Brahmagupta: The Ancient Indian Mathematician
01 Jan 2009-pp 185-192
TL;DR: The history of the passage of the extraordinarily brilliant and fundamental mathematical discoveries of the ancient Indian mathematician, Brahmagupta (598-665 c.d.a-khadyaka) from India to Arabia and then to Europe, through the centuries, has been vividly described.
Abstract: The history of the passage of the extraordinarily brilliant and fundamental mathematical discoveries of the ancient Indian mathematician, Brahmagupta (598–665 c.e.) from India to Arabia and then to Europe, through the centuries, has been vividly described. This article endeavors to appreciate Brahmagupta’s position as an original creative mathematician in the perspective of world mathematics. This paper primarily concentrates on the history of the Brahmagupta’s mathematics and his transmission to the Arab countries. The methodology adopted has a composite structure: history and mathematics. We have discussed Brahmagupta’s original contributions, which are contained in two illustrious treatises–the Brahma-sphutasiddh anta and the Khan. d.a-khadyaka–composed in Sanskrit verses. Brahmagupta’s original method of solving an indeterminate quadratic equation in two variables has been presented in some detail. The details of the Indian and Arab scholars and others involved in the intellectual scientific-mathematical transmission of knowledge processes, the roles played by the then rulers of Indian and the Arab countries in this type of transmission operation, the socio-political situations in these countries are presented. It has been concluded that Brahmagupta’s mathematics is now a part of the stat shared heritage of humankind.
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Book•
01 Jan 1894
TL;DR: In this paper, the authors define a set of fundamental postulates for the geometry of the triangle and circle, including the notion of a curve and the concept of a circle, as well as the notion and theory of groups.
Abstract: Introduction The Babylonians The Egyptians The Greeks The Romans The Maya The Chinese The Japanese The Hindus The Arabs Europe During the Middle Ages: Introduction of Roman mathematics Translation of Arabic manuscripts The first awakening and its sequel Europe During the Sixteenth, Seventeenth and Eighteenth Centuries: The Renaissance Vieta to Descartes Descartes to Newton Newton to Euler Euler, Lagrange and Laplace The Nineteenth and Twentieth Centuries. Introduction: Definition of mathematics Synthetic Geometry: Elementary geometry of the triangle and circle Link-motion Parallel lines, non-Euclidean geometry and geometry of $n$ dimensions Analytic Geometry: Analysis Situs Intrinsic co-ordinates Definition of a curve Fundamental postulates Geometric models Algebra: Theory of equations and theory of groups Solution of numerical equations Magic squares and combinatory analysis Analysis: Calculus of variations Convergence of series Probability and statistics Differential equations. Difference equations Integral equations, integro-differential equations, general analysis, functional calculus Theories of irrationals and theory of aggregates Mathematical logic Theory of Functions: Elliptic functions General theory of functions Uniformization Theory of Numbers: Fermat's "Last Theorem," Waring's theorem Other recent researches. Number fields Transcendental numbers. The infinite Applied Mathematics: Celestial mechanics Problem of three bodies General mechanics Fluid motion Sound. Elasticity Light, electricity, heat, potential Relativity Nomography Mathematical tables Calculating machines, planimeters, integraphs Editor's notes Alphabetical index.
155 citations
Book•
01 Jan 1962
TL;DR: The second volume of the three in which ooo the authors are writing the history of Hindu mathematics as discussed by the authors contained Part 1, dealing with numeral notation and arithmetic, which was issued in 1935, and noticed in NATURE of January 18, 1936, p. 88; the present volume (Part 2) contains the history OF algebra.
Abstract: THIS is the second volume of the three in which ooo the authors are writing the history of Hindu mathematics. The first contained Part 1, dealing with numeral notation and arithmetic, which was issued in 1935, and noticed in NATURE of January 18, 1936, p. 88; the present volume (Part 2) contains the history of algebra.History of Hindu Mathematics: a Source Book. Part 2: Algebra. By Bibhutibhusan Datta and Avadhesh Narayan Singh. Pp. xvi + 314. (Lahore: Motilal Banarsi Das, 1938.) 7.8 rupees; 13s.
53 citations
Book•
01 Jan 1936
TL;DR: The history of science could no longer be conceived as a sum of particular histories, but rather as an organic integration, whence no part could be abstracted without damage as mentioned in this paper, and the history of each science is necessarily more technical than that of science as a whole, more concerned with scientific than with cultural continuity.
Abstract: The remarks which I have made on another occasion with reference to the history of science.would apply equally well to the history of mathematics; there is no need of repeating them. However, the history of any special science suggests new considerations. As long as the history of science was conceived as the sum of the histories of special sciences, the relationship between the former and the latter was simple enough. The history of each special science was simply a part of a whole; a part which could easily be removed and isolated. However, that old Whewellian conception had to be abandoned, as it was borne in gradually upon scholars that one of the most valuable aspects of the history of science was the study of the interrelationships between different branches and their mutual enrichment. The history of science could no longer be conceived as a sum of particular histories, but rather as an organic integration, whence no part could be abstracted without damage. Moreover the history of each science is necessarily more technical than that of science as a whole, more concerned with scientific than with cultural continuity. As it deals with a more limited group of ideas it can hope to follow these more closely. To be sure, these differences are quantitative rather than qualitative, and would vary considerably from one historian to another. The one might write a history of science of a very abstract type; the other, a history, say, of chemistry, which would contain fewer technicalities than humanities. In general, however, we should expect the opposite.
51 citations