1. Leibniz versus Newton Fluxions Carolyn Carr

2.  Theories  Newtonian mechanics  Universal gravitation  Calculus  Optics and Color theory Founded Fluxions in1666 Newton’s Theory on Calculus Based on Motion Distance traveled in reference to time Fluent of the distance is velocity Fluent of Velocity or Fluxion of distance is acceleration The dividing the area under the curve

3.  Theories  Infinitesimal calculus  Monadology  Theodicy  Optimism  Leibniz formula for pi  Leibniz harmonic triangle  Leibniz formula for determinants  Leibniz integral rule  Principle of sufficient reason  Leibniz differential  Diagrammatic reasoning  Notation for differentiation  Proof of Fermat's little theorem  Kinetic energy  Entscheidungsproblem Founded Calculus in 1673 Leibniz’s Theory on Calculus Notation Triangle to find the tangent line Integral first 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

4. Newton writes De Analysi in 1666 Barrow obtained a copy Sent De Analysi to Collins Collins shows Oldenburg ->Oldenburg shows Leibniz Leibniz reads the information… Leibniz writes his Theory (1684), “A new method for Maxima and Minima as well as tangents, which is not restricted by fractional or irrational quantities

5. Duillier publishes “A Two-Fold Geometrical Investigation of the Line of Breifest Descent” An attack on Leibniz Newton first inventor. Was Leibniz an inventor at all? Leibniz Retaliates: Publishes in Acta Anonymous, States that Leibniz invented his theory after Newton

6. Leibniz’s Review of Optics: in Acta Eruditorum Implies plagiarism, but not directly Leibniz did not use his name Newton’s Optics Published due to controversy Included history of he invention of Fluxions

7. Newton reads Review on Optics Newton believes he has more grounds to complain Royal Society investigates again Leibniz Appeals to the Royal Society 1699 Requests an apology President: Sloane, was going to write Leibniz. John Keill Responds to Leibniz’s Review on Optics Questioning if Leibniz gets the credit of the inventing Calculus Did Newton have a hand in this?

8. Special Committee Constructed to Solve the Issue Commercium Epistolicum Findings: Newton was the only founder of Calculus, Leibniz stole this idea and changed the name and symbols. Royal Society Reviews the Situation Keill writes a letter to Leibniz based on the permission of the Royal Society Leibniz responds: unscientific, and bias

9. Brittan suffers from not being included in the other mathematical advances. England and the rest of Europe had different notation system National Pride England and continently Europe close ideas to each other

11.  Works Cited  [1] Ball, W. R. (1908). A Short Account of the History of Mathematics. New York: Dover Publications, INC.  [2] Cohen, B. I., & Smith, G. E. (2002). The Cambridge Companion to Newton. New York: Cambridge University Press.  [3] More, L. T. (1934). Isaac Newton: A Biography. New York: Dover Publications, INC..  [4] Eves, H. (1983). Great Moments in Mathematics (after 1650). Washington DC: Mathematical Association of America.  [5] Leibniz Fundamental Theorem of Calculus. (n.d.). Retrieved December 7, 2009, from New Mexico State Univserity Math Website: http://www.math.nmsu.edu/~history/book/leibniz.pdf  [6] Boyer, C. B. (1968). A History of Mathematics. New York: John Wiley & Son, INC.  [7] Westfall, R. S. (1980). Never a Rest: A Biography of Isaac Newton. New York: Cambridge University Press.  [8] Cajori, F. (1961). A History of Mathematics. New York: The MacMillan Company.  [9] Christianson, G. E. (1984). In the Presence of the Creator. New York: The Free Press.  [10] Adams, R. M. (1998). Leibniz: Determinist, Theist, Idealist. New York : Oxford University Press (US).  [11] Hall, A. R. & Tilling, L. (1975). The Correspondence of Isaac Newton. New York: The Royal Society of London.