The Sanskrit term Vargaprakṛti can be transliterated into English as Vargaprakrti or Vargaprakriti, using the IAST transliteration scheme (?).

In Hinduism

Ganitashastra (Mathematics and Algebra)

Source: archive.org: Hindu Mathematics

Vargaprakṛti (वर्गप्रकृति) refers to the “square-nature”, according to the principles of Bījagaṇita (“algebra” or ‘science of calculation’), according to Gaṇita-śāstra, ancient Indian mathematics and astronomy.—The indeterminate quadratic equation [Nx² ± c = y²], is called by the Hindus vargaprakṛti or kṛtiprakṛti, meaning the “square-nature” Bhāskara II (1150) states that the absolute number should be rūpa, which means “unity” as well as “absolute number” in general. [...] It was recognised that the most fundamental equation of this class is [Nx² + 1 = y²] where N is a non-square integer.

Kamalākara (1658) in the Siddhāntatattvaviveka: “Heat first the nature of the vargaprakṛti: in it the square (of a certain number) multiplied by a multiplier and then increased or diminished by an interpolator becomes capable of yielding a square-root”.

Kṛṣṇa (1580) in his commentary on the Bījagaṇita of Bhāskara II: “That in which the varga (square) is the prakṛti (nature) is called the vargaprakṛti; for the square of yāvat, etc., is the prakṛti (origin) of this (branch of) mathematics. because this (branch of) mathematics has originated from the number which is the prakṛti of the square of yāvat, etc., so it is called the vargaprakṛti. In this case the number which is the multiplier of the square yāvat, etc., is denoted by the term prakṛti. (In other words) it is the coefficient of the square of the unknown”.

We presume that the name vargaprakṛti originated from the following consideration: The principle (prakṛti) underlying the calculations in this branch of mathematics is to determine a number (or numbers) whose nature (prakṛti) is such that its (or their) square (or squares, varga) or the simple number (or numbers) after certain specified operations will yield another number (or numbers) of the nature of a square. So the name is, indeed, very significant. This interpretation seems to have been intended, at any rate, by the earlier writers who used the term in a wider sense. It is perhaps noteworthy that we do not find in the works of Brahmagupta the use of the word prakṛti either in the sense of N or of x².

context information

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

Source: DDSA: The practical Sanskrit-English dictionary

Vargaprakṛti (वर्गप्रकृति).—f. an affected square.

Derivable forms: vargaprakṛtiḥ (वर्गप्रकृतिः).

Vargaprakṛti is a Sanskrit compound consisting of the terms varga and prakṛti (प्रकृति).

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

Vargaprakṛti (वर्गप्रकृति):—[=varga-prakṛti] [from varga] f. (in [arithmetic]) an affected square, [Colebrooke]

[Sanskrit to German]

Vargaprakriti 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.

See also (Relevant definitions)

Partial matches: Varga, Prakriti.

Query error!

Full-text: Kritiprakriti, Prakriti.

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