1. How are  following terms connected to Euclid?

Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal..................

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it............................

2. What is Thales' Theorem? Draw a diagram

3. What is the difference between a theorem and a postulate or axiom?

4.Are all geometries Euclidean?  How can the sum of the angles of a 3-sided figure total 270 degrees?

5.Where and when(approximately) did Euclid live?

 6. What famous mathematical textbook is Euclid  the author of?

7.How did Eratosthenes calculate the size of the earth?

8. Who was Hypatia of Alexandria?

9.Why did Columbus assume that he had reached the Indies when he arrived in the Caribbean?

Axioms

Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of axioms.^[6] Near the beginning of the first book of the Elements, Euclid gives five postulates (axioms) for plane geometry, stated in terms of constructions (as translated by Thomas Heath):^[7]

"Let the following be postulated":

1. "To draw a straight line from any point to any point."
2. "To produce [extend] a finite straight line continuously in a straight line."
3. "To describe a circle with any centre and distance [radius]."
4. "That all right angles are equal to one another."
5. The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."
6.  

Although Euclid's statement of the postulates only explicitly asserts the existence of the constructions, they are also taken to be unique.

The Elements also include the following five "common notions":

1. Things that are equal to the same thing are also equal to one another.
2. If equals are added to equals, then the wholes are equal.
3. If equals are subtracted from equals, then the remainders are equal.
4. Things that coincide with one another equal one another.
5. The whole is greater than the part.