COURSE OF SOLID GEOMETRY – ENGLISH – INTRODUCTION
Presentation of the Contents of Each of the Chapters of the Course of Solid Geometry
Basic Elements of Plane Geometry
Points, Lines and Planes
Definitions of Points
Definitions of Lines
Definitions of Planes
Postulates of Euclides
Postulates of Lines and Planes
Determining a Plane
Conclusions on Determining a Plan
Lines and Planes
Intersection of Lines and Planes
Intersections of Planes
Lines and Planes Parallel
Parallelism between Line and Plane
Parallel Plans
Angles between Lines
Perpendicular Lines and Planes
Lines Perpendicular to a Plane
Postulates of Lines and Planes
Determining a Plane
Conclusions on Determining a Plan
Dihedral Angle
Definitions about Dihedral Angle
Theorems about Dihedral Angle
Consequences of Theorems
Trihedral and Polyhedral Solid Angles
Definitions about Solid Angles
Trihedrons and Polyhedrons
Definitions about Trihedrons and Polyhedrons
Properties about Trihedrons and Polyhedrons
Theorems about Trihedrons and Polyhedrons
Corollaries Resulting from Theorems
Equalities of Trihedrons
Cases of Equalities of Trihedrons
Supplementary Trihedrons Construction,
Solid Angles Properties
Review of the Plane Geometry – Polygons
Concave Polygons and Convex Polygons
Regular and Non-Regular Polygons
Important Structures of the Polygons
Plane Geometry – Polygons
Relations between Elements of the Lateral Triangle
Table of Values for Central Angles of the Polygons
Sum of the External Angles of the Polygons
Sum of the Internal Angles of the Polygons
Number of Diagonals
Values of the Angles in a Regular Polygon
Regular Polygons:
Hexagon
Triangle
Dodecahedron
Square
Octagon
Decagon
Pentagon
Heptagon
Nonagon
Undecagon
Final Considerations on Polygons
Prismatic Surfaces and Their Elements
Denomination of Prisms
Parallelepipeds, Right, Oblique, Rectangular
Dimensions of a Rectangular Parallelepipeds and Cubes
Properties of Parallelepipeds
Properties of Right and Oblique Prisms
Volume of Prisms and Parallelepids
Prismatic Surfaces and Their Elements
Denomination of Prisms
Parallelepipeds, Right, Oblique, Rectangular
Dimensions of a Rectangular Parallelepipeds and Cubes
Properties of Parallelepipeds
Properties of Right and Oblique Prisms