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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 else, besides a solution to cubic equations, was in Cardano's book?**
**(a)** An alegrabic solution to quintic equations, **(b)** A proof of the Pythagorean Theorem. **(c)** A solution to quartic equations. **(d)** A suggested method to depress all complex geometry.

**2. 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.

**3. What did Archimedes manage to prove using Euclid's ideas?**
**(a)** That the square of a diameter is equal to pi. **(b)** That the relationship of area to circumference is really the same as the relationship of radius to diameter. **(c)** That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference. **(d)** That the value of pi is proportional to the area of the circle.

**4. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has three sides whose squares are equal to the area of the triangle. **(b)** When a triangle has a side whose square is the sum of the squares of the two legs. **(c)** When a triangle can be constructed with three unequal sides. **(d)** When a triangle does not have a side which can be considered a hypotenuse.

**5. What did Hippocrates do that advanced mathematical methods?**
**(a)** He created a new ways to disprove theories. **(b)** He proved that mathematics can be applied in a unlogical order. **(c)** He demonstrated that geometry does not have to be based on previous knowledge. **(d)** He built theorems based on sequencially more complex proofs.

## Short Answer Questions

**1.** What did Heron's advances put into historical perspective for Dunham?

**2.** What did British scholars accuse Leibniz of?

**3.** What did Dunham consider as Archimedes's "masterpiece"?

**4.** What great theorem is presented by Dunham in this chapter?

**5.** Which words best describe how solid proofs were developed in Elements?

This section contains 477 words(approx. 2 pages at 300 words per page) |