In Hinduism

Ganitashastra (Mathematics and Algebra)

Source: archive.org: Hindu Mathematics

1) Kapāṭasandhi (कपाटसन्धि) refers to the “door-junction method” and represents one of the various methods of Guṇana (“multiplication”) 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 main features of the method are (i) the relative positions of the multiplicand and the multiplier and (ii) the rubbing out of figures of the multiplicand and the substitution in their places of the figures of the product. The method owes its name kapāṭasandhi to the first feature.—These methods were transmitted to Arabia in the eighth century and were thence communicated to Europe, where they occur in the writings of medieval mathematicians.

Śrīdhara in the Triśatikā: “Placing the multiplicand below the multiplier as in kapāṭasandhi, multiply successively, in the direct or inverse order, moving the multiplier each time. This method is called kapāṭa-sandhi”.

Āryabhaṭa II (950) in the Mahāsiddhānta gives the following without name: “Place the first figure of the multiplier over the last figure of the multiplicand, and then multiply successively all the figures of the multiplier by each figure of the multiplicand”.

Śrīpati (1039) in the Siddhāntaśekhara 13.2 and Gaṇitatilaka 15 gives the name kapāṭasandhi and states: “Placing the multiplicand below the multiplier as in the junction of two doors multiply successively (the figures of the multiplicand) by moving it (the multiplier) in the direct or inverse order”.

Mahāvīra (in the Gaṇitasārasaṃgraha) refers to a method known as kapāṭa-sandhi, but does not give the details of the process. Bhāskara II gives the method but not the name, while Nārāyaṇa (1356) gives the method in almost the same words as Śrīdhara, and calls it kapāṭasandhi.

2) Kapāṭasandhi (कपाटसन्धि) also refers to the “gelosia method” of Guṇana (“multiplication”) according to the Gaṇitamañjarī (16th century) by Gaṇeśa (son of Ḍhuṇḍhirāja).—It appears also in Gaṇeśa’s commentary on the Līlāvatī. As the description of the kapāṭasandhi given by the older mathematicians is incomplete and sketchy, it is difficult to say whether Gaṇeśa is right in identifying the gelosia method with the kapāṭa-sandhi of older writers. [...] The fact that he identified this method with the kapāṭasandhi which is the oldest known method shows that the gelosia method must have been in use in India from a long time before him.

Gaṇeśa in the Gaṇitamañjarī: “(Construct) as many compartments as there are places in the multiplicand and below these as many as there are places in the multiplier; the oblique lines in the first, in the one below, and in the other (compartments) are produced. Multiply each place of the multiplicand, by the places of the multiplier (which are) one below the other and set the results in the compartments. The sum taken obliquely on both sides of the oblique lines in the compartments gives the product. This is the kapāṭasandhi”.

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

Sanskrit dictionary

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

Kapāṭasandhi (कपाटसन्धि).—m.

(-ndhiḥ) 1. The junction of the leaves of a door. 2. A mode of multiplying, (in arithmetic.) E. kapāṭa, and sandhi junction.

Source: Cologne Digital Sanskrit Dictionaries: Yates Sanskrit-English Dictionary

Kapāṭasandhi (कपाटसन्धि):—[kapāṭa-sandhi] (ndhiḥ) 2. m. A joining in a door; a mode of multiplying.

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: Kapata, Sandhi.

Full-text: Gunana.

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