1. The Age of Euler

2. The Bernoullis Images from MacTutor 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

3. Leonard Euler Images from MacTutor

4. Joseph Louis Lagrange Guillaume François l’Hôpital Maria Gaetana Agnesi Jean Le Rond d’Alembert Bishop George Berkeley Colin Maclaurin Thomas Simpson

5. 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)

6. 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 5 th degree and above Lagrange – Also attempts to find a general solution for the n th degree eq. Number theory Euler – Gives his proof of Fermat’s Last Theorem for n = 3.