhaayaa: paschime dhanam. 

The time is calculated based on the meridian. Divide the time by 60… and the longitude is calculated. Towards the east subtract and towards the west add the number (Laghubhaskareeyam 1-31)

BHASKARA I LAGHUBHASKAREEYA (628 AD) 

 

 

 

MERIDIAN AND TIME 

Panchaasathaa thribhisthryamsaamyuthairyojanaischa naaddyekaa samapoorva paschimasthairnithyam sodhyaa cha deyaa cha 

One nadi for every 53 1/3yojanas has to be deducted or added (to Ujjaini) by the people in places east and west, respectively of the Ujjaini meridian. (Panchasiddhantika 9-10)

VARAHAMIHIRA – PANCHASIDDHANTIKA (605 AD) 

 

 

 

ECLIPSE-I 

Kimartham asura: kaschidraahurnaama saimhikeyoarkam chandram cha grasatha ithi srooyathe sraapi pouraanika sruthireva! ka: punariha raahurithyuchyathe

What does it mean that Asura is responsible for the eclipse? Others say that a snake Rahu swallows the Sun and the Moon! Those are puranic stories! Then what is called the Rahu?

SANKARANARAYANA COMMENTRAY TO LAGHUBHASKAREEYA 950 AD 

Cchadayathi sasi sooryam sasinam mahathee cha bhoocchaayaa 

Moon covers (shadows) the Sun and the great shadow of the earth covers the moon (which causes the eclipse)

ARYABHATAI ARYABHATEEYA (499 AD) 

 

 

 

ECLIPSE-II 

Atha eva bhoocchayaa chandragrahanasya kaaranam 

That is why it is said that the shadow of the earth is the cause for the lunar eclipse.

SANKARANARAYANA COMMENTRAY TO LAGHUBHASKAREEYA 

Asuro yadi maayayaa yutho niyatho athigrastheethi they mantham ganithena katham sa labhyathe grahakrutha parva vinaa kathanchana 

If you are of the opinion that an artifical demon is always the cause of an eclipse by swallowing, then how is it that an eclipse can be determined by means of calculations. Moreover why is then not an eclipse occur on a day other than the day of new or full moon (Sishyadhi vruddhi Tantra 20-22)

LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD 

 

 

 

BIOLOGICAL SCIENCES 
Health science (Health science  is  a part of ayurveda  which is  an upaveda of  Atharva veda. It is  also discussed in yoga sastra  which is one among the  six darsanas of the Hindus. The subject has also been dealt with in puranas and itihasas): The Indian vision on health  as given  by Maharshi Susrutha, Charaka  and Vagbhatachaarya  and  many others.  The  approach taken by Patanjali in Yoga saastra,  the spiritual  approach of body and mind, etc will be the part of the Indian health science.  Aswini devatha concept of hitha  aayaasa  and mitha aahaara (food & exercise), need of  appropriate exercise based of the age‐sex physiological conditions, etc. Yogaasanas, sooryanamaskaara,   effect of  medicines, identification of  diseases  through  saastram pramaanam/ aaptavaakyam pramaanam/prthyksham pramaanam/ anumaanam pramanam /  methods.  Use of drugs,  fastings and  pathyas  and  fasting as a part of customs/rituals.  Selection of   food based on climatic variation/age/health conditions/etc of the person/patient, physical and mental rest,   upaasana  and worship as a part of  day to day life, ethics and morality in the common man’s life  and also  for doctors, …  causes of  illness, pathogenic organisms,  precautions to be taken for  good health, solar therapy, music therapy, Yoga therapy, Reiki, energy healing, water therapy, as described in the Indian system. The  knowledge on surgery  and plastic surgery  and surgical equipments known sastras  and yanthras as described in Susrutha samhitha, practicing surgery as given by  Maharshi Susrutha. Variety of acharas/customs and rituals influencing the health. Importance of  vegetarian foods.  Indian  traditional  foods  and their  merits. Taking oil bath during selected days, hot/cold water bath. Allowing  children to play in the  soils  after  smearing the oil. Grandmaa’s technological foods’ for babies  and baby health care  system existed in  ancient India.

Mental Health / Psychology (this again is a subject of  ayurveda and yoga/ poorva meemamsa/uttarameemamsa/vaiseshika/ darsanas and Upanishads. It has been discussed in detail in Yogavasishta, Bhagavath geetha, dharma saastra  and so on):  Description of mind given in Upanishads, mental influence on health, the influence of yamaas and niyamaas: ahimsa‐ satyam‐ astheyam‐brahmacharya‐ aparigraham‐ oucham‐ snthosha‐ thapa‐ swadhyayam‐ eeswara pranidhaanam –etc. Effect of stabilised vision on life, controlling the angr,fear,and attachment, mental preparations  to face ups and downs/loss and profit/ success  and failures/ animosity and friendship/ appreciations and criticisms  …as described in Indian  philosophical books.  Influence  of puranic  / epic  related stories in mind  to face the  realities of the life. Influence of pranayam/ dhyaana/dharana  etc on the mental development. Impact of food on  mind as  proved by the modern science, effect of saatwic  food, dreams, effect of manthras on mind,  customs  influencing the  mental health  and  family relations. Analyses of the purpose of living, family‐social‐and national  goals to be  put forth  for  a purposeful life
and its impact on mind.  Spirituality  and faith in healing. Effect of curative chemical on mind and body. Bhajans /keerthans/ prayer/ manthras etc on mind.  The positive  songs and images influencing the mind. Psychologically influencing  acharas.

Food science (very specific explanations  are givenin ayurveda‐ as told it is  a part of atharvaveda. It has been given in dharma saastra  and gruhyasootra part of kalpasastra  and to some extent in puraanaas):
Variety of  Indian foods,  balanced nutritious foods, natural traditional baby foods, the  medicinal components usually added in Indian foods (like asafoetida, turmeric, spices, mustard,  etc), pathya based  food during illness, specialized  cooking, roasting, fermenting, processing, preserving,  etc. done for variety of  foods and their science. Generation of specific flavors in foods by suitably modifying spices. The science of altering the foods during  fasting  on  specific  days like  ekaadasi/ somavaar vratha/ karthika month/ vaisaakha month/ etc. Opting for integrated balanced foods through  fasting and vrathaas,  importance of selecting  cooking vessels like ceramics / iron/copper/ brass vessels ( for getting  micro nutrients like, iron, zinc, copper, silica, magnesium, sodium, potassium etc), variety of vegetables  and  their  significance in balanced healthy foods.  Many more   significant scientific observations can be made  if  a student  carefully  examines the Indian foods, naturopathy, and vegetarian food.

Chemistry (Rasachikitsa is  a part of  atharvaveda based  ayurveda prevalent in north India.  All the  authors  of  Rasachikitsa  were  Siddhas or Maharshies.  The chemistry descriptions, one  can see sytematically in the rasa books) :
The ancient Indian chemistry books like rasarnava, rasaratna samucchaya, rasendra choodamany, rasarnavakalpa, rasa chandrika, rasaratnakara, and  hundreds of  rasa based books . (These books  are  available  in Sanskrit  with English or Hindi translations.).  The knowledge on chemicals, particularly in inorganic chemicals, like  sulphides/ sulphates/oxides/ etc.  Sanskrit names of chemicals,  detailed description given for setting up a laboratory, scientific temper, qualification of laboratory assistants,  research scholars as described in Rasaratna samucchaya.  properties of  inorganic  chemicals  and their use described by Vagbhatacharya, centuries ago. Chemicals used for   various purposes as described in Bharadhvaja in yantra sarvaswa, Varahamihira in Bruhath samhita and  also by others in the  above chemistry books.

Bio -pesticides (biopesticides are part of vruksh ayurveda which again is  a part of Ayurveda or Bhruhat samhitha):Variety of plant products,  Neem, sweet neem, neem cake, mustard cake, tulasi, clove,  pepper, turmeric, tobacco,  oils from  sesame , cotton seed,  castor  etc.,  used as  bio pesticides and  as  preservatives, traditional methods of pest control like fumigation with neem/ sulphur/camphor/ coconut husk(since it contains  sulphur /coconut shell (rawfor its  phenolic content) / cow dung (since it contains  ammonia). The use of panchagavya / aqueous cow dung filtrate /extract as pesticide. The traditional knowledge available from farmers. Detailed descriptions for controlling the pests/microorganisms/etc given in Vruksha ayurvedic books.

Plant drugs/pharmacology ( this  is  a part of the  atharvavedic  ayurveda):
Active  plant bio‐chemicals possessing  medicinal plants, as described in Charaka samhita, Ashtanga hrudaya, ashtanga sangraha, sahasrayoga, etc. comparative studies on  modern and traditional knowledge of medicinal plants. Thestudent  can try to understand as many plants  as possible which are  good  sources of the  bio‐active principles.  Variety of  plants ( herbs, shrubs, creepers, grass, trees  etc.) used for  curing  diseases. The plant leaves, buds, flowers, stems, roots, latex, etc used for  treating specific  diseases.  Single drug treatment.

Medicines and medicinal preparations /plant biochemistry ( Charaka samhitha  and  Susrutha samhitha  are  written  by  Rishies  of the caliber of those  of vedic Rishies,  this  also include sages like Chyavana/Brugu/Vagbhata/Agastya and so on):  The descriptions of   inorganic chemicals used  as medicines in ancient Indian  Rasa chikitsa books, their preparations/processing  and  preservation.  The plant  products used as drugs, the raw drugs, their  harvesting, drying, storage,  mixing,  drug formulation,  decoction  preparation, etc.  Variety of  Ayurvedic drug formulation obtained by mixing
many raw drugs. Knowledge on the  possible  chemical changes taking place in ayurvedic drug preparation  while  drying,  storing,  heating,  roasting,  boiling with  water,  concentration, etc (all ayurvedic preparations). Here we have to focus only on the knowledge existed  and their  scientific merits,  in the area of  plant drugs. The scientific  knowledge behind kashaya/decoction preparation, choorna, kwatha, lehya, arishta, ghrutha, thyla. etc reparations  and their  basic principles of applications.

Basic plant sciences/botany: Detailed description given  in Vrukshayurveda by Rishies like Saarngadhara, Katyayana, Varahamihira, Parasara, and others. Plant  growth, grafting, irrigation, use of manure, seeds preservation,  phototropism, agricultural practices both basic and applied. Seasons of sowing/planting/ biodynamics of agricultural practice, etc., Variety of the traditional knowledge still
practiced in villages, in the production of agriculture commodities.

Fermentation  technology. The knowledge  of microorganisms  existed in India   as described in ayurvedic books. Fermentation of milk to curd and yoghurt,  fruit juice fermentation to vines,  medicinal
preparation of  arishtas, etc. Fermentation procedures followed in  four  major  types liquors mentioned in Chanakya’s Artha saastra ( Arthasastra is  an upaveda of  Rigveda), the source of microorganisms, cultures,  fermentation products mentioned in the  ayurvedic  and vrukshayurvedic books. Fermented rice based  common solid foods like pan cake, fermentation of  traditional liquors from coconut  and
palm  products .

TECHNOLOGICAL SCIENCES

Ancient Indian mines:  Knowledge on the ancient Indian  mines  which were active  during the last  three or more millenia,  the ores/ minerals  of copper, gold, zinc, lead, silver,  distributed through out Rajasthan, Haryana, Bihar, Bengal, Gujarath , Karnataka, Uttar Pradesh, Madhya Pradesh, etc…. The technology adopted for digging, mining, transportation,   processing  and  refining the above ore prior to
metallurgical processing,  provisions given for  aeration  and lighting in mines, etc.  the  present day scenes of  ancient  metallurgical sites.

Ancient Indian knowledge in Metallurgy (metallurgy is  a part of lohathanthra which again is becoming a part of Rasachikitsa/saastra):
The production  and purification of metals, the use of flux and slag,  temperature attained,   technology  for the production and purification of  metals  like  tin, copper, iron,  silver, gold, zinc, lead.  An understanding of the  chemical reactions  accomplished like, oxidation, reduction,. slag formation, distillation  of low boiling  metals, etc.  The fine  technology used for  the large scale production of  bronze,  brass, panchaloha, bell metal, coin making metals  and many alloys  mentioned in  chemistry books  and also in the books like  Chanakya’s Arthasaastra.  Impressive metallic alloy preparation techniques mentioned in  the Rasa books , rasopanishad and Bharadvaajaa’s writings. The kilns and mooshas used for the  metallurgical applications. Special methods adopted  for
the preparation of zinc and  lead.  Preparation of the purest form of copper  and  alpha and beta  brass. Identification of  alpha and beta  tin  and  descriptions of the physical characteristics of these metals.
The metal ingots, sheets, plates etc  of zinc/lead/iron/brass/bronze/copper/gold/silver/…of ancient Indian origin  excavated from   other countries like Athens,  Babylonia, Rome,  Egypt,..

Ancient Indian  Iron  making technology. Production of  pig iron, cast iron  and wrought iron, Delhi  and Dhar iron pillar, forge welding, lamination, paint coating for  preventing the rusting,. Making the swords,
the Banaras  and  Kodumanal swords, carburization in iron instruments  used in agriculture  and  surgery. Rust free preservation  techniques  adopted for iron, woortz steel.  Large scale production of iron alloys,
export of iron to  European/ middle east  countries. The iron technology existed in North Kerala/Andra/Nasic/ Gujarath/Bengal/Varanasi/etc. the  Damascus sword from India.

Ceramics science and technology in ancient India (detailed description of the  moosha is given in  Rasa based  books)   :
The  top quality ceramics  vessels, tiles, glazed  vessels,  beads,  bricks  etc. produced in Harappa, Mohanjo daro, Lothal, Varanasi, Thakshasila, Kalibhangan,  Hastinapura,  and many other North and south Indian  archeological sites.  Variety of  coloring materials used  for the ceramics vessels and decoration ceramics  articles which were also used in the glass making. The great bath of Mohen jo
dara, thelost city of Cambay, Dwaraka, Hastinapura, etc

Industrial and instrumental glass technology existed in India:  Variety of  multi colored  glasses  with different  size, shape,  appearance and  capacity  produced  in India .  The glass beads, ornaments,
plates, vessels,  made using variety of inorganic coloring  materials like the oxides, carbonates, sulfates, phosphates, etc of chromium,  lead, copper,  iron , nickel, calcium, sodium.  The  non metallic
compounds used  as  coloring materials.  Technology  introducing the  golden/ silver  leaf/plates  in glasses.

General Instruments used in ancient India:  Description of  a variety of  instruments  given in Bharadvaja’s yanthra sarvaswa  (Bharadwaja is now  a clan ordered  after the great   Vedic sage of
Bharadwaja . He is  known  as Maharshi Bharadwaja. Only a part of his book  Yantra sarvaswa/amsubhodini  is now available)  the Vaimanika saastra, dvaantha pramapaka yantra, etc. The numbering
systems with serial numbers of the components of instruments,  alloy preparations, quality of glass lenses, prisms, glass plates, variety of Krithaka loha, ( artificial metallic alloys having  non metallic
compounds also) dies used for molding the  instrument  parts/components,  in required size and shape. The instruments used in astronomical calculations  known under the title  jyothir yantra .

Musical instruments ( Music  is  Gandharva veda  which is an upaveda of  Saamaveda. Music/ dance/ drama/ musical instrument  are  all originated  from Saamagaana) : Variety of  string instruments for music/dance performances, the metallic alloys used for the preparation of  strings, wind  instruments, the knowledge of  sound waves , the membrane instruments, preparation/processing  of the
membranes  for  these  musical instruments.  The  basic  knowledge of sound  in  music.  The granite music  pillars  known as sangeetha mandapa  seen  in  ancient south Indian temples.  Traditional  Indian
musical instruments like flute, idakka, mrudanga, chenda, thaala, naadaswara,  veena, violin, harmonium,  and so on. The basic principles  adopted in their making and use.

Surgical instruments ( detailed  descrtiptionof these  instruments  and their  pictures  are  given in the books written by Maharshi Susrutha  as  a part of  Salya chikitsa which again  is  a part of  ayurveda/
upaveda of atharva veda):  The  surgical  instruments  known  as  sastras and  yanthras  numbering more than a hundred, as mentioned in  Susrutha samhitha, the metals used for making these instruments. Their size, shape and comparison  with the modern instruments used for the purpose. Description of  plastic surgery techniques.  The instruments for kidney stone removal, stitching, cutting
open, etc.  all these  instruments used in the  modern surgery tables  may be compared  with those available  thousands  of years  ago, in India.

Laboratory equipments ( this descrtiptionis coming as part of  rasa  books):  More than  35 types of ceramics, glass and metallic  equipments mentioned  in Rasaratna samucchaya  for the use  in chemical
laboratories for the processes like, distillation, sublimation, extraction, drying, heating, roasting, mixing, decanting, etc. generally known  under the name yanthras made using specific quality  clays. Many
varieties of mooshaas , put yantras  were also used  here  for processing themetals  and other compounds.

Kilns/furnaces, mushas  & Putas used for metallurgy.  Variety of  furnaces  and  kilns, crucibles  used for the production of  various metals  and alloys. The  temperature  attained  for  oxidation, reduction, slag
preparation   and  distillation  of variety of  metals and  correspondingly suitable selection of putas/furnaces.  Heating materials  and their proportions, heating time, flux used  for removing the impurities  in the  metal processing . description of  maha gajaputa,  gajaputa, kukkuta  puta, kapotha puta  ……etc  and their preparations.

Painting Technology/organic and  inorganic colorants ( this  subject coming as part of sthaapathya veda /architecture which  is an upaveda of  Rigveda sometimes it is  also said  as the upaveda of
atharva veda) .  The  chemistry of the  paints used in Ajantha, Ellora, and other cave temple  paintings, mural paintings, the inorganic  colors  and  plant products  used for  paintings, their preparation, mixing,
applying on the  preprocessed surfaces. Selecting  and processing plant  products  used as  paints.  Thepreparation of inks, for variety of applications. Mural paintings, oil paintings,   preparation of painting beds/ walls/ canvass, etc  as done in cave temples and walls.

Textiles technology  (  detailed  dscrtiption can be  seen in dharma saastra  and also artha saastra  part of  either kalpasastra or upaveda): Ancient Indian textile  industry as mentioned in Chanakya’s Artha
saastra,  textiles produced  using  cotton, silk, wool, jute,  and also incorporation of   gold, silver and lead metallic  threads  as boarders for the textiles.  The famous  Kancheepuram, Banaras,.. sarees/textiles.
the  dying technology and  coloring materials  used.  The textile dyes, leather colors,  variety of coloring materials produced in different parts of India   and method of  application  of the dyes.

Civil engineering  and architecture ( The subject matter is dealt with systematically in Sthapathya veda which is  upaveda – as mentioned above. Detailed descrtiption is  also available  in artha sasstra
books)  :
The civil engineering skill demonstrated   in the famous south Indian temples  constructed by the kings of the  Chola, Chera, Pandya, Hoysaalsa, Kakateeya, Vijaya nagara …periods.  The  huge and tall
entrances/gopurams  of these  temples.  The mortars/cements   used for the construction of these temples.  The instruments used for measuring / maintaining  the geometry of these structures. The
granite/ marble/ laterite stone cutting and polishing equipment/devises  existed during then.  The transportation techniques adopted  for the huge granite pieces. Construction  of marble  temples, palaces  and lake palaces in Rajasthan . The temples of Kancheepuram, Rameswaram, Chidambaram, Kumbhakonam, Thiruvannamali, Sucheendram,  Trivandrum,  Konark and Khajuraho,….   The  music
pillars   and music mandapas, the knowledge on the  sound waves produced  by these  granite pillars and granite  stone  carvings (thick‐thin ‐ pointed and so on)  The carving undertaken  with top precision, in all
the above structures.

The construction of  cave temples, of Ajanta, Ellora, Elephanta, knowledge  on geological aspects of rocks in which the Chaityaas and Viharas  were carved out.  Huge palaces constructed  particularly like
Jaisalamar palace, palaces in the pink city Rajasthan, Gwalior, Mysore, Hyderabad, etc  the  air conditioning/temperature maintaining mechanisms adopted, glazed and non glazed  tiles/glasses  used
for flooring/windows.  The  ponds and water reservoirs  made  thousands of years ago. (learn as many structures constructed as possible and their technologies) The civil engineering  sciences and technologies of forts  and walls, channels,  rivers etc.  the archeologically important  sites of Mohan jo daro, Lothal, Harappa, Dwaraka, the lost city of Cambay  etc

BASIC SCIENCES:

Basic principles of  physics (for  these basic  principles one has to search  very many books;  examples are sited   against  each subject)  the velocity of  light ( Sayana Bhashya for Vedas), wave  nature of
sound  (Maharshi Gouthama’s nyaaya saastra), seven colors of  light (Rigveda),  Heisenberg’s uncertainty principles Patanjali’s yoga sastra), definition and explanation of atoms, gravitational forces (siddhanta
siromany of Bhaskaracharya II),  different types of  rays (UV, IR, Heat rays, visible  rays ‐ as explained by Bharadvaja)  lenses,  prisms, magnetic materials like  iron and variety of magnets, time,  weights and
measures, linear parameters.  Modern scientific principle  equivalent  ancient  observations. Explanations  given in yantra sarva sarvawa of Bharadwaja , the vaimanika saastra, dwanthapramapaka
yantra/ spectro photometer, etc the scale used in measuring the temperature, the  serialization of instrument parts commonly used., graduation method adopted, metallic alloys used in measuring the light waves, etc (all yantra sarvaswa of Maharshi Bhardvaja)

Ancient Indian Mathematics  & Astronomy ( Mathematics  and  astronomy are the fifth vedanga of vedic literature kown  as Jyothisha.  There are  four vedanga jyothis  connected  with Rigveda‐ archa
jyothisha‐ Yajurveda – Yajusha jyothisha, Samaveda  samjyothisha  and  Atharva veda  Atharva jyothisha).  The later  development of th subject matter  are directly  connected with  these jyothisha
books) :
Detailed knowledge  are given in the books written by  Aryabhatta  (I & II), Bhaskara  (I & II), Vateswara, Manjula, Lalla, Varahamihira, Parameswara, Sankaranarayana, and many other
mathematicians. The four number systems, (Sanskrit number, Aryabhatta number, Bhootha sankya and Katapayaadi number) arithmetic and geometrical progressions  and their  variety of  applications,
interest calculations, moving bodies, forward and backward motions, linear  and  angular measurements,  number theories, square/cube roots and power series, determinations,
degree/minutes/seconds/ microseconds both for  time and  angular measurements,   various geometrical figures  both inscribed one another  and independent figures, parameters  connected with area, perimeter, volume  of  squares, triangles, circles, trapeziums, spheres, cones, cyclic quadrilaterals, polygonals,  detailed algebra,  quadratic equations, monomial and  binomial theorems, etc. Hundreds of
theorems  developed by Aryabhatta, Bhaskara I  &  II, Sankaranarayana, Sangamagrama Madhavacharya, Puthumana Somayaji, Vateswarana, Aryabhatta II, Sankara Varman,
Paramewaracharya…… the  application of  ka ta pa ya adi  number  and bhootha sankhya systems made by the above mathematicians.

Determination of  Sine, cosine  and tangent, Rsine values their  squares, square roots,  additions and subtractions, determination  at  degree/minute/second levels. and  their tables,  as explained in detailed by Varahmihira/ Vateswara/ Aryabhata II/ Puthumana Somayaji/ Parameswaracharya/ Nilakanta/ Sankaranrayana/ Achuta/ jayadeva/ Manulacharya/ and so on, method of  determining  these values,
angles in degrees and radians, calculations and theorems  connected with these  values . Relation among radius‐ arc‐chord‐circumference ‐ sine ‐ cosine ‐ tangent – angles.Indian theorems  known in foreign
scientists  names such as : Newton’s theorems, Gregory’s theorem’s, Kelvin’s theorem, Lhulers theorem, Lebnitzs’ series, Taylor series, Tycho Brahe equations, etc.

Astronomical parameters( As mentioned above; Jyothisaastra  is applied ganithasaatra  accordind to the  fifth vedanga known  as jyothisha):
Various astronomical and geographical parameters mentioned in the above books:  The  spherical shape, size, diameter,  circumference, gravity, declination,  rotation speed, revolution, celestial/terestrial latitude and longitude,  parallax in latitude and longitude, earthsine, etc of earth.  Many more astronomical parameters  described with definition by Vatewaracharya,  like co‐latitude,  prime meridian, and its relation with  time, sun rise and sun set, eight type of  revolutions of planets,  visibility of planets, declination,  precision equinox,  alpha Aeries point, apogee, perigee,  solar and lunar eclipse, calculation of  eclipse, diameter of shadow  and  movement of shadow, instruments  used for time calculation and also for the calculation of various astronomical parameters  known  as  yanthras.

Hundreds of parameters  described  systematically  and  calculated  mathematically  on  solar  and lunar eclipses,  changes  in the signs, latitude/ longitude,  time  variations, east –west lines, avanti lines of
international importance,  the inferior plants and superior planets,  occulting of planets and stars,  the star constellations,  the comets,  and their appearance, etc., etc

Indian  Management science ( All Indian management books  are directly connected with Itihasa(epics) puranas, subhashitas):
Thousands of  modern  and  relevant management principles  explained by  Chanakya  in (Chanakya) neetisara  also known  as  Chanakya upadesa, ,  Bharthru Hari in  upadesa sathaka  in hundred  points, , Vidura in Vidura neetisara  as  a question answer  method of presentation to Dhrutharashtra  and Vidura, Bhishma in Bhishmopadesa  to the questions  asked by Dharma putra,, and also books like  Yoga Vaasishta as given  by Mahrshi Vasishta, Bhagavath geetha advise given to Arjuna by Lord Krishna, Sukra neeti sara  by Sukra muni  and  many subhashtaas ( advises)  mentioned in
Pancha thantra, Ramayana, Mahabharata, Thirukkural  and so on.  They are  all applicable  even  for  the management in the  21st century.

Ancient  Indian  knowledge in Economics (This subject  is  the upaveda of  Rigveda):
The  book on artha saastra  written by Chanakya known as Koutlileeyam, many cross reference books are also mentioned in arthasaastra,  books of  dharma sastras/ smruthies  dealing with this subject  The detailed explanations about money, budget, banking, interest, loans, compound interest, penal interest,  surety, witness, documents preparations for loans,   pledging of materials, leasing, etc. the detailed method of implementing  sales tax, agricultural tax,  property tax, gift tax, land tax, house tax,  customs duty  and penal taxes,  etc.  ( as described in dharma saastra) can be  seen in  many books written  during  BC 500 and before.

Indian Philosophy  (Philosophies  either part of Upanishads  which are known  as vedantas  or  as part of  shaddarsanas:
The philosophical compilations known  as darsanas by Vyasa, Jaiminee,  Patanjali, Gouthama,  Kapila   and  Kanaada ‐ poorva & uttara meemamsa, yoga, nyaaya,  vaiseshikaa,  are the
most important books known  as shad darsanas.  Many fundamental  principles of physics, chemistry, biology,  etc are mentioned in  the above darsanaas.  Sankara’s Adwaitha  and  Madhva’s dwaitha.  The book of Charvaka  known  as Charvaka samhita  of atheism.  Other  than the  specific philosophical compilations,   the  philosophy described  in upanishad, Bhagavath geetha, Yogavasishta, etc.  Thus  the knowledge of Hindus  did not restrict upon mere spirituality and  achaaras but  also focused on every branch of modern science and technology. That is the reason why many of these  knowledge, the
western  scientists  are patenting now.

Modern  India’s Achievements  (The modern Indian  achievements in every field is  a continuation  of the ancient  Indian  blood  and achievements) :
Since   large amount of  data  are available in this subject, the reader/student can select/collect as much details  as possible  for continuous learning of the great scientists of modern India   and  our  achievement in space science,  harnessing  atomic energy,  technology of exploding  atom bombs,   Antarctica expedition,  the green revolution, the  blue revolution ,  white  revolution, chemistry  and  achievements in the  area  of  biotechnology,   in telecommunication,  roads  and  transportation,  education at lower  and higher levels,  professional education,  information technology and  computer science and super   computer  technology, revolutions in  print and electronic  media.  The student can add  much more than this, as the specialization  has  achieved in India,  in  almost  all  subject areas.

3 thoughts on “Vedic Literature and the Amazing Sciences and Knowledge that was Already Known

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