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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. Who was the author of the book Elements?**
**(a)** Euclid. **(b)** Einstein. **(c)** Lindemann. **(d)** Hippocrates.

**2. Which city was the center of thinking and learning in Third century BC?**
**(a)** Athens. **(b)** Alexandria. **(c)** Rome. **(d)** Olympia.

**3. What does the Pythagorean Theorem state?**
**(a)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(b)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse. **(c)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(d)** For any right triangle the diagonal side is equal to the sum of the legs.

**4. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?**
**(a)** The area of a triangle is one half the base times the height. **(b)** Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference. **(c)** Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr². **(d)** Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

**5. What was true about Hippocrates's proof?**
**(a)** It was useful for circles. **(b)** It was fairly easy and simple. **(c)** The proof was exceedingly difficult and not understood at the time. **(d)** The proof was easy if their was advanced technology available.

## Short Answer Questions

**1.** What did Newton's calculus involve?

**2.** In the Bernoulli's time, what was the current definition of a series?

**3.** Who else, besides Newton, independently discovered a calculus method?

**4.** Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

**5.** Who was Eratosthanes?

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