Basic Euclid's Geometry

Euclid's geometry is study of geometrical figures and solid shapes. In general, basic Euclid's geometry is the study of figure constructed by a straight edge and a pair of compasses. A straight edge is used to construct a straight line, while a pair of compasses is used to construct a circular arc.

Elements of Euclid's Geometry

Euclid's Space

Euclid's space is a geometrical space used as an abstraction of the physical space in constructing geometrical figures and solid shapes. Euclid's space is indefinitely extended in all directions as in the physical world. The extension of Euclid's space has three dimensions, namely length, breadth, and thickness. Geometrical elements in Euclid's space may have maximum three extensions.

Euclid's Point

A Euclid's point is only used to specify a geometrical position without any extension in Euclid's Space. A Euclid's point is therefore has no extension, that is neither length, breadth, nor thickness.

Euclid's Line

A Euclid's line can be considered as the locus of a smoothly moving point object in one extension to form a path in Euclid's space. A point object moves in two opposite direction one extension to form a geometrical line path. In other words, a line is a set of points in Euclid's Space with one dimension. A Euclid's line is therefore a breadthless length of one extension. The extremities of a lines is points.

Euclid's Surface

A Euclid's surface can be considered as the locus of a smoothly moving point object in two extensions to form an area in Euclid's space. A point object moves first in one extension to form a line, and moves in another extension to form a geometrical surface area. In other words, a surface is a set of points in Euclid's Space with two dimensions. A Euclid's surface is therefore has extensions of length and breadth, but no thickness. The limits of surfaces are lines.

Euclid's Solid

A Euclid's solid can be considered as the locus of a smoothly moving point object in three extensions to form a volume in Euclid's space. A point object moves first in one extension to form a line, then moves in second extension to form a surface, and finally moves in the third extension to form a geometrical solid volume. In other words, a solid is a set of points in Euclid's Space with three dimensions. A Euclid's solid is therefore has extensions of length, breadth, and thickness. The boundaries of solids are surfaces. A Euclid's solid is a geometrical solid used to abstract the space occupied by a physical solid.

The Point

The term, point, is not defined formally in Euclid's geometry. However, a point is a geometrical point object used to specify a geometrical position in Euclid's space. Virtually, a point is usually considered as an infinitely tiny sphere with length, breadth, and thickness approaching zero, and center located at the specified position in Euclid's space. The location of a point in Euclid's space is usually represented by either a dot or a cross. Usually, a uppercase letter is used to name the position of a point in Euclid's space. Any point in Euclid's space can be taken as the reference of origin. The position of a point is then determined by its direction and distance with reference to any known point. The distance of a point is the length of the shortest line drawn between two points in Euclid's space. The direction of a point with respect to a reference point is the direction of the shortest line drawn between two points in Euclid's space.

The Line

The term, line, is not defined formally in Euclid's geometry. However, a line can be understood as the path, or locus, of a moving point object in Euclid's space. Virtually, a line can be described by placing geometrical point objects along the length only. The collection of points along a line in Euclid's space is usually represented by a thick line.

Sources And References

• https://en.wikipedia.org/wiki/Euclidean_geometry
• Chauvenet's Treatise on Elementary Geometry
• Foundations of Euclidean and Non-Euclidean Geometry
• An elementary Treatise on Plane and Solid Geometry
• Geometry Demystified A Self-Teaching Guide
• https://en.wikipedia.org/wiki/Straightedge_and_compass_construction
• https://en.wikipedia.org/wiki/Euclidean_space
• https://simple.wikipedia.org/wiki/Point_(geometry)
• https://simple.wikipedia.org/wiki/Line
• https://simple.wikipedia.org/wiki/Plane_(mathematics)
• https://mathworld.wolfram.com/EuclideanSpace.html
• https://www.cuemath.com/geometry/euclids-geometry/