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|\((1)\)||$:$||\(\ds \forall A, B \in P: \exists l \in L:\)||\(\ds A, B \in l \)|
|\((2)\)||$:$||\(\ds \forall l \in L: \exists A, B \in P:\)||\(\ds A, B \in l \land A \ne B \)|
The elements of $P$ are referred to as points.
The elements of $L$ are referred to as lines.
- $(1): \quad$ For every two points $A, B \in P$ there is a line $l \in L$ such that $A, B \in l$
- $(2): \quad$ Every line has at least two points
- Results about abstract geometries can be found here.