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TULSI-PRAJÑA, Oct.-Dec., 1992
translators use the word as a synonym for "chapter" (as can be seen from phrases like rasi vyavahāra and rajju vyavahāra). In the context of the verse we are studying it is possible that the word vyavahāra meant wordly affairs.
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Topic 6th provides for a means of analysis; presumably it is a problem-solving technique which enables one to solve an applied problem by reducing it to a state in which "all you need to do" is to use arithmetic. One imagines a teacher saying to a pupil; "use yavattavat and then it is all parikarma from then on". In other words, problems in topics 2-3-4 are "set-up" using topic 6 and then all one need to do is use the techniques in topics 1-5-7-8-9.
Topic 10th is a category by itself; it does not use arithmetic operations and fractions but it is concerned with numbers (i.e. integers) of arrangements.
We have to assume that the programme of mathematics was influential in directing both scholars and "just common plain folks" to what mathematics is
The topics 1,5,7,8 and 9 in the Sthānāñga Sutra evolve into the twenty parikarm. Topics 2,3 and 4 evolve into the eight vyavahāra. All these 20 parikarm and 8 vyavahāra are subsumed under the subject needed for patiganita. Patiganita contains all the mathematics practical purposes-constructions of road and buildings, calculating volumes of grain and other heaps, estimating of amounts in pieces of bricks and timber, interest and capital calculations, barter and exchanges as well as recreational problems. Thus practical mathematics and the underpinnings needed for it has been part of ancient Indian Mathematics.
These are the kinds of mathematical problem which are seen in the west in a rudimentary form in problems for the Quickening of the Mind' by Alcuin of York (735-804 A. D.).
The 'Sthānanga Sutra' programme of mathematics provided a paradigm for a thonsand years-from about 300 B. C. until about 650 A. D. Then Brahmagupta and Bhaskara provided a revision of the That revision pravided a framework for the next five programme. hundred years. Manāvīra (850), Śridhara (950) (?) and Bhaskara II (1150) adhere to the revised framework.
It is reported that Suśruta (who lived in the fifth century before the Christian era) was enumerating the combinations of the six tastes taken one at a time, two at a time, etc. and all at a time as 63. It is stated that the precursor of a general rule appeared in about 300 B. C.
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