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Name: _________________________ | Period: ___________________ |

This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. Which of the following was NOT one of Gauss' discoveries?**
**(a)** "Non-euclidean" geometry. **(b)** That angles in a triangles can not add up to more than 180 degrees. **(c)** That under Euclid's definition parallel lines can intersect. **(d)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

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

**3. In Elements, how many postulates must be accepted as given?**
**(a)** Twelve, **(b)** Eighteen. **(c)** Twenty-two. **(d)** Five.

**4. What did Dunham consider extraordinary about the Elements?**
**(a)** How geometric proofs were presented. **(b)** The content was totally unique. **(c)** The content was not based on previous authors' work. **(d)** How Hippocrates ordered the book.

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

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

**7. Where was Neil's Abel from?**
**(a)** Norway. **(b)** Finland. **(c)** Ireland. **(d)** Great Britian,

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

**9. What is a "depressed cubic"?**
**(a)** A method to simplify measuring complex geometric forms. **(b)** A method to logically square all the factors in a cubic equation. **(c)** A method to solve equations with two variables. **(d)** A method to simpify the x squared value in a cubic equation.

**10. What was the title of Cardano's book which contained the solution to the cubic?**
**(a)** La Magnifica. **(b)** Elements. **(c)** Tarsisia. **(d)** Ars Magna.

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

**12. What did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The ability to find square roots. **(b)** The concept of providing a logical proof. **(c)** The concept of constructing useful mathematics. **(d)** The ability to measure angles.

**13. How many definitions were stated in Elements?**
**(a)** Five. **(b)** Twenty-three. **(c)** Eighteen. **(d)** Thirty.

**14. Who was Eratosthanes?**
**(a)** He was a teacher and philosopher. **(b)** He was a mathematician, and leading doctor. **(c)** He was the first to study political sciences. **(d)** He was the chief librarian, and a mathematician.

**15. What allowed Cardano to justify publishing his book?**
**(a)** He found Fior's documents which spoke against Tartaglia. **(b)** He was dead, and the book was really published by his student. **(c)** He found del Ferro's orgininal solution to the cubic. **(d)** He was punished as a heretic,

## Short Answer Questions

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

**2.** Who was the first of ancient philosophers to consider why geometric properties existed?

**3.** Dunham showed that Heron's proof could also be used as which of the following?

**4.** In general, what did Euclid's number theory describe?

**5.** Which of the following is false about the modern implications of Euclid's number theory?

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