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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. How many sides did the pentadecagon have, as presented by Euclid?**
**(a)** Ten. **(b)** Fifteen. **(c)** Twenty. **(d)** Five.

**2. Which of the following was NOT defined by Euclid?**
**(a)** Nominal numbers. **(b)** Whole numbers. **(c)** Even numbers. **(d)** Odd numbers.

**3. What did Gauss set out to prove?**
**(a)** That a circle can have less than 360 degrees. **(b)** That a right angle is always equal to 90 degrees. **(c)** That Euclid's postulate on straight lines was incorrect. **(d)** That the sum of the angles in a triangle is 180 degrees.

**4. Which is one of the common notions presented in Elements?**
**(a)** "The inverse of a line makes a circle." **(b)** "Things with are equal have an inverse that is equal." **(c)** "Points with equal values can be connected with a line of equal value." **(d)** "Things which are equal to the same thing are also equal to each other."

**5. Who was del Ferro's student?**
**(a)** Gerolamo Cardano. **(b)** Niccolo Fontana. **(c)** Luca Pacioli. **(d)** Antonio Fior.

## Short Answer Questions

**1.** Which of the following is true about pi, as described by Dunham.

**2.** In what time period did mathematicians find a solution to cubic equations?

**3.** Who acted as the gate keepers of knowledge?

**4.** What allowed Cardano to justify publishing his book?

**5.** What instruments did the Greeks use to square a shape?

## Short Essay Questions

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

**2.** What was Euclid's definition of composite and perfect numbers?

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

**4.** Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

**5.** 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.

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

**7.** What was already known about circles before Archimedes?

**8.** Describe in two sentences Archimedes's method for determining circular area.

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

**10.** What did Dunham explain about the shift in learning from the West to the East?

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