Katz 13.2.1: Simpson's 1737 derivation of the rule
using Roger Cotes' 1716 proof. (pp.561-562)
Katz 13.2.2: MacLaurin's 1742 analytic derivation of part of the Fundamental
Theorem of Calculus for
.
(p.564)
Dunham Chap. 9: Great Theorem and Proof: Euler's 1734 Proof that
.
Katz 13.2.5: Euler's derivation of the quotient rule for derivatives. (p.571)
Courant & Robbins: Proof that
is irrational. (Class notes)
Katz 14.1.2: DeMoivre's Problem III and Solution from the 1718 Doctrine of Chances. (p.601)
Dunham Chap. 10: Great Theorem and Proof: Euler's 1732 refutation of Fermat's conjecture (4 theorems). [Preliminary Theorems A, B, C can be collapsed into one general result.]
Euler's 1735 solution to the Königsberg Bridge Problem. (Class notes)
Dunham Chap. 11: Great Theorem and Proof: Cantor's 1891 "diagonal" proof that
is uncountable. Def of denumerable (countable); Proof that
is denumerable (countable) (pp.251-258).
Dunham Chap. 12: Great Theorem and Proof: Cantor's 1891 proof that the cardinality of any set is strictly less than the cardinality of its set of subsets (its power set)