# Trairashika, Trairāśika: 12 definitions

## Introduction:

Trairashika means something in Hinduism, Sanskrit, Marathi. 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.

The Sanskrit term Trairāśika can be transliterated into English as Trairasika or Trairashika, using the IAST transliteration scheme (?).

## In Hinduism

### Jyotisha (astronomy and astrology)

Source: Wikibooks (hi): Sanskrit Technical TermsTrairāśika (त्रैराशिक).—Rule of three quantities, simple proportion. Note: Trairāśika is a Sanskrit technical term used in ancient Indian sciences such as Astronomy, Mathematics and Geometry.

*context information*

Jyotisha (ज्योतिष, *jyotiṣa* or *jyotish*) refers to ‘astronomy’ or “Vedic astrology” and represents the fifth of the six Vedangas (additional sciences to be studied along with the Vedas). Jyotisha concerns itself with the study and prediction of the movements of celestial bodies, in order to calculate the auspicious time for rituals and ceremonies.

### Ganitashastra (Mathematics and Algebra)

Source: archive.org: Hindu MathematicsTrairāśika (त्रैराशिक) refers to the “rule of three” and 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 Rule of Three terms is *trairāśika* (“three terms”, hence “the rule of three terms”). The term *trairāśika* can be traced back to the beginning of the Christian era as it occurs in the Bakhshali Manuscript, in the Āryabhaṭīya and in all other works on mathematics. About the origin of the name Bhāskara I (c. 525) remarks: “Here three quantities are needed (in the statement and calculation) so the method is called *trairāśika* (‘the rule of three terms’)”.

The Rule of Three (*trairāśika*) was highly appreciated by the Hindus because of its simplicity and its universal application to ordinary problems. The method as evolved by the Hindus gives a ready rule which can be applied even by the “ignorant person” to solve problems involving proportion, without fear of committing errors.

Āryabhaṭa I in the Āryabhaṭīya: “In the Rule of Three, the *phala* (‘fruit’), being multiplied by the *icchā* (‘requisition’) is divided by the *pramāṇa* (‘argument’). The quotient is the fruit corresponding to the *icchā*. The denominators of one being multiplied with the other give the multiplier (i.e., numerator) and the divisor (i.e., denominator)”.

Brahmagupta in the Brāhmasphuṭasiddhānta: “In the Rule of Three *pramāṇa* (‘argument’), *phala* (‘fruit’) and *icchā* (‘requisition’) are the (given) terms; the first and the last- terms must be similar. The *icchā* multiplied by the *phala* and divided by the *pramāṇa* gives the fruit (of the demand)”.

Śrīdhara in the Triśatikā: “Of the three quantities, the *pramāṇa* (‘argument’) and *icchā* (‘requisition’) which are of the same denomination are the first and the last; the *phala* (‘fruit’) which is of a different denomination stands in the middle; the product of this and the last is to be divided by the first”.

Mahāvīra in the Gaṇitasārasaṃgraha: “In the Rule of Three, the *icchā* (‘requisition’) and the *pramāṇa* (‘argument’) being similar, the result is the product of the *phala* and *icchā* divided by the *pramāṇa*”.

Āryabhaṭa II (950) in the Mahāsiddhānta: “The first term is called *māna*, the middle term *vinimaya* and the last one *icchā*. The first and the last are of the same denomination. The last multiplied by the middle and divided by the first gives the result”.

*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 Dictionarytrairāśika (त्रैराशिक).—m n (S) The rule of three. The words expressing the terms are *ādyaṅka, madhyāṅka, antyāṅka *or *icchāṅka*; also *ādi, madhya, anta *or *icchā*; also *ādi, pramāṇa, icchā, icchāphala*. And the two divisions are *kramatrairāśika *& *vyasta *or *vilōma trairāśika*.

trairāśika (त्रैराशिक).—*m n* The Rule of Three.

*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 dictionaryTrairāśika (त्रैराशिक).—The rule of three (in Math.).

Derivable forms: *trairāśikam* (त्रैराशिकम्).

--- OR ---

Trairāśika (त्रैराशिक).—*a.* Relating to 3 zodiacal signs.

Trairāśika (त्रैराशिक).—mf.

(*-kaḥ-kā*) (In Arithmetic,) The rule of three: it is of two kinds *kramatrairāśikaḥ* Rule of three direct, *vyasta* or *vilomatrairāśikaḥ* Rule of three inverse. E. *tri* three, *rāśi* quantity, *ṭhañ* aff.

1) Trairāśika (त्रैराशिक):—[from *traiṃśa*] mfn. ‘relating to 3 (*rāśi*) numbers’, with or without *gaṇita* or *karman*, the rule of three (in [arithmetic]; cf. *krama*-, *viloma*-, *vyasta*-), [Laghujātaka, by Varāha-mihira [Scholiast or Commentator]; Sūryaprajñapti [Scholiast or Commentator]]

2) [v.s. ...] relating to 3 zodiacal signs, [Hāyana-ratna, by Balabhadra]

Source: Cologne Digital Sanskrit Dictionaries: Yates Sanskrit-English DictionaryTrairāśika (त्रैराशिक):—[*trai-rāśika*] *(kaḥ-kā)* 1. *m. f.* The Rule of Three, direct is *kramatrairāśikaḥ;* inverse is *vilomatrairāśika*.

Trairāśika (त्रैराशिक) in the Sanskrit language is related to the Prakrit words: Terāsi, Terāsia.

#### [Sanskrit to 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.

### Kannada-English dictionary

Source: Alar: Kannada-English corpusTrairāśika (ತ್ರೈರಾಶಿಕ):—[noun] = ತ್ರೈರಾಶಿ *[trairashi*].

--- OR ---

Trairāsika (ತ್ರೈರಾಸಿಕ):—[noun] = ತ್ರೈರಾಶಿ *[trairashi*].

*context information*

Kannada is a Dravidian language (as opposed to the Indo-European language family) mainly spoken in the southwestern region of India.

## See also (Relevant definitions)

Partial matches: Rasika, Trai.

Starts with: Trairashikalinga.

Ends with: Kramatrairashika, Samatrairashika, Vilomatrairashika, Vividhatrairashika, Vyastatrairashika.

Full-text (+6): Vilomatrairashika, Terasi, Tericcha, Vyastatrairashika, Trirashi, Vyasta, Antyanka, Trairashya, Terasia, Madhyanka, Adyanka, Kramatrairashika, Dashamshaapurnanka, Vyavahari Apurnanka, Pramana, Pancarashika, Navarasika, Saptarashika, Ekadasharashika, Trairashikalinga.

## Relevant text

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