Madhyamaharana, Madhyamāharaṇa, Madhyama-aharana: 6 definitions

Introduction:

Madhyamaharana 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)

[«previous next»] — Madhyamaharana in Ganitashastra glossary
Source: archive.org: Hindu Mathematics

Madhyamāharaṇa (मध्यमाहरण) refers to “equations with one, two or more unknowns in their second and higher powers” and represents one of the classes of Samīkaraṇa (“equations”), according to the principles of Bījagaṇita (“algebra” or ‘science of calculation’), according to Gaṇita-śāstra, ancient Indian mathematics and astronomy.—Brahmagupta (628) in the Brāhmasphuṭasiddhānta has classified equations as three classes [e.g., equations with one, two or more unknowns in their second and higher powers (madhyamāharaṇa)] [...]. Pṛthūdakasvāmī (860) in his commentary on the Brāhmasphuṭasiddhānta by Brahmagupta adopts four classes.—As the method of solution of an equation of the third class is based upon the principle of the elimination of the middle term, that class is called by the name madhyamāharaṇa (from madhyama, “middle”, āharaṇa “elimination”, hence meaning “elimination of the middle term”).

Bhaskara II distinguishes two types in the third [madhyamāharaṇa] class, viz.,

  1. equations in one unknown in its second and higher powers and
  2. equations having two or more unknowns in their second and higher powers.
Ganitashastra book cover
context information

Ganitashastra (शिल्पशास्त्र, gaṇitaśāstra) 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.

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Languages of India and abroad

Sanskrit dictionary

[«previous next»] — Madhyamaharana in Sanskrit glossary
Source: DDSA: The practical Sanskrit-English dictionary

Madhyamāharaṇa (मध्यमाहरण).—(in alg.) elimination of the middle term in an equation.

Derivable forms: madhyamāharaṇam (मध्यमाहरणम्).

Madhyamāharaṇa is a Sanskrit compound consisting of the terms madhyama and āharaṇa (आहरण).

Source: Cologne Digital Sanskrit Dictionaries: Shabda-Sagara Sanskrit-English Dictionary

Madhyamāharaṇa (मध्यमाहरण).—n.

(-ṇaṃ) The elimination of the middle term in an equation, (in algebra.)

Source: Cologne Digital Sanskrit Dictionaries: Monier-Williams Sanskrit-English Dictionary

Madhyamāharaṇa (मध्यमाहरण):—[from madhyama > madhya] n. the elimination of the middle term of an equation, [Colebrooke]

[Sanskrit to German]

Madhyamaharana in German

context information

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.

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