Publication Date


Document Type


First Advisor

Beach, James W.||Miller, Herbert (Professor of mathematics)

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematics




This paper tries to show that as soon as mathematicians began to concern themselves with the problems of motion, they found themselves severly handicapped by the Arabic Algebra, which devised its principles from classical geometry. In intellectual, as well as political enterprises, numerous forces and numerous individual contributions determine the outcome. For example; Galileo did not fashion the quantitative approach to modern science single-handed. Similarly, the calculus is almost as much the creation of Eudoxes, Archimedes, and a dozen others of the seventeenth century, as it is that of Newton and Leibniz. It is especially true of mathematics that while the creative work is done by Individuals, the results are the fruits of centuries of thought and development. This paper attempts to illustrate the problems and partial solutions that were tried, until, at last, the scientists devised a new instrument of calculation: the Infinitesimal Calculus. For certain purposes, other methods yield results which are more in accordance with the facts, but the Newtonian methods remain, and will long remain, the basis of calculations in natural science.


Includes bibliographical references.


49 pages




Northern Illinois University

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