Brihat – Samhita
Another important contribution of Varahamihira is the Brihat-Samhita. It covers wide ranging subjects of human interest, including astrology, planetary movements, eclipses, rainfall, clouds, architecture, growth of crops, manufacture of perfume, matrimony, domestic relations, gems, pearls, and rituals. 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”.
He was also an astrologer. He wrote on all the three main branches of Jyotisha astrology:
- Brihat Jataka – is considered as one of the five main treatises on Hindu astrology on horoscopy.
- Laghu Jataka – also known as ‘Swalpa Jataka’
- Samasa Samhita – also known as ‘Lagu Samhita’ or ‘Swalpa Samhita’
- Brihat Yogayatra – also known as ‘Mahayatra’ or ‘Yakshaswamedhiya yatra’
- Yoga Yatra – also known as ‘Swalpa yatra’
- Tikkani Yatra
- Brihat Vivaha Patal
- Lagu Vivaha Patal – also known as ‘Swalpa Vivaha Patal’
- Lagna Varahi
- Kutuhala Manjari
- Daivajna Vallabha (apocryphal)
His son Prithuyasas also contributed in the Hindu astrology; his book Hora Sara is a famous book on horoscopy. Khana (also named Lilavati elsewhere) the medieval Bengali poetess astrologer is believed to be the daughter-in-law of Varahamihir.
The Romaka Siddhanta (“Doctrine of the Romans”) and the were two works of Western origin which influenced Varahamihira’s thought, though this view is controversial as there is much evidence to suggest that it was actually Vedic thought indigenous to India which first influenced Western astrologers and subsequently came back to India reformulated. Number of his writings share similarities with with the earlier texts like Vedanga Jyotisha .
A comment in the Brihat-Samhita by Varahamihira says: “The Greeks, though Barbarians, must be honored since they have shown tremendous interest in our science…..” (“mleccha hi yavanah tesu samyak shastram kdamsthitam/ rsivat te ‘p i pujyante kim punar daivavid dvijah” (Brihat-Samhita 2.15)).
Buddhist Emperor Asoka built thousands of Stupas and Viharas for Buddhist followers. One of his stupas, the Great Sanchi Stupa, has been declared as a World Heritage Site by UNECSO. The Ashoka Pillar at Sarnath has a four-lion capital, which was later adopted as the national emblem of the modern Indian republic. Throughout his life, ‘Asoka the Great’ followed the policy of nonviolence or ahimsa. Even the slaughter or mutilation of animals was abolished in his kingdom. He promoted the concept of vegetarianism. The caste system ceased to exist in his eyes and he treated all his subjects as equals. At the same time, each and every person was given the rights to freedom, tolerance, and equality.
Missions to Spread Buddhism
The third council of Buddhism was held under the patronage of Emperor Ashoka. He also supported the Vibhajjavada sub-school of the Sthaviravada sect, now known as the Pali Theravada. He sent his missionaries to the following places:
- Kashmir – Gandhara Majjhantika
- Mahisamandala (Mysore) – Mahadeva
- Vanavasi (Tamil Nadu) – Rakkhita
- Aparantaka (Gujarat and Sindh) – Yona Dhammarakkhita
- Maharattha (Maharashtra) – Mahadhammarakkhita
- “Country of the Yona” (Bactria/ Seleucid Empire) – Maharakkhita
- Himavanta (Nepal) – Majjhima
- Suvannabhumi (Thailand/ Myanmar) – Sona and Uttara
- Lankadipa (Sri Lanka) – Mahamahinda
His missionaries also went to the below mentioned places:
- Seleucid Empire (Middle Asia)
- Cyrene (Libya)
- Epirus (Greece and Albania)
Maharishi Vatsyayana (IND.) is the name of a Hindu Philosopher in the Vedic tradition who is believed to have lived around 3rd century CE in India. His name appears as the author of the Kama Sutra and of Nyaya Sutra Bhashya, the first commentary on Gotama’s Nyaya Sutras. India is developing country also before 18th century we are provide to knowledge all of world many discovery and research’s also completed
His name is sometimes confused with Mallanaga, the prophet of the Asuras, to whom the origin of erotic science is attributed. This is an error; as Danielou says:
The attribution of the first name Mallanaga to Vatsyayana is due to the confusion of his role as editor of the Kama Sutra with that of the mythical creator of erotic science.
Hardly anything is known about him, although it is believed that his disciples went on his instructions, on the request of the Hindu Kings in the Himalayan range to influence the hill tribals to give up the pagan cult of sacrifices. He is said to have created the legend of Tara among the hill tribes as a tantric goddess. Later as the worship spread to the east Garo hills,the goddess manifest of a ‘yoni’ goddess Kamakhya was created. His interest in human sexual behavior as a medium of attaining spirituality was recorded in his treatise Kama Sutra.
At the close of the Kama Sutra this is what he writes about himself:
|“After reading and considering the works of Babhravya and other ancient authors, and thinking over the meaning of the rules given by them, this treatise was composed, according to the precepts of the Holy Writ, for the benefit of the world, by Vatsyayana, while leading the life of a religious student at Benares, and wholly engaged in the contemplation of the Deity. This work is not to be used merely as an instrument for satisfying our desires. A person acquainted with the true principles of this science, who preserves his Dharma (virtue or religious merit), his Artha (worldly wealth) and his Kama (pleasure or sensual gratification), and who has regard to the customs of the people, is sure to obtain the mastery over his senses. In short, an intelligent and knowing person attending to Dharma and Artha and also to Kama, without becoming the slave of his passions, will obtain success in everything that he may do.”
It is impossible to fix the exact date either of the life of Vatsyayana or of his work. It is believed that he must have lived between the 1st and 6th century AD, on the following grounds: He mentions that Satakarmi Sattavahna, a king of Kuntal, killed Malayevati his wife with an instrument called Katamari by striking her in the passion of love. Vatsyayana quotes this case to warn people of the danger arising from some old customs of striking women when under the influence of sexual passion. This king of Kuntal is believed to have lived and reigned during the 1st century AD, and consequently Vatsyayana must have lived after him. On the other hand, another author, Varahamihira, , in the eighteenth chapter of his “Brihatsanhita”, discusses of the science of love, and appears to have borrowed largely from Vatsyayana on the subject. Varahamihira is believed to have lived during the 6th century, and therefore Vatsyayana must have written his works before the 6th century.
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Brahmagupta (598–.670 CE)Pi
In verse 40, he gives values of
12.40. The diameter and the square of the radius [each] multiplied by 3 are [respectively] the practical circumference and the area [of a circle]. The accurate [values] are the square-roots from the squares of those two multiplied by ten.
So Brahmagupta uses 3 as a “practical” value of π, and as an “accurate” value of π.
Measurements and constructions
In some of the verses before verse 40, Brahmagupta gives constructions of various figures with arbitrary sides. He essentially manipulated right triangles to produce isosceles triangles, scalene triangles, rectangles, isosceles trapezoids, isosceles trapezoids with three equal sides, and a scalene cyclic quadrilateral.
After giving the value of pi, he deals with the geometry of plane figures and solids, such as finding volumes and surface areas (or empty spaces dug out of solids). He finds the volume of rectangular prisms, pyramids, and the frustum of a square pyramid. He further finds the average depth of a series of pits. For the volume of a frustum of a pyramid, he gives the “pragmatic” value as the depth times the square of the mean of the edges of the top and bottom faces, and he gives the “superficial” volume as the depth times their mean area.
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Brahmagupta (598–.670 CE)Triangles
Brahmagupta dedicated a substantial portion of his work to geometry. One theorem gives the lengths of the two segments a triangle’s base is divided into by its altitude:
12.22. The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular [altitude] is the square-root from the square of a side diminished by the square of its segment. Thus the lengths of the two segments are .
He further gives a theorem on rational triangles. A triangle with rational sides a, b, c and rational area is of the form:
for some rational numbers u, v, and w.
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Brahmagupta (598–.670 CE) Bramhgupta Formla
Main article: Bramhagupta’s formual
Brahmagupta’s most famous result in geometry is his format for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure’s area,
12.21. The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral.
So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area
is while, the exact area is
Although Brahmagupta does not explicitly state that these quadrilaterals are cyclic, it is apparent from his rules that this is the case. Heron’s formula is a special case of this formula and it can be derived by setting one of the sides equal to zero.
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Brahmagupta (598–.670 CE) was an Indian Mathematician and astronomer who wrote two important works on Mathematics and Astronomy: the Brahmaphutasiddhanta (Extensive Treatise of Brahma) (628), a theoretical treatise, and the Khandakhadyaka, a more practical text. There are reasons to believe that Brahmagupta originated from Bhinmal. the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma’mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta’s Brahmasphuta-siddhanta.
Brahmagupta was the first to give rules to compute with Zero. The texts composed by Brahmagupta were composed in elliptic verse, as was common practice in Indian mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta’s mathematics was
the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta’s case, the disagreements stemmed largely from the choice of astronomical parameters and theories. Critiques of rival theories appear throughout the first ten astronomical derived.
Although Brahmagupta was familiar with the works of astronomers following the tradition of Aryabhatta, it is not known if he was familiar with the work of Bhaskara I, a contemporary. Brahmagupta had a plethora of criticism directed towards the work of rival astronomers, and in his Brahmasphutasiddhanta is found one of the earliest attested schisms among Indian mathematicians. The division was primarily about chapters and the eleventh chapter is entirely devoted to criticism of these theories, although no criticisms appear in the twelfth and eighteenth chapters.
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