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Garga-samhita (Garga And Bharadvaja)
''Garga-samhita'' ( IAST: Garga-saṃhitā), is an Indian Sanskrit-language text on jyotisha (ancient Indian astrology and astronomy), written as a dialogue between the sages Bharadvaja and Garga. Although attributed to Garga, it was definitely not composed by the ancient astrologer of that name, and can be dated to 6th-7th century CE. Date and manuscripts The text is of uncertain date, but was definitely composed after Brahmagupta's '' Brahma-sphuta-siddhanta'' (6th-7th century CE). Based on its mathematical contents, Michio Yano dates ''Garga-samhita'' to 6th-7th century CE. The text is known from a manuscript kept at the Vishveshvaranand Vedic Research Institute (VVRI), Hoshiarpur. The VVRI manuscript 2069 was copied by Thakura Datta Joshi and collated by Hariprasada Sharma at Hoshiarpur in 1960. Content The text is also known as the "astronomical Garga-samhita" to distinguish it from the "astrological" '' Gargiya-jyotisha'', an earlier text which is also known as ''Garga ...
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IAST
The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Indic scripts as employed by Sanskrit and related Indic languages. It is based on a scheme that emerged during the nineteenth century from suggestions by Charles Trevelyan, William Jones, Monier Monier-Williams and other scholars, and formalised by the Transliteration Committee of the Geneva Oriental Congress, in September 1894. IAST makes it possible for the reader to read the Indic text unambiguously, exactly as if it were in the original Indic script. It is this faithfulness to the original scripts that accounts for its continuing popularity amongst scholars. Usage Scholars commonly use IAST in publications that cite textual material in Sanskrit, Pāḷi and other classical Indian languages. IAST is also used for major e-text repositories such as SARIT, Muktabodha, GRETIL, and sanskritdocuments.org. The IAST scheme represents more than ...
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Hindu Cosmology
Hindu cosmology is the description of the universe and its states of matter, cycles within time, physical structure, and effects on living entities according to Hindu texts. Hindu cosmology is also intertwined with the idea of a creator who allows the world to exist and take shape. Matter All matter is based on three inert '' gunas'' (qualities or tendencies):James G. Lochtefeld, Guna, in The Illustrated Encyclopedia of Hinduism: A-M, Vol. 1, Rosen Publishing, , pages 224, 265, 520Theos Bernard (1999), ''Hindu Philosophy'', Motilal Banarsidass, , pages 74–76 * ''sattva'' (goodness) * '' rajas'' (passion) * '' tamas'' (darkness) There are three states of the ''gunas'' that make up all matter in the universe: * '' pradhana'' (root matter): ''gunas'' in an unmixed and unmanifested state (equilibrium). * '' prakriti'' (primal matter): ''gunas'' in a mixed and unmanifested state (agitated). * '' mahat-tattva'' (matter or universal womb): ''gunas'' in a mixed and manifested state ...
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Sanskrit Texts
Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late Bronze Age. Sanskrit is the sacred language of Hinduism, the language of classical Hindu philosophy, and of historical texts of Buddhism and Jainism. It was a link language in ancient and medieval South Asia, and upon transmission of Hindu and Buddhist culture to Southeast Asia, East Asia and Central Asia in the early medieval era, it became a language of religion and high culture, and of the political elites in some of these regions. As a result, Sanskrit had a lasting impact on the languages of South Asia, Southeast Asia and East Asia, especially in their formal and learned vocabularies. Sanskrit generally connotes several Old Indo-Aryan language varieties. The most archaic of these is the Vedic Sanskrit found in the Rig Veda, a collec ...
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Nakshatra
Nakshatra ( sa, नक्षत्रम्, translit=Nakṣatram) is the term for lunar mansion in Hindu astrology and Indian Astronomy. A nakshatra is one of 27 (sometimes also 28) sectors along the ecliptic. Their names are related to a prominent star or asterisms in or near the respective sectors. The starting point for the nakshatras according to Vedas is "Krittika" (it has been argued because the Pleiades may have started the year at the time the Vedas were compiled, presumably at the vernal equinox), but, in more recent compilations, the start of the nakshatras list is the point on the ecliptic directly opposite to the star Spica called ''Chitrā'' in Sanskrit, which would be Ashwinī, a part of the modern constellation Aries, and these compilations therefore may have been compiled during the centuries when the sun was passing through the area of the constellation Aries at the time of the vernal equinox. This version may have been called ''Meshādi'' or the " star ...
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Aryabhatta
Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the '' Aryabhatiya'' (which mentions that in 3600 ''Kali Yuga'', 499 CE, he was 23 years old) and the ''Arya-siddhanta.'' Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables. Later commentators such as Brahmagupta divide his work into ''Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy")''. His pure mathematics discusses topics such as determination of square and cube roots, geometrical figures with their properties and mensuration, arithmetric progression problems on the shadow of the gnomon, quadratic equations, linear and indeterminate equations. Aryabhata calculated the value of pi (''π)'' to the fourth decimal digit and was likely aware th ...
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Versine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',The Āryabhaṭīya by Āryabhaṭa
Section I) s. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the of navigation.


Overview

The versine
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Sine And Cosine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and li ...
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Kalpa (time)
A ''kalpa'' is a long period of time (aeon) in Hindu and Buddhist cosmology, generally between the creation and recreation of a world or universe. Etymology ''Kalpa'' ( sa, कल्प, , a formation or creation) in this context, means "a long period of time (aeon) related to the lifetime of the universe (creation)." It is derived from ''कॢप्'' (kḷp) +‎ -अ (-a, nominalizing suffix) ( sa, कॢप्, kḷp, to create, prepare, form, produce, compose, invent). Hinduism In Hinduism, a ''kalpa'' is equal to 4.32 billion years, a "day of Brahma" (12-hour day proper) or one thousand '' mahayugas'', measuring the duration of the world. Each ''kalpa'' is divided into 14 ''manvantara'' periods, each lasting 71 ''Yuga Cycles'' (306,720,000 years). Preceding the first and following each ''manvantara'' period is a juncture (''sandhya'') equal to the length of a ''Satya Yuga'' (1,728,000 years). A ''kalpa'' is followed by a ''pralaya'' (dissolution) of equa ...
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Patala
In Indian religions, Patala (Sanskrit: पाताल, IAST: pātāla, lit. ''that which is below the feet''), denotes the subterranean realms of the universe – which are located under the earthly dimension. Patala is often translated as underworld or netherworld. Patala is described as more beautiful than Svarga (subtle dimensions, loosely translated as heaven). Patala is described as filled with splendid jewels, beautiful groves and lakes. In Vajrayana Buddhism, caves inhabited by asuras are entrances to Patala; these asuras, particularly female asuras, are often "tamed" (converted to Buddhism) as dharmapala or dakinis by famous Buddhist figures such as Padmasambhava. In Hindu cosmology, the universe is divided into the three worlds: Svarga, Prithvi or Martya (earth/mortal plane) and Patala (gross dimensions, the underworld). Patala is composed of seven realms/dimensions or lokas, the seventh and lowest of them is also called Patala or Naga-loka, the region of the N ...
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Jambudvīpa
Jambudvīpa ( sa, जम्बुद्वीप; Pali: Jambudīpa) is a name often used to describe the territory of Greater India in Ancient Indian sources. The term is based on the concept of ''dvīpa'', meaning "island" or "continent" in Ancient Indian cosmogony. The term ''Jambudvipa'' was used by Ashoka to represent his realm in the third century BCE. The same terminology was used in subsequent texts, for instance Kannada inscriptions from the tenth century CE which also described the region, presumably Ancient India, as ''Jambudvipa''. The word Jambudvīpa literally refers to "the land of Jambu trees" where jambu (''Syzygium cumini'') grows. Puranic description According to Puranic cosmography, the world is divided into seven concentric island continents (''sapta-dvipa vasumati'') separated by the seven encircling oceans, each double the size of the preceding one (going out from within). The seven continents of the Puranas are stated as Jambudvipa, Plaksadvipa, S ...
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Puranas
Purana (; sa, , '; literally meaning "ancient, old"Merriam-Webster's Encyclopedia of Literature (1995 Edition), Article on Puranas, , page 915) is a vast genre of Indian literature about a wide range of topics, particularly about legends and other traditional lore. The Puranas are known for the intricate layers of symbolism depicted within their stories. Composed originally in Sanskrit and in other Indian languages,John Cort (1993), Purana Perennis: Reciprocity and Transformation in Hindu and Jaina Texts (Editor: Wendy Doniger), State University of New York Press, , pages 185-204 several of these texts are named after major Hindu gods such as Vishnu, Shiva, Brahma, and Adi Shakti. The Puranic genre of literature is found in both Hinduism and Jainism. The Puranic literature is encyclopedic, and it includes diverse topics such as cosmogony, cosmology, genealogies of gods, goddesses, kings, heroes, sages, and demigods, folk tales, pilgrimages, temples, medicine, astronomy ...
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Sanskrit
Sanskrit (; attributively , ; nominalization, nominally , , ) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had Trans-cultural diffusion, diffused there from the northwest in the late Bronze Age#South Asia, Bronze Age. Sanskrit is the sacred language of Hinduism, the language of classical Hindu philosophy, and of historical texts of Buddhism and Jainism. It was a lingua franca, link language in ancient and medieval South Asia, and upon transmission of Hindu and Buddhist culture to Southeast Asia, East Asia and Central Asia in the early medieval era, it became a language of religion and high culture, and of the political elites in some of these regions. As a result, Sanskrit had a lasting impact on the languages of South Asia, Southeast Asia and East Asia, especially in their formal and learned vocabularies. Sanskrit generally connotes several Indo-Aryan lang ...
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