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This quiz consists of 5 multiple choice and 5 short answer questions through The Bernoullis and the Harmonic Series.

## Multiple Choice Questions

**1. What was the bases of Hippocrates's proof ?**
**(a)** Properties of points and lines. **(b)** Properties of triangles and semicircles. **(c)** Properties of area to volume measurements. **(d)** Properties of squares and cubes.

**2. As described by Archimedes, what is always true about he diameter of the circle?**
**(a)** It's always proportional to its circumference. **(b)** It's equal to pi. **(c)** It's never proportional to its circumference. **(d)** It's equal to the square of the radius.

**3. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?**
**(a)** The sum diverges to infinity. **(b)** The sum converges to infinity. **(c)** The sum grows ever smaller. **(d)** The sum converges to a finite term.

**4. Dunham showed that Heron's proof could also be used as which of the following?**
**(a)** A proof of Archimedes' number theory. **(b)** A proof of the Pythagorean Theorem. **(c)** A proof of Euclid's number theory **(d)** A proof of Hippocrates' squared areas.

**5. What was Euclid's definition of a prime number?**
**(a)** Numbers which do not, and can not, contain a perfect number. **(b)** Numbers which can only be divided by themselves and 1. **(c)** Numbers which contain an infinite number of composite numbers. **(d)** Numbers which are divisible by 2.

## Short Answer Questions

**1.** Which of the following is an example of a postulate that must be accepted in Elements?

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

**3.** Which mathematician was first to take the challenge to solve cubic equations?

**4.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

**5.** Which of the following is an example of a perfect number?

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