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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. Who wrote a treatise that supposed that cubic equations may be impossible to solve?**
**(a)** Gerolamo Cardano. **(b)** Luca Pacioli. **(c)** Scipione del Ferro. **(d)** Niccolo Fontana.

**2. That properties of specific shapes were early Egyptians aware of?**
**(a)** Right triangles. **(b)** Pi and the diameter of a circle. **(c)** Irregular solids. **(d)** Parallelograms.

**3. Who was the first of ancient philosophers to consider why geometric properties existed?**
**(a)** Thales. **(b)** Pythagoras. **(c)** Hippocrates. **(d)** Aristotle.

**4. What did Euclid do in his 48th proposition?**
**(a)** Euclid demonstrated the faults of the Pythagorean Theorem. **(b)** Euclid proved the Pythagorean Theorem. **(c)** Euclid proved the converse of the Pythagorean Theorem. **(d)** Euclid demonstrated how to use the Pythagorean Theorem.

**5. Why did Cardano take an oath to secrecy?**
**(a)** It was the only way to get his book published. **(b)** It was the only way he could become a priest, **(c)** It was to the only way to win the contest with Fior, **(d)** It was the only way to get Tartaglia's solution to cubic equations.

## Short Answer Questions

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

**2.** What did Dunham claim about Archimedes's determination of a number value for pi?

**3.** Where was Archimedes born?

**4.** What was true about Hippocrates's proof?

**5.** Who asked Tartaglia for his solution to cubic equations?

## Short Essay Questions

**1.** Who was Heron, and what is known about him today?

**2.** Explain what Neils Abel proved.

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

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

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

**6.** Describe how Cardano eventually publishes the solution to cubic equations.

**7.** Describe what the Egyptians knew about geometry and triangles before Hippocrates.

**8.** According the Dunham, how did Euclid prove his theory on the infinitude of primes?

**9.** Describe what is quadrature and why it was useful in the time of Hippocrates.

**10.** Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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