Exercise 2. Describe two aspects of the work of Diophantus that marked a difference in conception of number/arithmetic/algebra/geometry from that of Euclid.

Exercise 3. (a) The astronomer Regiomantus in the 15-th century planned on translating Diophantus' Arithmetic. What is the generally accepted reason he did not carry this out? (b) The work of Diophantus then appears in the book Algebra by Bombelli. Which number system is Bombelli credited with being one of the first to use? (c) Fermat learned Diophantus' methods from a book by Bachet. The duplication formula of Bachet is an example of what method?

Exercise 4. (a) Explain the relevance of Vieta's formulas for the method of the tangent and the secant. (b) Vieta is regarded as a leading exponent of what algebraic innovation? Exercise 5. (a) Along with Descartes, Fermat is considered a pioneer of what subject? (b) Describe the principle behind Fermat's method of infinite descent.