Date of Award
7-15-1931
Document Type
Thesis
Keywords
Calculus, History of Mathematics, Method of Exhaustion, Infinitesimals, Newton, Leibnitz, Archimedes, Differential Calculus, Integral Calculus, Mathematical History, HBCU Thesis, Cavalieri
Abstract
This thesis, submitted to Xavier University in partial fulfillment of requirements for a Bachelor of Science degree in 1931, traces the historical development of the calculus from ancient Greek mathematics through the early twentieth century. The study is organized chronologically across eight sections. The introduction defines key mathematical terms including calculus, variable, and limit, and situates the calculus as the most powerful instrument of mathematical investigation. The thesis then examines the Method of Exhaustion developed by Greek mathematicians including Antiphon (430 B.C.), Eudoxus (370 B.C.), and Archimedes (225 B.C.), whose summation of infinite series represents the nearest ancient approach to integration. Medieval contributions are addressed through the mensuration work of Oresme in 1360. The study then traces the seventeenth-century pioneers of infinitesimals including Kepler, Cavalieri, Descartes, Fermat, Wallis, Pascal, and Barrow, whose differential triangle anticipated later developments. The concurrent and independent contributions of Newton and Leibnitz are examined, followed by the influence of eighteenth-century analysts Euler, Lagrange, and Legendre. The thesis concludes with nineteenth and twentieth-century extensions of calculus principles and their applications in astronomy, physics, chemistry, mechanics, engineering, elasticity, and electricity. No original abstract was included; this abstract is provided by the XULA Digital Commons editors.
Recommended Citation
Virginia, Sister Mary SSF, "General Steps in the Evolution of the Calculus from the Time of the Ancients to the Present" (1931). Electronic Theses and Dissertations. 127.
https://digitalcommons.xula.edu/etd/127