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Name: _________________________ | Period: ___________________ |

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

## 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 squares and cubes. **(d)** Properties of area to volume measurements.

**2. Which of the following best describes Cardano's character?**
**(a)** Religious. **(b)** Eccentric. **(c)** Arrogant. **(d)** Flirtacious.

**3. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the volume and surface area of spheres, cones, and cylinders. **(b)** He studied the relationship of sine to cosine. **(c)** He studied the relationship between ratios in triangles. **(d)** He studied the volume to surface area ratios of cubes.

**4. What instruments did the Greeks use to square a shape?**
**(a)** A compass and a ruled straight-edge. **(b)** A small grid. **(c)** A pendulum. **(d)** A sphere and ruler.

**5. Which is one of the common notions presented in Elements?**
**(a)** "Things which are equal to the same thing are also equal to each other." **(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)** "The inverse of a line makes a circle."

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

**7. 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.

**8. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?**
**(a)** Perfect numbers. **(b)** Composite numbers. **(c)** Discrete numbers. **(d)** Even numbers.

**9. Where was Archimedes born?**
**(a)** Sicily. **(b)** Olympia. **(c)** Athens. **(d)** Rome.

**10. In what time period did mathematicians find a solution to cubic equations?**
**(a)** Fifteen century. **(b)** Twentieth century. **(c)** Thirteenth century. **(d)** Seventeeth century.

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

**12. What did Dunham discuss for many pages in this chapter?**
**(a)** Heron's religious beliefs- **(b)** Heron's complicated proof. **(c)** Heron's political tendancy. **(d)** Heron's origins of the universe.

**13. What was true about Heron's theorem as described by Dunham?**
**(a)** It was to determine the volume of a sphere without measuring the circumference. **(b)** It was to find the area of a triangle when only the length of the sides are known. **(c)** It was to solve equations were only two varibles are known. **(d)** It was to determine the area of a circle by measuring a right triangle inside the circle.

**14. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that square roots are irrational numbers. **(b)** Lindeman proved that all numbers are constructable with a compass and ruler. **(c)** Lindeman proved that some numbers are constructable without the use of a compass. **(d)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

**15. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.

## Short Answer Questions

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

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

**3.** What were the proofs in Elements based on?

**4.** In Elements, how many postulates must be accepted as given?

**5.** What was Hippocrates famous for?

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