1. Point - has position but not magnitude. Practi cally, it is represented by the smallestvisiblemark or dot, but geometrically understood, it occupies no space. The
extremities or ends of lines are points; and when two or more lines cross one another, the places that mark their intersections are also points.
2. Line - has length, without breadth or thickness, and, consequently, a true geometrical line cannot be exhibited; for however finely a line may be drawn, it will always occupy a certain extent of space.
3. Superficies or Surface - has length and breadth, but no thickness. For instance, a shadow gives a very good representation of a superficies: its length and breadth can be measured; but it has no depth or substance. The quantity of space contained in any plane surface is called its area.
4. Plane Surface - a flat surface, which will coincide with a straight line in every direction.
5. Curved Surface - an uneven surface, or such as will not coincide with a straight line in any direction. By the term surface is generally understood the outside of any body or object; as for instance, the exterior of a brick or stone, the boundaries of which are represented by lines, either straight or curved, according to the form of the object. It is assumed that the lines bounding the figure occupy no part of the surface. Those lines and points marked on any body or surface play a symbolic role of the true geometrical lines and points.
6. Solid - anything that has length, breadth and thickness.
7. Line Types:
Straight - a line that lies in the same direction between its extremities, and represents the shorthest distance between its two end points.
Curved - a line that does not lie in a straight direction between its extremities, but it continuously change direction by inflection. There are regular and irregular curves.
Mixed (Compound) - a line that is a composition of both straight and curved lines connected together in any form.
Concave (Convex) - a line that cannot be cut by a straight line in more than two points; the concave (hollow side) is turned towards the straight line, the convex (swelling side) looks away from it (straight line).
8. Parallel Straight Lines - lines that run concurrently and have no inclination and are at an equal distance anywhere along their length. They are of two types:
Straight
Curved
9. Oblique (Converging Lines) - straight lines which will, if continued/extended on the same plane, change the distance between them so as to meet or intersect each other.
10. Plane Figure, Scheme, Diagram - lineal representation of any object on a plane surface. if bound by straight lines, it is called a rectangular (rectilinear) figure; and if by curved lines, it's called a curvilinear figure.
11. Angle - a formation of two lines meeting at a point. The lines forming the angle are called sides; the point where the lines meet is called a vertex or angular point. If the angle is defined by 3 letters, as A-B-C, the middle letter should always denote the vertex or angular point. Another way to describe an angle is using only one letter placed next to the angular point.
12. Angle Measurement - the angle defined by two lines and a vertex is measured by the arc of any circle contained between the two sides/lines forming the angle. The vertex is the center from which the arc is described. As the circumferences of all circles are proportional to their diameters, the arcs of similar sectors also bear the same proportion to their respective circumferences. As a consequence they are proportional to their diameters and to their radii (semi-diameters). Thus, the proportion which the arc of any circle bears to the circumference of that circle, determines the magnitude of the angle. As a result of this, the quantity or magnitude of the angles does not depend on the length of the sides (radii) forming them, but solely upon the number of degrees contained in the arc cut from the circumference of the circle by the opening of these lines. A circle's circumference is divided into 360 equal parts, degrees. Each degree is additionally divided into 60 equal parts, minutes, and each minute is further divided in 60 equal parts, seconds.
13. To be continued...
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