Maharshi Panini was a Sanskrit grammarian from Pushkalavati, Gandhara, in modern day Charsadda District of Khyber Pakhtunkhwa, Pakistan (fl. 6th century BC).Panini is known for his Sanskrit grammar, particularly for his formulation of the 3,959 rules of Sanskrit morphology, syntax and semantics in the grammar known as Ashtadhyayi (अष्टाध्यायी Ashtadhyayi, meaning "eight chapters"), the foundational text of the grammatical branch of the Vedanga, the auxiliary scholarly disciplines of Vedic religion.

12. Maharshi Panini

is one of the earliest known grammars of Sanskrit, although Pāṇini refers to previous texts like the Unadisutra, Dhatupatha, and Ganapatha. It is the earliest known work on descriptive linguistics, and together with the work of his immediate predecessors (Nirukta, Nighantu, Pratishakyas) stands at the beginning of the history of linguistics itself. His theory of morphological analysis was more advanced than any equivalent Western theory before the mid 20th century, and his analysis of noun compounds still forms the basis of modern linguistic theories of compounding,

which have borrowed Sanskrit terms such as bahuvrihi and dvandva.Panini's comprehensive and scientific theory of grammar is conventionally taken to mark the end of the period of Vedic Sanskrit, so by definition introducing Classical Sanskrit.

though it is generally agreed that he knew of a form of writing, based on references to words such as "script" and "scribe" in his Ashtadhyayi. These must have referred to Aramaic or early Kharosthi writing. It is believed by some that a work of such complexity would have been difficult to compile without written notes, though others have argued that he might have composed it with the help of a group of students whose memories served him as 'notepads' (as is typical in Vedic learning).

Writing first reappears in India in the form of the Brahmi script from c. the 3rd century BC in the Ashokan inscriptions.While Panini's work is purely grammatical and lexicographic, cultural and geographical inferences can be drawn from the vocabulary he uses in examples, and from his references to fellow grammarians, which show he was a northwestern person. New deities referred to in his work include Vasudeva (4.3.98). The concept of dharma is attested in his example sentence (4.4.41) dharmam carati "he observes the law" (cf. Taittiriya Upanishad 1.11).

Works

Nothing certain is known about Panini's personal life. According to later traditions, his mother's name was Daksi and his maternal uncle's name was Vyadi. Some scholars suggest that his brother's name was Pingala. Still less is known about his father, whose name may have been Paṇi, but most scholars reject this suggestion. More than a thousand years after the fact, the Panchatantra mentions that the Grammarian Panini was killed by a lion.

Life

The Ashtadhyayi is the central part of Panini's grammar, and by far the most complex. It is the earliest complete grammar of Classical Sanskrit, and in fact is of a brevity and completeness unmatched in any ancient grammar of any language. It takes material from the lexical lists (Dhatupatha, Ganapatha) as input and describes algorithms to be applied to them for the generation of well-formed words. It is highly systematised and technical. Inherent in its approach are the concepts of the phoneme, the morpheme and the root. His rules have a reputation for perfection -

Ashtadhyayi

that is, they are claimed to describe Sanskrit morphology fully, without any redundancy. A consequence of his grammar's focus on brevity is its highly unintuitive structure, reminiscent of modern notations such as the "Backus–Naur Form". His sophisticated logical rules and technique have been widely influential in ancient and modern linguistics.It is likely that Panini's grammar and the Rg Veda are the only texts that were passed from one generation to another without being amended. In the Ashtadhyayi language is observed in a manner that has no parallel among Greek or Latin grammarians.

Panini's grammar marks the entry of the non-sacred into Indian thought, and according to Renou and Filliozat, it then defines the linguistic expression of that thought.The great thinkers of ancient India were primarily linguists. It is not possible to understand fully the works of theologians/philosophers such as Shankara, Ramanuja and Madhva without a knowledge of Panini.The Ashtadhyayi is fundamental to the structure of their thinking. It is not a didactic grammar, as it presupposes a knowledge of Sanskrit.

Ashtadhyayi is fundamental to the structure of their thinking

Gradually,mainly after the X century, manuals were produced that reorganised the Ashtadhyayi for didactic purposes. These generally had simpler structures and were less ambitious than their Ashtadhyayi source.Panini made use of a technical metalanguage consisting of a syntax, morphology and lexicon. This metalanguage is organised according to a series of meta-rules, some of which are explicitly stated while others can be deduced. The fundamental principles on which the metalanguage is based are non-redundancy,or the principle of economy,and the necessity of all the rules in the Ashtadhyayi.

The Ashtadhyayi consists of 3,959 sutras (Sutrani) or rules, distributed among eight chapters, which are each subdivided into four sections or padas (padah).From example words in the text, and from a few rules depending on the context of the discourse, additional information as to the geographical, cultural and historical context of Panini can be discerned.You can find some of the Rules in the link attached above with article.

More Over...

Pāṇini's Ashtadhyayi has three associated texts.The Shiva Sutras are a brief but highly organized list of phonemes. The Dhatupatha is a lexical list of verbal roots sorted by present class.The Ganapatha is a lexical list of nominal stems grouped by common properties.

Auxiliary texts

The Shiva Sutras describe a phonemic notational system in the fourteen initial lines preceding the Ashtadhyayi. The notational system introduces different clusters of phonemes that serve special roles in the morphology of Sanskrit, and are referred to throughout the text. Each cluster, called a pratyāhara ends with a dummy sound called an anubandha (the so calledIT index), which acts as a symbolic referent for the list. Within the main text, these clusters, referred through the anubandhas, are related to various grammatical functions.

Shiva Sutras

The Dhatupatha is a lexicon of Sanskrit verbal roots subservient to the Ashtadhyayi. It is organized by the ten present classes of Sanskrit, i.e. the roots are grouped by the form of their stem in the present tense.The ten present classes of Sanskrit are:    1. bhū-ādayaḥ (root-full grade thematic presents)    2. ad-ādayaḥ (root presents)    3. ju-ho-ti-ādayaḥ (reduplicated presents)    4. div-ādayaḥ (ya thematic presents)    5. su-ādayaḥ (nu presents)    6. tud-ādayaḥ (root-zero grade thematic presents)    7. rudh-ādayaḥ (n-infix presents)    8. tan-ādayaḥ (no presents)

Dhatupatha

9. krī-ādayaḥ (ni presents) 10. cur-ādayaḥ (aya presents, causatives)Most of these classes are directly inherited from Proto-Indo-European. The small number of class 8 verbs are a secondary group derived from class 5 roots, and class 10 is a special case, in that any verb can form class 10 presents, then assuming causative meaning. The roots specifically listed as belonging to class 10 are those for which any other form has fallen out of use (causative deponents, so to speak).

The Ganapatha (gaṇapāṭha) is a list of groups of primitive nominal stems used by the Ashtadhyayi.After Pāṇini, the Mahābhāṣya ("great commentary") of Patañjali on the Ashtadhyayi is one of the three most famous works in Sanskrit grammar. It was with Patañjali that Indian linguistic science reached its definite form. The system thus established is extremely detailed as to shiksha (phonology, including accent) and vyakaran(morphology). Syntax is scarcely touched,but nirukta (etymology) is discussed, and these etymologies naturally lead to semantic explanations.

Ganapatha And Commentary 

The learning of Indian curriculum in late classical times had at its heart a system of grammatical study and linguistic analysis. The core text for this study was the Aṣṭādhyāyī of Pāṇini, the sine qua non of learning. This grammar of Pāṇini had been the object of intense study for the ten centuries prior to the composition of the Bhaṭṭikāvya. It was plainly Bhaṭṭi’s purpose to provide a study aid to Pāṇini’s text by using the examples already provided in the existing grammatical commentaries in the context of the gripping and morally improving story of the Rāmāyaṇa.

Bhaṭṭikāvya

To the dry bones of this grammar Bhaṭṭi has given juicy flesh in his poem. The intention of the author was to teach this advanced science through a relatively easy and pleasant medium. In his own words:This composition is like a lamp to those who perceive the meaning of words and like a hand mirror for a blind man to those without grammar. This poem, which is to be understood by means of a commentary, is a joy to those sufficiently learned: through my fondness for the scholar I have here slighted the dullard.Bhaṭṭikāvya 22.33–34.

General purpose high-level programming language such as C++ or Python. This includes object-oriented concepts of classes, parent/child inheritance or base/derived classes, overriding of inherited methods in derived classes, concept of functions, concept of keywords, etc. Of course, algorithmic derivation of results is a given.The defining feature of Pāṇini’s Aṣṭādhyāyī sūtras is the use of its own special meta-language to describe the rules of the real language i.e. Sanskrit. Let that thought sink in — a language being defined using a meta-language constructed from the same language!

Pāṇini’s Aṣṭādhyāyī grammar has all the features of a modern 

 Detailed Information about Maharshi Panini With Photo Available at myguru.in

Jai Hind

Maharshi Panini Father of Linguistics 

Hinduism is not a religion but a way of life because life, worship and religious duties are inseparable in Hinduism. A devout Hindu lives upon earth religiously, feeling the presence of God in every aspect of his life, and worshipping Him uninterruptedly in the sacrifice called life. It is difficult to say where his worship begins or ends in his daily life.Hinduism is not considered a religion, because it does not fit into the common definition of a religion. It does not have a founder, nor does it have a particular scripture or sacred text which is universally followed by all Hindus.

Hinduism Isn't a "Ism"

It is traditionally known as Dharma, which is considered eternal (Sanatana) because God is its source and support, which he reveals through Brahma, the creator God at the beginning of creation for the order and regularity of the world.The eternal religion of God is practiced not only by humans but also by gods, demons and other celestial beings. Even Brahma, Vishnu and Shiva practice it and exemplify it through their words and deeds. Hinduism has no founder, because God is its founder, preacher and teacher. He is also its upholder and savior.

Sanatana Dharma 

Whenever Dharma declines, he personally incarnates to restore it, or manifests partially in some forms to revive it. Hidden within the layers of Hinduism is an eternal wisdom, whose source is God himself.Since the duties of God define human life upon earth and determine his fate and destiny and since they are inseparable from it, Hinduism or Hindu Dharma is more appropriately called a way of life. Hindu scriptures make it abundantly clear that when a person lives for himself he incurs sin, whereas when he lives for God or in the service of God he attains liberation.

A Way Of Life

e life of a human being upon earth is not for his enjoyment but for service to God. When people engage in selfish actions they accumulate evil and remain bound to the cycle of births and deaths, whereas when they offer the fruit of their actions to God they remain pure and become free.

In other words,

Thus, Dharma or Godly duty is deeply interwoven into the life of a Hindu the way nerves are interwoven into the organs of the body. In Hinduism, it is difficult to separate a person from his Dharma. It is also difficult to say where life ends and where religious practice begins, or vice versa. The practice of Hinduism is not confined to the performance of sacrificial rituals, observation of Sacraments (Samskaras), ritual or domestic worship, going to temples and pilgrim places, uttering mantras or praying, but to the whole life.

Justification why for a devotee of God Hinduism is a way of life

It begins from the time one wakes up and continues even in deep sleep where one is said to remain in a state of self-absorption. Dharma, which is the collection of divine duties, is at the center of human life, and life is the means to practice it and manifest it in the being and in the world.In the following discussion, we will examine the reasons or the justification why Hinduism is a way of life rather than a mere body of rituals, religious observances and doctrines, and why Dharma is central to its tenets. In doing so, we must acknowledge the diversity of the people who practice Hinduism.

In truth, Hinduism is a way of life only for a few who are pure, committed to their faith and deeply integrate its tenets into their lives. For the rest, it is mostly a concept, an ideal or a mere talking point.. The Isa Upanishad begins with the declaration that all this is inhabited by God, and everything belongs to him.

Purity Is Surity

What it means is that you cannot claim ownership of anything in this world because you do not own anything. Nothing belongs to you. You are a mere guest in the universe of God, and you can only enjoy your life in his name. You live in God, supported by God, nourished by God and protected by God. Hence, a devout Hindu forsakes all worldly possessions and lives in constant reverence to God as the provider and the sustainer. He lives with restraint, expressing his gratitude as a way of life for all that he enjoys or derives from God.

1. God is the true owner of all things. Therefore, one must live in gratitude.

According to the Vedas the world is made up of God only. It is part of his body, which has been sacrificed by Him for creation. He is hidden in all and pervades everything. A devout Hindu knows that since he is pervaded and enveloped by God he lives in His constant presence, and he is never separate from Him both from within and without. He sees Him everywhere and in everything. Therefore, he worships Him numerously in numerous forms as a way of life, seeing Him in everything and treating alike all as His forms, aspects or manifestations.

2. The world is a sacred place filled with the presence of God. One must see him everywhere and in all things.

Both the Upanishads and the Bhagavadgita affirm that all actions arise from God only.We merely share his duties and responsibilities and cannot claim the doership,or the outcome of any action.Knowing it, a devout Hindu does not take credit for his successes or failures.He performs his duties without desires and expectations,renouncing doership and offering the fruit of his actions to God only.Further, he knows that he is his best friend when he lives responsibly and his worst enemy when he indulges in evil.Hence,he constantly remembers God as he performs his obligatory duties as an offering a

3. All actions arise from God, the real doer. Hence, all actions must be offered to God, taking no credit for their outcomes.

For a devout Hindu life is a sacrifice, in which he is the sacrificer as well as the sacrificed, and God is the final recipient of the sacrifice. Therefore, he lives with detachment, offering his every breath, thought and action in the service of God and dedicating himself to His cause. In the sacrifice of life, he offers his mind and body for the order and regularity of the world, taking no credit for himself and holding on to nothing.

4. Life is a continuous sacrifice, in which one becomes an offering (bhakta) in the service of God.

Whether he lives as a householder seeking the four aims of human life, or as a renunciant pursuing his liberation, he conducts himself with this sacrificial attitude as a way of life, with his mind fixed on God.

Our scriptures clearly suggest that you are neither the mind nor the body, but an eternal, indestructible, transcendental Self. A devout Hindu knows that God lives in him as the lord of his body, as much as He lives outside as the lord of the universe. Therefore, he cultivates detachment towards his name and form and remains centered in his spiritual identity, with his mind stabilized in it. He also strives to keep himself pure, living righteously and renouncing worldly pleasures,

5. You are an eternal Self. Therefore, you should live responsibly, without losing sight of your spiritual identity and higher purpose.

knowing that his body is the city or the temple of nine gates where God resides and which he cannot defile with evil thoughts. Hence, spiritual awareness of the Self becomes a way of life for him.

Hinduism acknowledges that all beings are equal, despite the diversity in their names and forms. They all possess the Self, which is eternal, indestructible and immutable, and which transmigrates from one body to another during rebirth as it is bound to the cycle of births and deaths. Thus, for a devout Hindu the world is God’s playground, in which He appears as many. Since he sees Him in others when he interacts with them, he is undistracted or untroubled by their presence or their diversity. Instead it helps him stabilize his mind in the thoughts of God and remain in His constant presence.

6. All living beings embody souls. The same Self is hidden in all. Hence, one should always see the Self in all and respect all forms of life.

Whether he goes to a temple or stays at home or engages in worldly actions, he is never separate from God and never forsakes his reverential attitude. For him, worship becomes a way of life.

People, who lack discretion, engage in desire-ridden actions, which produce karma and lead to their bondage,ignorance and delusion. Karma is not resolved until its causes are fully understood and arrested.The idea of performing actions without desires for their fruit and offering them to God as a sacrifice, this is the essence of karma sanyasa yoga. Action means any mental, physical, voluntary or involuntary action, including those which are performed by the organs in the body.Since one cannot live without performing actions even for a moment, karma yoga becomes a continuous practice.

7. Karma arises from desire ridden actions which in turn leads to bondage. Therefore, one should constantly be on guard and live responsibly.

Human life is precious and a unique opportunity to work for liberation. Only after innumerable births does a person achieve the noble birth of awakened soul in a pious family and finds favorable conditions to work for his liberation, having realized that he has suffered enough in the mortal world and needs to find a permanent release. Therefore, he assiduously works for his self-transformation and engages in selfless actions, studying the scriptures, engaging in religious discussions, austerities, rules and restraints, the practice of meditation, contemplation and self-absorption. And way of

8. You are a bound soul and not free. Hence, you should continuously strive for liberation and take no chances.

Dharma is central to Hinduism. Living for the sake of Dharma is also the essence of Hinduism. Dharma in its highest sense means a set of duties which are derived from God and which God himself performs as part of his eternal duties as the creator, sustainer and destroyer, which why Hinduism is known as the eternal religion or Sanatana Dharma. Some of his duties are meant to be performed by humans also upon earth as part of their obligation and as a service to him.

9. The purpose of human life is to express Divine Will and uphold the eternal Dharma (Sanatana Dharma) of God upon earth at all times.

Performing those duties and manifesting the divine will in the mortal world are inseparable from human life. It is their highest purpose. Hence, for a devout Hindu upholding Dharma is a way of life and the means to liberation.

One is never separate from God, and therefore one is never separate from the ideals and qualities which God represents. For the humans who seek liberation, God is the role model. He sets the standards and the framework so that they can follow his example and stay free from sin and karma. An incarnation of God also serves the same purpose. Each incarnation sets an example for humans to learn from him and emulate him in their personal lives, as the divine souls who repeatedly incarnate in their microcosms from birth to birth.

10. Expressing your devotion to God by doing his duties upon earth as your own, without desires and expectations, this is the end of all the yogas.

Thus, for a devout Hindu devotion to God and contemplation of upon his virtues, qualities and manifestations become a way of life on the path to devotion.Through its insistence upon selfless Duty (Dharma), Hinduism suggests a way of life to facilitate the purification and liberation of the embodied souls (jivas), who are caught in delusion and ignorance. Belief in God, belief in soul, belief in karma, belief in the possibility of liberation through devotional worship and the practice of yoga are deeply ingrained in the minds of Hindus.

They help them to cleanse their minds and bodies and express the highest and the best which is hidden in them. Although the mortal world is subject to dualities, delusion and other impurities, human life is not insignificant, but an opportunity to express the will of God through selfless action, purity and devotion. One is expected to live upon earth, making them as his or her guiding principles.

And For Me God is none other than you. The different and Vibrant Weapons of Different Gods mean The Different Vibrant Potential in within You. Everyone is Different in His way But his End Actions ( Offerings )should only be for Truth The Real Truth.We all Are One And Simultaneously Different.

What I SAY:

This essay lists ten reasons why Hinduism is considered a way of life rather than a religion.

Ten Reasons Why Hinduism is a Way of Life

Varahamihira was born in 505 A.D. into a family of Brahmins settled at Kapittha, a village near Ujjain. His father, Adityadasa was a worshipper of the Sun god and it was he who taught Varahamihira astrology. On a visit to Kusumapura (Patna) young Varahamihira met the great astronomer and mathematician, Aryabhata. The meeting inspired him so much the he decided to take up astrology and astronomy as a lifetime pursuit.At that time, Ujjain was the centre of learning, where many schools of arts, science and culture were flourishing in the prosperity of the Gupta reign.

10. Varahamihira 

Varahamihira, therefore, shifted to this city, where scholars from distant lands were gathering. In due course, his astrological skills came to the notice of King Yashodharman Vikramaditya of Malwa, who made him one of the Nine Gems of his court.Varahamihira was learned in the Vedas, but he was not a blind believer in the supernatural. He was a scientist.Like Aryabhata before him, he declared that the earth was spherical.In the history of science he was the first to claim that some “force” might be keeping bodies stuck to the round earth.

The force is now called gravity. He proposed that the Moon and planets are lustrous not because of their own light but due to sunlight.Varahamihira’s main work is the book Pancha Siddhantika (Treatise on the five Astronomical Canons gives us information about older Indian texts which are now lost). The work it seems is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely, the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitama Siddhanta.

Gravity 

It is acclaimed that Pancha Siddhantika of Varahamihira is one of the most important sources for the history of Hindu Astronomy from before the time of Aryabhata.Another important contribution of Varahamihira is the encyclopaedic Brihat-Samhita. It covers wide ranging subjects of human interest, including astrology, planetary movements, eclipses, rainfall, rainfall, clouds even domestic relations, gems, pearls and rituals.

Brihat-Samhita 

Brihat- Samhita: Varahamihira's most notable work, the Brihat- Samhita is an encyclopaedic work, mostly about divination but also includes work on architecture, temples, planetary motions, eclipses, timekeeping, astrology, seasons, cloud formation, rainfall, agriculture, mathematics, gemology, perfumes and many other topics. The volume expounds on gemstone evaluation criterion found in the Garuda Purana, and elaborates on the sacred nine Pearls from the same text. It contains 106 chapters and is known as the "great compilation".

Varahamihira in 550 AD have described a large number of comets in the Brhat Samhita. He wrote over sixty couplets about comets. He did not have the modern facilities like Telescope or other electronic equipment. He says that sages Garga, Parasara, Asita, Devala and others had already written about the comets. He was also an astrologer and has written on all the three branches of astrology. His son Prithuyasas has also contributed in the Hindu astrology through his work, Hora Sara.

Comets 

the discovery of the trigonometric formulas. He improved the accuracy of the sine tables of Aryabhata l. He defined the algebraic properties of zero as well as of negative numbers. Furthermore, He was among the first mathematicians to discover a version of what is now known as the Pascal’s triangle. He used it to calculate the binomial coefficients.Varahamihira made some significant observations in the field of ecology, hydrology and geology too. He was the first person who predicted underground water.

Varahamihira’s mathematical work included the discovery of the trigonometric formulas. He improved the accuracy of the sine tables of Aryabhata l. He defined the algebraic properties of zero as well as of negative numbers. Furthermore, He was among the first mathematicians to discover a version of what is now known as the Pascal’s triangle. He used it to calculate the binomial coefficients.Varahamihira made some significant observations in the field of ecology, hydrology and geology too. He was the first person who predicted underground water. His claim that plants and termites serve as indicators of underground water is now receiving attention in the scientific world.Varahamihira, without any scientific equipment, derived the true value of equinox. This value is very important for the modern day Geostationary Satellites.

Varahamihira’s mathematical work included the discovery of the trigonometric formulas. He improved the accuracy of the sine tables of Aryabhata l. He defined the algebraic properties of zero as well as of negative numbers. Furthermore, He was among the first mathematicians to discover a version of what is now known as the Pascal’s triangle. He used it to calculate the binomial coefficients.Varahamihira made some significant observations in the field of ecology, hydrology and geology too. He was the first person who predicted underground water. His claim that plants and termites serve as indicat<warningtag>ors of underground water is now receiving attention in the scientific world.</warningtag><warningtag>Varahamihira, without any scientific equipment, derived the true value of equinox. This value is very important for the modern day Geostationary Satellites.</warningtag>

His claim that plants and termites serve as indicators of underground water is now receiving attention in the scientific world. Varahamihira, without any scientific equipment, derived the true value of equinox. This value is very important for the modern day Geostationary Satellites.

Varahamihira made some important mathematical discoveries. Among these are certain trigonometric formulae which translated into our present day notation correspond to \sin x = \cos(\large\frac{\pi}{2}\normalsize - x)sinx=cos(2π​−x), \sin^{2}x + \cos^{2}x = 1sin2x+cos2x=1, and \large\frac{1}{2}\normalsize (1 - \cos 2x) = \sin^{2}x21​(1−cos2x)=sin2x.

Trigonometric 

Varahamihira made some important mathematical discoveries. Among these are certain trigonometric formulae which translated into our present day notation correspond to \sin x = \cos(\large\frac{\pi}{2}\normalsize - x)sinx=cos(2π​−x), \sin^{2}x + \cos^{2}x = 1sin2x+cos2x=1, and \large\frac{1}{2}\normalsize (1 - \cos 2x) = \sin^{2}x21​(1−cos2x)=sin2x.

Another important contribution to trigonometry was his sine tables where he improved those of Aryabhata I giving more accurate values. It should be emphasised that accuracy was very important for these Indian mathematicians since they were computing sine tables for applications to astronomy and astrology. This motivated much of the improved accuracy they achieved by developing new interpolation methods. The Jaina school of mathematics investigated rules for computing the number of ways in which rr objects can be selected from nn objects over the course of many hundreds of years.

Another important contribution to trigonometry was his sine tables where he improved those of Aryabhata I giving more accurate values. It should be emphasised that accuracy was very important for these Indian mathematicians since they were computing sine tables for applications to astronomy and astrology. This motivated much of the improved accuracy they achieved by developing new interpolation methods. The Jaina school of mathematics investigated rules for computing the number of ways in which rr objects can be selected from nn objects over the course of many hundreds of years. They gave rules <warningtag>to compute the binomial coefficients _{n}C_{r}n​Cr​ which amount to</warningtag>

Permutation And Combinations

However, Varahamihira attacked the problem of computing _{n}C_{r}n​Cr​ in a rather different way. He wrote the numbers nn in a column with n = 1n=1 at the bottom. He then put the numbers rr in rows with r = 1r=1 at the left-hand side. Starting at the bottom left side of the array which corresponds to the values n = 1, r = 1n=1,r=1, the values of _{n}C_{r}n​Cr​ are found by summing two entries, namely the one directly below the (n, r)(n,r) position and the one immediately to the left of it.

Of course this table is none other than Pascal's triangle for finding the binomial coefficients despite being viewed from a different angle from the way we build it up today. Full details of this work by Varahamihira is given in Hayashi, in , examines Varahamihira's work on magic squares. In particular he examines a pandiagonal magic square of order four which occurs in Varahamihira's work.

Pascal’s Triangle And Magic Square 

Pancha siddhantika includes Surya Siddhanta, an astronomical treatise which explains or determines the true motions of the luminaries.Under this work,he has also explained the estimated diameters of the planets, like Mercury,Venus,Mars,Saturn and Jupiter.The book gave the locations of several stars other than the lunar nakshatras(constellations) and the calculation of solar eclipses.The book also had a significant coverage on kinds of time, the length of the year of gods and demons,day and night of god Brahma,the elapsed period since creation,how planets move eastwards and sidereal revolution.

Surya Siddhanta & description on planet Mars:

Surya Siddhanta mentioned the Mars’s diameter (which was calculated to be 3,772 miles that has an error within 11% of the currently accepted diameter of 4,218 miles), circumference and also carries calculations on and about solar eclipses and lunar eclipses, its color and portion of the moon as well.Apart from these, Varahamihira also predicted the presence of water on Mars. The book had a detailed description of planet Mars. He had said in his book that planet Mars has both water and iron present on its surface, which have now been revealed by NASA and ISRO.

Mars 

He was the first to mention and explain how each planet in the solar system has been created by and centered on the sun.It’s intriguing to know that during NASA’s Mars mission, Arun Upadhyay, a retired IPS, did a comparative study of Varāhamihira’s calculations about Mars and found certain similarities.Though the original book of Surya Siddhanta till date remains untraced, but somehow a few scholars had taken their notes for their own research work. Many fear that the original version was stolen by the other astronomers from overseas.

Solar Sy

The present version of Surya Siddhanta, which is often used by Panchang experts to predict festive dates and nakshatras, was modified by Bhaskaracharya during the Middle Ages.It is learnt, Varahamihira humbly said about his own treatises: “The science of Astrology is a vast ocean and is not easy for everyone to cross it. My treatises provide a safe boat.” Truly, even now they are acknowledged as masterpieces.

Varahamihira made great contributions not only in the field of mathematics; he was also an astrologer and is considered among the greatest Acharyas of modern astrology. Varahamihira’s son Prithuyasas also contributed to Hindu astrology and his book Hora Sora is a famous book on horoscopy. Listed below are some of the important works of Varahamihira. Pancha- Siddhantika: Also known as the Treatise on the Five Astronomical Canons dated 575 AD that now give us information about older lost Indian texts. The book of Pancha- Siddhantika is one of the main works by Varahamihira.

Works of Varahamihira

The work is a treatise on mathematical astronomy and it summarises 5 earlier astronomical treatises, namely the Surya, Romaka, Paulisa, Vasishtha and Paitamaha Siddhantas. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy including Greek and Roman elements. The five siddhantas are elaborated below-• Surya Siddhanta, which is the Siddhantika of the Sun was actually composed by the ancient asura king Mayasura, who was also known as Mamuni Mayan as stated in the text by Varahamihira.

The 5 Siddhantas 

• Vasishtha Siddhanta, which is so called from one of the stars of the Great Bear, was composed by Vishnucandra.• Paulisa Siddhanta was taken from Pulisa which is supposed to be from Alexandria and was composed by Pulisa.• Romaka Siddhanta was the Doctrine of the Romans, which is the subjects of the Roman Empire and was composed by Srishena.• And lastly there is the Patiamaha Siddhanta.

•Varahamihira made some significant observations in the field of ecology, hydrology and geology too. His claim that plants and termites serve as indicators of underground water is now receiving attention in the scientific world. He was also a prolific writer. His mastery of Sanskrit grammar and poetic metre enabled him to express himself in a unique style.

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•His encyclopaedic knowledge and his lively presentation of subjects, as dry as astronomy, made him a celebrated figure. His treatise such as Pancha Siddhantika (Five Principles), Brihatsamhita (Master Collection), Brahjataka(Astrological work) have put him on as high a pedestal in Astrology as Kautilya’s in Political philosophy, Manu’s in Law or Panini’s in Grammar.

Varahamihira – Indian Sage Who Predicted Water Discovery on Mars 1500 Years Ago and A lot More...

Chanakya (350-275 BCE) was a great Indian teacher, philosopher, statesman, royal adviser, economist and jurist. Alternatively known as Kautilya or Vishnugupta, he penned the ancient Indian political treatise, the Arthashastra. He is said to be the pioneer of economics and political science in India. A Brahmin, originally hailing from Northern India, he was also a professor of political science and economics at the University of Takshashila, also known as Taxila. A past master of Vedas and ancient Indian literature, he is believed to have had some knowledge of Zoroastrianism as well.

9. Chanakya 

Chanakya was as shrewd as he was wise. He helped the first Mauryan Emperor, Chandragupta, to establish the Mauryan Empire and was an immense asset to him during his rule. Chanakya also served as Chief Advisor and Prime Minister to both Chandragupta and his son, Bindusara. His immense works were lost towards the end of the Gupta Empire and were rediscovered only in the early 20th Century.

Chanakya is often associated with the Arthashastra, which identifies its author's name as Kautilya. Only one verse in it refers to him as Vishnugupta. Some believe that Chanakya was given the name Kautilya as that was the gotra (clan) that he came from. However, there is yet another more interesting theory about the emergence of this name.The word "Kutila" in Sanskrit means "crooked". He could have been given this name, as he was a shrewd politician, who knew the ins and outs of administration.

As Kautilya Or Vishnugupta

Vishnu Sharma's Panchatantra (3rd Century BCE) explicitly identifies Chanakya as Vishnugupta. However, there is no historical record about this – it is possible that these three names belonged to three different people.

Some believe that he was born in Takshashila, while others aver that he was born in South India. He was the son of Chanak (or Canin) and Canesvari. He hence got his name from his father.He was educated at the ancient University of Takshashila and later, went on to become a professor there. Though he was raised as an orthodox Brahmin, he knew that he had the capability to rule a kingdom. He was not handsome, but his tremendous knowledge more than made up for his lack of looks.

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As mentioned earlier, there are several versions of Chanakya's life story. Check the weblink for the Buddhist and the Jain versions of the legend.

Other Legends About Chanakya

When Chanakya was old enough, he began searching for a true king. That is when he met Dhana Nanda, the king of the Nanda dynasty. According to the Mahabodhivamsa, Dhana Nanda was the last ruler of the Nanda dynasty. He is referred to as Agrammes or Xandrames in Greek history. The name Agrammes may have come the Sanskrit word, "Augrasainya", which means, "son or descendant of Ugrasena". Dhana Nanda inherited the throne from his father, Mahapadma Nanda. He is believed to have been powerful and ruled over the Parsii (Prachya) and the Gangaridai people.

Dhana Nanda And Chanakya  

During his tenure, the Nanda Empire spanned from Bihar to Bengal in the east and from Punjab to Sindh in the west. His army was very large – it consisted of 200,000 infantry, 20,000 cavalry, 2,000 war chariots and 3,000 war elephants. He, however, was quite unpopular, both with his own subjects and with the neighboring states as well. That was probably because his government levied heavy taxes and fleeced the people of their wealth.The people of Kalinga especially despised the Nanda clan, as they belonged to the Shudra varna (the lowest caste). In order to diffuse the political tension,

Nanda Empire

He also provided them with a mere handful of grains and very little water, which was barely sufficient for one human being to survive. Eventually, Sakatala lost his entire family, one by one and he was the only survivor.Seeing that the land was vulnerable, the foreign invaders again declared war. Realizing what an asset Sakatala was, Nanda freed him and requested his assistance. Wanting to avenge the death of his family at the hands of the king, Sakatala refused to help and left. He then joined hands with Chanakya.

Prince Shaurya Nanda wedded Damyanti of Kalinga. However, that only worsened the situation – the marriage itself was short-lived. That further complicated the equation between the two dynasties. During his reign, Dhana Nanda carried on the same ill-feeling for the Kalinga dynasty.Dhana Nanda had four ministers, namely, Bandu, Subandu, Kubera and Sakatala. Sakatala spent the entire money in the treasury to purchase peace from the Mleccha invaders. When the king knew of this, he got furious and punished him by casting him into a subterranean dungeon, along with his family.

Sakatala

Chanakya was interested in a position available at a daankendra or charity center. The king wanted only a Brahmin to run the center. He was well aware that he was very unpopular – there was even a rumor that he could be assassinated at any time. Dhana Nanda opened up this daankendra in a bid to salvage his flagging image. Chanakya entered the palace to apply for the royal position. On entering, he saw nine seats lined up on either side of the throne. Out of these, eight were for the Nanda Princes.Chanakya promptly rested on the empty seat, which was reserved for

the person who would become the manager of the daankendra. He then boldly declared that, his unkempt appearance notwithstanding, he was indisputably the best man for the job.Disgusted by Chanakya's unsightly countenance, Dhana Nanda and a few other princes assembled there, insulted him, calling him an ugly monkey. The king also thought that he was not refined enough in behavior and hence, refused to offer him the position. Humiliated and angry, Chanakya vowed that he would not re-tie his topknot until he had destroyed king Dhana Nanda and his entire clan.

The exact circumstances of Dhana Nanda's destruction and ultimate death are not clear. Some narratives suggest that he was killed by Chandragupta Maurya himself,after the latter captured Pataliputra. When he lost the battle, he was permitted to leave his capital, along with his two wives.He also gave away his daughter in marriage to the Mauryan Emperor.Other stories relate that Dhana Nanda went into exile after Chanakya stealthily captured Pataliputra. He was never seen or heard of after he fled from there. Some other sources seem to suggest that Chanakya ordered that he be killed while on his

Chanakya Fulfils His Vow

exile, thus clearing the path for Chandragupta to occupy Pataliputra's throne. Yet another interesting version suggests that Dhana Nanda adopted Buddhism just before going on exile. He completely renounced the material world after his clan got wiped out during the war. When Chanakya realized that he was no longer a threat, he left him alive and let him leave from there forever.

Realizing by then that king Nanda had to be defeated in order to bring Chandragupta into power, Chanakya approached king Parvataka (often identified with Porus) and made an alliance with him. Chanakya met the Greek generals as well, to discuss the possibility of an alliance with them as well. Knowing how strong and able they were, he knew that getting them on his side would be immensely beneficial to Chandragupta. He knew that this joint army could easily defeat Dhana Nanda. Sure enough, this alliance gave Chandragupta a formidably powerful army, made up of the Greeks, the Scythians, Nepalese,

Chanakya's Role In The Rise Of Chandragupta

Persians and several other sects. This joint army laid siege on Pataliputra from all directions. Seeing the sheer size of the army, the Nanda rulers had no other option but to surrender their beautiful kingdom. Chanakya then founded the Mauryan Empire and placed Chandragupta at its helm.

Chanakya is identified as the author of two important books, namely, the Chanakya Neeti (alternatively referred to as Chanakya-Niti-Shastra) and the Arthashastra. Arthashastra speaks in detail about several aspects of administration, such as monetary and fiscal policies, war strategies, welfare, international relations and so on. This treatise also relates the duties of a ruler. Some experts aver that the Arthashastra is actually a compilation of several earlier texts penned by various authors, and that Chanakya may have been one of those authors.

Arthashastra And Chanakya Neeti

Chanakya's political ideas and maxims,as specified in the Arthashastra are completely practical,unsentimental,controversial and, sometimes,even downright ruthless.This book takes a rather impersonal stance on conducting assassinations,killing family members, managing spies and secret agents,chalking out treaties and then violating them and so on and so forth. Due to this, he is often compared to Machiavelli.That said;his attitude is not so merciless throughout the treatise.He also talks about the moral duties of a king and how he should always place the happiness of his subjects above his own.

Arthashastra 

which consists of 17 chapters, is a collection of aphorisms and maxims, which are believed to be selected and gathered by Chanakya from the various shastras. This book is filled with interesting quotes, most of which are relevant even in the present times.Several Indian nationalists consider Chanakya as one of the greatest ever thinkers. His Arthashastra is still regarded as one of the best resources to learn about developing and implementing strategic national and administrative policies. Several Indian institutes, involved in training, leadership and politics are named after Chanakya.

Chanakya Neeti,

This article is about the historical character of Chanakya, who through his strategic prowess helped Chandragupta Marya establish the Maurya dynasty which ruled most of northern Indian subcontinent. He was a great administrator and political strategist and helped form good relations with the Greek dynasty.

Chanakya - Scholar and Administrator Par Excellence

Kapila was a Vedic sage who lived around the 6th century BCE and is considered a founder of Samkhya, the oldest of the six orthodox schools of Indian philosophy, or darshans. His name comes from the Sanskrit meaning “reddish brown” and is translated as “the red one.” Kapila is considered an incarnation of Vishnu who came to earth to restore spiritual order. He is also known for teaching Bhakti yoga, the spiritual path of liberation or enlightenment.

8. Rishi Kapila 

Kapila is a given name of different individuals in ancient and medieval Indian texts, of which the most well-known is the founder of the Samkhya school of Hindu philosophy. Kapila of Samkhya fame is considered a Vedic sage, estimated to have lived in the 6th-century BCE, or the 7th-century BCE.Rishi Kapila is credited with authoring the influential Samkhya-sutra, in which aphoristic sutras present the dualistic philosophy of Samkhya. Kapila's influence on Buddha and Buddhism have long been the subject of scholarly studies.

Biography

Many historic personalities in Hinduism and Jainism, mythical figures, pilgrimage sites in Indian religion, as well as an ancient variety of cow went by the name Kapila.Kapila is credited with authoring an influential sutra, called Samkhya-sutra(also called Kapila-sutra),which aphoristically presents the dualistic philosophy of Samkhya.These sutras were explained in another well studied text of Hinduism called the Samkhyakarika. Beyond the Samkhya theories,he appears in many dialogues of Hindu texts, such as in explaining and defending the principle of Ahimsa (non-violence) in the Mahabharata.

Kapila And Ahimsa

The Rigveda X.27.16 – estimated to have been composed between 1500 and 1200 BCE – mentions Kapila (daśānām ekam kapilam ) which the 14th-century Vedic commentator Sayana thought refers to a sage; a view which Chakravarti in 1951 and Larson in 1987 consider unreliable, with Chakravarti suggesting that the word refers to one of the Maruts, while Larson and Bhattacharya state kapilam in that verse means "tawny" or "reddish-brown"; as was also translated by Griffith.

In Vedic texts

Kapila is mentioned in chapter VIII of the Uttaradhyayana-sutra , states Larson and Bhattacharya, where a discourse of poetical verses is titled as Kaviliyam , or "Kapila's verses". The name Kapila appears in Jaina texts. For example, in the 12th century Hemacandra's epic poem on Jain elders, Kapila appears as a Brahmin who converted to Jainism during the Nanda Empire era. According to Jnatadharmakatha , Kapila was a contemporary of Krishna and the Vasudeva of Dhatakikhanda . The text further mentions that both of them blew their shankha (counch) together.

Jainism

Buddhists literature, such as the Jataka tales, state the Buddha was Kapila in one of his previous lives.Scholars have long compared and associated the teachings of Kapila and Buddha. For example, Max Muller wrote (abridged),There are no doubt certain notions which Buddha shares in common, not only with Kapila, but with every Hindu philosopher.It has been said that Buddha borrowed his atheism from Kapila. But atheism is an indefinite term, and may mean very different things. In one sense, every Indian philosopher was an atheist,for they all perceived that the gods of the populace could not

Buddhism

claim the attributes that belong to a Supreme Being (Absolute,the source of all that exists or seems to exist,Brahman).Kapila,when accused of atheism,is not accused of denying the existence of an Absolute Being.He is accused of denying the existence of an Ishvara.As Buddhist art often depicts Vedic deities, one can find art of both Narayana and Kapila as kings within a Buddhist temple, along with statues of Buddhist figures such as Amitabha, Maitreya, and Vairocana.In Chinese Buddhism, the Buddha directed the Yaksha Kapila and fifteen daughters of Devas to become the patrons of China.

The following works were authored by Kapila, some of which are lost, and known because they are mentioned in other works; while few others are unpublished manuscripts available in libraries stated:<ul><li>Manvadi Shrāddha - mentioned by Rudradeva in Pakayajna Prakasa .</li><li>Dṛṣṭantara Yoga - also named Siddhāntasāra available at Madras Oriental Manuscripts Library.</li><li>Kapilanyayabhasa - mentioned by Alberuni in his works.</li><li>Kapila Purana - referred to by Sutasamhita and Kavindracharya. Available at Sarasvati Bhavana Library, Varanasi.</li></ul>

•Kapila Samhita - there are 2 works by the same name. One is the samhita quoted in the Bhagavatatatparyanirnaya and by Viramitrodaya in Samskaras . Another is the Samhita detailing pilgrim centers of Orissa.•Kapilasutra - Two books, namely the Samkya Pravacana Sutra and the Tattvasamasasutra, are jointly known as Kapilasutra.Bhaskararaya refers to them in his work Saubhagya-bhaskara.•Kapila Stotra - Chapters 25 to 33 of the third khanda of the Bhagavata Mahapurana are called Kapila Stotra.•Kapila Smriti - Available in the work Smriti-Sandarbha, a collection of Smritis, from Gurumandal Publica.

•Kapilopanishad - Mentioned in the Anandasrama list at 4067 (Anandasrama 4067).•Kapila Gita - also known as Dṛṣṭantasara or Siddhāntasāra .Kapila Pancharatra - also known as Maha Kapila Pancharatra. Quoted by Raghunandana in Saṃskāra Mayukha .Ayurveda books mentioning Kapila's works are:Vagbhatta mentions Kapila's views in chapter 20 of Sutrasthana .Nischalakara mentions Kapila's views in his commentary on Chikitsa Sangraha .Kapila's views are quoted in Ayurvedadipika .The Kavindracharya list at 987 mentions a book named Kapila Siddhanta Rasayana .

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Hemadri quotes Kapila's views in Ashtangahradaya (16th verse) of the commentary Ayurveda Rasayana .Sarvadarsanasamgraha (Sarva-darśana-saṃgraha ) mentions Kapila's views on Raseśvara school of philosophy.TeachingsKapila's Samkhya is taught in various Hindu texts:

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<ul><li>"Kapila said, "Acts only cleanse the body. Knowledge, however, is the highest end (for which one strives). 5 When all faults of the heart are cured (by acts), and when the felicity of Brahma becomes established in knowledge, benevolence, forgiveness, tranquillity, compassion, truthfulness, and candour, abstention from injury, absence of pride, modesty, renunciation, and abstention from work are attained. These constitute the path that lead to Brahma. By those one attains to what is the Highest." </li><li>"Bhishma said (to Yudhishthira), 'Listen, O slayer of foes! The Sankhyas or followers of Kapila, </li></ul>

Mahabharata

who are conversant with all paths and endued with wisdom, say that there are five faults, O puissant one, in the human body. They are Desire and Wrath and Fear and Sleep and Breath. These faults are seen in the bodies of all embodied creatures. Those that are endued with wisdom cut the root of wrath with the aid of Forgiveness. Desire is cut off by casting off all purposes. By cultivation of the quality of Goodness (Sattwa) sleep is conquered, and Fear is conquered by cultivating Heedfulness.Breath is conquered by abstemiousness of diet. (Book 12: Santi Parva: Part III, Section CCCII.)

<ul><li>"My appearance in this world is especially to explain the philosophy of Sankhya, which is highly esteemed for self-realization by those desiring freedom from the entanglement of unnecessary material desires. This path of self-realization, which is difficult to understand, has now been lost in the course of time. Please know that I have assumed this body of Kapila to introduce and explain this philosophy to human society again."</li><li>"When one is completely cleansed of the impurities of lust and greed produced from the false identification of the body as "I" and bodily possessions as "mine," </li></ul>

Bhagavata Purana

Continued above - one's mind becomes purified. In that pure state he transcends the stage of so-called material happiness and distress." Kapila, the founder of Samkhya, has been a highly revered sage in various schools of Hindu philosophy. Gaudapada (~500 CE), a Advaita Vedanta scholar, in his Bhasya called Kapila as one of the seven great sages along with Sanaka, Sananda, Sanatana, Asuri, Vodhu and Pancasikha. Vyasa, the Yoga scholar, in his Yogasutra-bhasya wrote Kapila to be the "primal wise man, or knower".

Recognition

Kapila: Vedic sage, of the Samkhya school of Hindu philosophy, Philosopher

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