Debating the Founder of CalculusLeibniz versus Newton

Fluxions

Carolyn Carr

Theories Newtonian mechanics Universal gravitation Calculus Optics and Color theory

Isaac Newton (1643-1727)

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

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

Gottfried Wilhelm Leibnitz (1646-1716)

Founded Calculus in 1673Leibniz’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     11    5    10    10     5    1

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…• L

eibniz writes his Theory (1684), “A new method for Maxima and Minima as well as tangents, which is not restricted by fractional or irrational quantities

De Analysi and LeibnizLetters between Newton and Leibniz:• Binomial Theorem• Series to find the quadratures of a circle

One letter, did contain an anagram of Fluxions: 6a cc d….12vx Which translated to:“Data Auatione quotcunque fluentes quantitates involvente fluxiones invenire, et vice versa”Translation:Having any given equation involving never so many flowing quantities, to find the fluxions and vice versa.”

Fatio de Duillier versus Liebniz

Duillier publishes “A Two-Fold Geometrical Investigation of the Line of

Breifest Descent”

An attack on Leibniz• Newton first inventor, Leibniz second if

that

Leibniz Retaliates: Publishes in Acta• Anonymous, States that Leibniz invented his

theory after Newton

Newton’s Optics and the Review

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

The Review, Reviewed

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?

The Royal Society and Their Findings

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

What they all caused…

Brittan suffers from the 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

Notation Difference

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.

Citations