Book I Dependencies

At the bottom of this page will see a dependency chart for the propositions of Book I. Proposition I starts at the bottom of the image in green. The chart is available for anyone to use from: pdf file.

The colored groups refer to the classification of the propositions in the Book: Euclid's Elements Book I, a new rendering.

The three top propositions are:

If in a triangle the square on one of the sides equals the sum of the squares on the remaining two sides of the triangle, then the angle contained by the remaining two sides of the triangle is right. 

In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.

To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle. 

The colored groups are as follows:

Group 1: Equilateral triangles, basic manipulation theorems, and SAS theorem.
Group 2: Isosceles Triangles
Group 3: SSS Theorem
Group 4: Bisection and Perpendicular Theorem  
Group 5: Opposite Angles  
Group 6: Properties of Triangles
Group 7: Parallel Lines
Group 8: Angles of Triangles
Group 9: Parallelogram and Triangle Theorems Related to Areas
Group 10: Area Arithmetic Propositions
Group 11: Pythagoras’ Theorem