are line-oriented: one line is one statement.
Simple Statements
refer to only one wholesome object which may or may not consist of some number of atomic objects like points.
For example, the following statement:
$$A$$refers to a single point, \(A\).
The statement:
$$Ln(A, B)$$refers to a straight line passing through two points, \(A\) and \(B\).
The statement:
$$Cir(O, r)$$refers to a circle with a center located at the point \(O\) and a radius \(r\).
The statement:
$$\angle ABC$$refers to an angle.
The exact meaning of these statements is explained in Interpretation section.
Compound Statements
refer to two or more wholesome objects at a time. For example, the statement:
$$A, B, C, D$$refers to four points \(A\), \(B\), \(C\) and \(D\).
The statement:
$$A \in Ln(B, C)$$refers to two wholesome objects - a point and a straight line and means "a point \(A\) is on a straight line passing through the points \(B\) and \(C\)".
The statement:
$$Ln(A, B) \cap Ln(C, D) = E$$refers to three wholesome objects - two straight lines and a point and means "a straight line passing through the points \(A\) and \(B\) and a straight line passing through the points \(C\) and \(D\) intersect at a point \(E\)".
The statement:
$$Cir(O_1, R) \cap Cir(O_2, r) = K, L$$refers to four wholesome objects - two circles and two points and means "a circle with a center at a point \(O_1\) and a radius \(R\) intersects with a circle with a center at a point \(O_2\) and a radius \(r\) at the points \(K\) and \(L\)".
The statement:
$$Ln(A, B) \bot Ln(C, D)$$refers to two wholesome objects - two straight lines and means "a straight line passing through the points \(A\) and \(B\) is perpendicular to a straight line passing through the points \(C\) and \(D\)".
And so on. Compound statements of arbitrary complexity can be built up as long as they make geometric sense.
\(\blacksquare\)