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The Age of Euler
The Bernoullis
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Jakob I 1654-1705 Johann I 1667-1748
Nicholaus III 1695-1726 Daniel I 1700-1782 Johann II 1710-1795
Nicholaus I 1662-1716
Nicholaus II
1662-1716
Nicholaus 1623-1708
Jakob II 1759-1789
Johann III 1746-1807
Daniel II 1751-1834
Christoph 1751-1834
Johann Gustave 1751-1834
Leonard Euler
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Images from MacTutor
Joseph Louis Lagrange
Guillaume François l’Hôpital
Maria Gaetana Agnesi
Jean Le Rond d’Alembert Bishop George
BerkeleyColin MaclaurinThomas Simpson
Calculus Texts in the 1700’s
• England (fluxions)
• Charles Hayes – A Treatise of Fluxions
• Simpson – A New Treatise of Fluxions (1737)
• Maclaurin – A Treatise of Fluxions (1742)
• Continental Europe (differentials)
• l’Hôpital – Analysis of Infinitely Small Quantities… (1690)
• Maria Agnesi – Foundations of Analysis for the Use of Italian Youth (1748)
• Euler – Introduction to Analysis of the Infinite (1748), Methods of Differential Calculus (1755), Methods of the Int. C. (1768)
• Lagrange – The Theory of Analytic Functions, containing the principles of the differential calculus, released…quantities (1797)
Algebra and Number Theory
• Systems of linear equations
• Maclaurin – Introduces Cramer’s Rule (before Cramer!) (1730’s)
• Polynomial equations
• Maclaurin – Gives well-organized form for solving polynomial equations through degree 4 and Newton’s numerical approx.
method
• Euler – Gives a fuller treatment and notes that he cannot give any formulas for 5th degree and above
• Lagrange – Also attempts to find a general solution for the nth degree eq.
• Number theory
• Euler – Gives his proof of Fermat’s Last Theorem for n = 3.