Udvartaka: 5 definitions
Introduction:
Udvartaka means something in Hinduism, Sanskrit. If you want to know the exact meaning, history, etymology or English translation of this term then check out the descriptions on this page. Add your comment or reference to a book if you want to contribute to this summary article.
In Hinduism
Ganitashastra (Mathematics and Algebra)
Udvartaka (उद्वर्तक) refers to an “augmenter” (i.e., a number multiplying the first and second roots), according to the principles of Bījagaṇita (“algebra” or ‘science of calculation’), according to Gaṇita-śāstra, ancient Indian mathematics and astronomy.—According to Pṛthūdakasvāmī (860) in his commentary on the Brāhmasphuṭasiddhānta by Brahmagupta (628): “Here are stated for ordinary use the terms which are well known to people. [...] If there be a number multiplying both these roots [i.e., the first and the second], it is called the augmenter (udvartaka); and, on the contrary, if there be a number dividing the roots, it is called the abridger (apavartaka)”.
Ganita (गणित) or Ganitashastra refers to the ancient Indian science of mathematics, algebra, number theory, arithmetic, etc. Closely allied with astronomy, both were commonly taught and studied in universities, even since the 1st millennium BCE. Ganita-shastra also includes ritualistic math-books such as the Shulba-sutras.
Languages of India and abroad
Sanskrit dictionary
Udvartaka (उद्वर्तक).—a.
1) Causing to rise.
2) Rubbing and cleaning the body.
-kaḥ (In Math.) The quantity assumed for the purpose of the operation (Colebrooke).
1) Udvartaka (उद्वर्तक):—[=ud-vartaka] [from ud-vṛt] mfn. causing to rise, increasing, [Monier-Williams’ Sanskrit-English Dictionary]
2) [v.s. ...] (ifc.) rubbing, [Pāṇini]
3) [v.s. ...] m. (in [mathematics]) the quantity assumed for the purpose of an operation.
Udvartaka (उद्वर्तक):—(wie eben)
1) adj. wird mit seinem obj. componirt und hat alsdann den Acut auf der letzten Silbe, gaṇa yājakādi zu [Pāṇini’s acht Bücher 2, 2, 9. 6, 2, 151.] einreibend. —
2) m. bei den Mathemm. the quantity assumed for the purpose of the operation [Algebra 363.]
Udvartaka (उद्वर्तक):——
1) Adj. am Ende eines Comp. einreibend. —
2) m. in der Mathem. the quantity assumed for the purpose of the operation.
Sanskrit, also spelled संस्कृतम् (saṃskṛtam), is an ancient language of India commonly seen as the grandmother of the Indo-European language family (even English!). Closely allied with Prakrit and Pali, Sanskrit is more exhaustive in both grammar and terms and has the most extensive collection of literature in the world, greatly surpassing its sister-languages Greek and Latin.
See also (Relevant definitions)
Full-text: Apavartaka.
Relevant text
Search found 1 books and stories containing Udvartaka, Ud-vartaka; (plurals include: Udvartakas, vartakas). You can also click to the full overview containing English textual excerpts. Below are direct links for the most relevant articles:
Brahmasphutasiddhanta by Brahmagupta (Introduction) (by Acharyavara Ram Swarup Sharma)
Part 21 - The concept of Square-Nature (Varga-prakriti or Kriti-prakriti) < [Chapter 10 - Brahmagupta as an Algebraist]