This subsection is dedicated to the propositions of Book 1 of "Euclid's Elements".

- Proposition: 1.01: Constructing an Equilateral Triangle
- Proposition: 1.02: Constructing a Segment Equal to an Arbitrary Segment
- Proposition: 1.03: Cutting a Segment at a Given Size
- Proposition: 1.04: "Side-Angle-Side" Theorem for the Congruence of Triangle
- Proposition: 1.05: Isosceles Triangles I
- Proposition: 1.06: Isosceles Triagles II
- Proposition: 1.07: Uniqueness of Triangles
- Proposition: 1.08: "Side-Side-Side" Theorem for the Congruence of Triangles
- Proposition: 1.09: Bisecting an Angle
- Proposition: 1.10: Bisecting a Segment
- Proposition: 1.11: Constructing a Perpendicular Segment to a Straight Line From a Given Point On the Straight Line
- Proposition: 1.12: Constructing a Perpendicular Segment to a Straight Line From a Given Point Not On the Straight Line
- Proposition: 1.13: Angles at Intersections of Straight Lines
- Proposition: 1.14: Combining Rays to Straight Lines
- Proposition: 1.15: Opposite Angles on Intersecting Straight Lines
- Proposition: 1.16: The Exterior Angle Is Greater Than Either of the Non-Adjacent Interior Angles
- Proposition: 1.17: The Sum of Two Angles of a Triangle
- Proposition: 1.18: Angles and Sides in a Triangle I
- Proposition: 1.19: Angles and Sides in a Triangle II
- Proposition: 1.20: The Sum of the Lengths of Any Pair of Sides of a Triangle (Triangle Inequality)
- Proposition: 1.21: Triangles within Triangles
- Proposition: 1.22: Construction of Triangles From Arbitrary Segments
- Proposition: 1.23: Constructing an Angle Equal to an Arbitrary Rectilinear Angle
- Proposition: 1.24: Angles and Sides in a Triangle III
- Proposition: 1.25: Angles and Sides in a Triangle IV
- Proposition: 1.26: "Angle-Side-Angle" and "Angle-Angle-Side" Theorems for the Congruence of Triangles
- Proposition: 1.27: Parallel Lines I
- Proposition: 1.28: Parallel Lines II
- Proposition: 1.29: Parallel Lines III
- Proposition: 1.30: Transitivity of Parallel Lines
- Proposition: 1.31: Constructing a Parallel Line from a Line and a Point
- Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle
- Proposition: 1.33: Parallel Equal Segments Determine a Parallelogram
- Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms
- Proposition: 1.35: Parallelograms On the Same Base and On the Same Parallels
- Proposition: 1.36: Parallelograms on Equal Bases and on the Same Parallels
- Proposition: 1.37: Triangles of Equal Area I
- Proposition: 1.38: Triangles of Equal Area II
- Proposition: 1.39: Triangles of Equal Area III
- Proposition: 1.40: Triangles of Equal Area IV
- Proposition: 1.41: Parallelograms and Triagles
- Proposition: 1.42: Construction of Parallelograms I
- Proposition: 1.43: Complementary Segments of Parallelograms
- Proposition: 1.44: Construction of Parallelograms II
- Proposition: 1.45: Construction of Parallelograms III
- Proposition: 1.46: Construction of a Square on a Given Segment
- Proposition: 1.47: Pythagorean Theorem
- Proposition: 1.48: The Converse of the Pythagorean Theorem