1. Euclid zVery little is known about his life zProfessor at the university of Alexandria z“There is no royal road to geometry”

2. Euclid’s Elements zNo work, except the Bible has been more widely used zOver 1000 editions since first printed in 1482 zNo copy of Euclid’s Elements has been found that dates to the author’s time zFirst complete English translation, 1570

3. Euclid’s Elements zA highly successful compilation and systematic arrangement of works of other writers zThe work is composed of 13 books with a total of 465 propositions zContrary to widespread impressions, it is not devoted to geometry alone, but contains much number theory and elementary (geometric) algebra.

4. Euclid’s Elements zBook I - Definitions, Pythagorean Theorem zBook II - Geometric algebra zBook III - Circles, chords, secants, tangents and measurement of associated angles

5. Euclid’s Elements zBook IV - Construction of regular polygons zBook V - Eudoxus’ theory of proportion zBook VI - Theory of proportion to plane geometry

6. Euclid’s Elements zBooks VII,VIII,IX - Elementary number theory zBook X - Irrationals zBooks XI,XII,XIII - Solid geometry

7. Proposition I-6 If in a triangle two angles are equal to one another, then the opposite sides are also equal.

8. Proposition II-1 If there are two straight lines, and one of them is cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by the uncut straight line and each of the segments.

9. Proposition II-11 To divide a given straight line into two parts so that the rectangle contained by the whole and one of the parts is equal in area to the square on the other part.

10. Proposition III-16 The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle, and into the space between the straight line and the circumference another straight line cannot be interposed.

11. Proposition IV-10 How to construct an isosceles triangle with each base angle equal to two times the vertex angle.

12. Construction of the Regular Pentagon 1. Take an arbitrary line segment; let a be its length 2. Construct a line segment of length 3. Construct the isosceles triangle ABC with sides x,a and a. 4. Circumscribe a circle about the triangle 5. Complete the pentagon

13. Proposition VII-31 Any composite number is measured by some prime number.

14. Proposition VII-32 Any number is either prime or measured by some prime.