The Sanskrit term Vyastatrairāśika can be transliterated into English as Vyastatrairasika or Vyastatrairashika, using the IAST transliteration scheme (?).

In Hinduism

Ganitashastra (Mathematics and Algebra)

Source: archive.org: Hindu Mathematics

Vyastatrairāśika (व्यस्तत्रैराशिक) refers to the “reverse rule of three”, as opposed to the regular Trairāśika (“rule of three”), which represents one of the twenty operations (logistics) of pāṭīgaṇita (“science of calculation which requires the use of writing material—the board”), according to Pṛthudakasvāmī’s commentary on the Brāhmasphuṭasiddhānta by Brahmagupta, a Sanskrit treatise on ancient Indian mathematics (gaṇita-śāstra) and astronomy from the 7th century.—The Hindu name for the Inverse Rule of Three is vyastatrairāśika (lit. “inverse rule of three terms”). After describing the method of the Rule of Three the Hindu writers remark that the operation should be reversed when the proportion is inverse.

Śrīdhara in the Triśatikā: “The method is to multiply the middle term by the first and to divide by the last, in case the proportion is different”.

Mahāvīra in the Gaṇitasārasaṃgraha: “In the case of this (proportion) being inverse, the operation is reversed”.

Bhāskara II in the Līlāvatī: “In the inverse (proportion), the operation is reversed. [...] Where with increase of the icchā (requisition) the phala decreases or with its decrease the phala increases, there the experts in calculation know the method to be the Inverse Rule of Three. [...] Where the value of living beings is regulated by their age; and in the case of gold, where the weight and touch are compared; or when heaps are subdivided, let the Inverse Rule of Three be used (vyastatrairāśika)”.

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.

Languages of India and abroad

Marathi-English dictionary

Source: DDSA: The Molesworth Marathi and English Dictionary

vyastatrairāśika (व्यस्तत्रैराशिक).—m n S pop. vyastatrirāśi f The Rule of three inverse.

Source: DDSA: The Aryabhusan school dictionary, Marathi-English

vyastatrairāśika (व्यस्तत्रैराशिक).—m n-trirāśi f The rule of three inverse.

context information

Marathi is an Indo-European language having over 70 million native speakers people in (predominantly) Maharashtra India. Marathi, like many other Indo-Aryan languages, evolved from early forms of Prakrit, which itself is a subset of Sanskrit, one of the most ancient languages of the world.

Sanskrit dictionary

Source: DDSA: The practical Sanskrit-English dictionary

Vyastatrairāśika (व्यस्तत्रैराशिक).—the rule of three inverted.

Derivable forms: vyastatrairāśikam (व्यस्तत्रैराशिकम्).

Vyastatrairāśika is a Sanskrit compound consisting of the terms vyasta and trairāśika (त्रैराशिक).

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

Vyastatrairāśika (व्यस्तत्रैराशिक):—[=vy-asta-trairāśika] [from vy-asta > vy-as] n. the rule of three inverted, [Colebrooke]

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.

See also (Relevant definitions)

Partial matches: Trairashika, Vyasta.

Full-text: Samatrairashika, Vyasta, Patiganita.

Relevant text

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