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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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.