Euclid index

An introduction to Euclid - Propositions of Book 1


Index --- introduction --- definitions --- axioms and postulates --- propositions --- other

ConstructionsProofs
1. Construct an equilateral triangle on a given line
2. Construct a line from a point equal to another line
3. Cut off part of line equal to another line





9. Construct bisection of an angle
10. Construct bisection of a line
11. Construct a right angle at a point on a line
12. Construct a right angles from a point to a line









22. Construct a triangle from three lines
23. Copy an angle on a line at a point







31. Construct a parallel line through a point










42. Construct parallelogram equal to triangle in a given angle

44. Given line, angle and triangle, construct parallelogram
45. Given angle and quadrilateral, construct parallelogram
46. Construct a square on a given straight line




4. Congruent triangles if two sides and included angle are equal
5. Isosceles triangle base angles are equal
6. If triangle base angles are equal, then it's isosceles
7. Only one triangle with given sides on same side of given line
8. Congruent triangles if all three sides are equal




13. Angles on a straight line add up to 180°
14. Angles adding up to 180° make a straight line
15. Opposite angles are equal
16. External angle of triangle greater than either opposite angles
17. Two angles of triangle less than 180°
18. In triangle, greater angle is opposite greater side
19. In triangle, greater side is opposite greater angle
20. In triangle, sum of two sides greater than third
21. Triangle within a triangle, sides are smaller, angle is greater


24. Two triangles, two sides same, angles different
25. Two triangles, two sides same, other side different
26. Congruent triangles if two sides and corresponding angle are equal
27. Alternate angles equal means straight lines parallel
28. Opposite angles equal means straight lines parallel
29. Parallel lines makes angles equal
30. Lines parallel to another line are parallel to each other

32. Angles of a triangle add up to 180°
33. Lines joining ends of equal parallel lines are equal and parallel
34. Parallelograms have the opposite sides and angles equal
35. Parallelograms on the same base and in the same parallels are equal
36. Parallelograms on equal bases and in the same parallels are equal
37. Triangles on same base and in the same parallels are equal
38. Triangles on equal bases and in the same parallels are equal
39. Equal triangles which are on the same base and side are also in the same parallels
40. Equal triangles which are on equal bases and side are also in the same parallels
41. Parallelogram on same base as triangle, in the same parallels, is double the area

43. In a parallelogram, complements of parallelograms about diameter are equal



47. Pythagoras' theorem
48. Inverse of Pythagoras' theorem