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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. What allowed Cardano to justify publishing his book?**
**(a)** He was dead, and the book was really published by his student. **(b)** He was punished as a heretic, **(c)** He found del Ferro's orgininal solution to the cubic. **(d)** He found Fior's documents which spoke against Tartaglia.

**2. In Elements, how many postulates must be accepted as given?**
**(a)** Twenty-two. **(b)** Eighteen. **(c)** Five. **(d)** Twelve,

**3. Who acted as the gate keepers of knowledge?**
**(a)** Greek tradesman. **(b)** Roman emporers. **(c)** Greek philosophers. **(d)** Arabian scholars.

**4. What provided most of the content in the book Elements?**
**(a)** Hypotheses. **(b)** Notions. **(c)** Postulates. **(d)** Propositions.

**5. What did Heron's advances put into historical perspective for Dunham?**
**(a)** A change in learning foundations in the ancient scholarly universities. **(b)** A shift in information flow that ignored socioeconomic order. **(c)** A change in political theory across the globe. **(d)** A shift in learning across continents.

## Short Answer Questions

**1.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

**2.** How did Archimedes arrive at a number value for pi?

**3.** Which of the following was NOT one of the basic definitions in Elements?

**4.** What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

**5.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

## Short Essay Questions

**1.** Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

**2.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

**3.** Explain what Neils Abel proved.

**4.** What did Dunham describe in the epilogue of the chapter?

**5.** Describe Lindeman's work on the square of a circle, and state what he discovered.

**6.** Describe who was Archimedes and how Dunham described his character.

**7.** Describe Euclid's postulates and notions in how they were important in constructing his proofs.

**8.** Explain some puzzles suggested by Euclid's theories.

**9.** Who was Luca Pacioli, and what controversy was sparked over his writings?

**10.** How many definitions were in Euclid's book? List some of the definitions he included.

This section contains 878 words(approx. 3 pages at 300 words per page) |