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A Calculus Collection - Leibniz

Selections from the 1684 volume of "Acta Eruditorum."

Leibniz's paper comprises pp.
467-473 and Plate 12.  This was the first publication of the rules for finding a derivative.

The symbol for equality
(=) was not in common usage at that time.  In the following rules Leibniz used the Latin abbreviation
"œqu"  for "aequales" meaning the modern (=) symbol and (--) for subtraction.  Look for . . .

These images and links are taken from his original publication:

  The Derivative
  Button Addition and Subtraction

Addition Subtraction Rules


Multiplication Rule

  Button  Division

 Division Rule

Full Page View
  Plate 12
  Page 467   Note the article is simply signed "GGL."

Letter from Leibniz to James Bernoulli
  ButtonLeibniz and Geometry (1703)

L'Hospital on Leibniz
  Button L'Hospital on Leibniz:

"I must here in justice own, (as Mr. Leibnitz (sic) himself has done in Journal des Scavans for August, 1694) that the learned Sir Isaac Newton likewise discovered something like the Calculus Differentialis,
as appears by his excellent Principia, published first in the year 1687 which almost wholly depends upon the use of the said Calculus.

But the method of Mr. Leibnitz's is much more easy and expeditious, on account of the notation he uses, not to mention the wonderful assistance it affords on many occasions."


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Marquis de l'Hôspital
(1661 - 1704)

Johann van Waveren Hudde
(1628 - 1704)

Starting with the study of tangents to curves, all of the men represented on this web page made significant contributions to the initial formulation of what today we call  The Calculus.

See the Acta Eruditorum of 1697.


Galileo Galilei

Descartes stamp
René Descartes
(1596 - 1650)

Pierre de Fermat
(1601 - 1665)

Blaise Pascal
(1623 - 1662)

(1646 - 1716)

Ja Bernoulli
Jacob Bernoulli
(1654 - 1705)
Editor of  Acta Eruditorum

Leonhard Euler
(1707 - 1783)

The Acta Eruditorum images are reproduced by permission of The Huntington Library, San Marino, CA.  Students of mathematics are most grateful for the opportunity to view original  sources.