Section Book_1_part_2.
(** For the next 27 propositions, we do not need the 5th axiom of Euclid, nor any continuity axioms, except for Proposition 22, which needs Circle/Circle intersection axiom. *)
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** * Proposition 2 To place at a given point (as an extremity) a straight line equal to a given straight line. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container2"></div> # **)
(** * Proposition 3 Given two unequal straight lines, to cut off from the greater a straight line equal to the less. *)
(** # <div style="width:748px;height:397px;display:block" id="applet_container3"></div> # **)

Lemma prop_3 : forall A B C1 C2, Le C1 C2 A B -> exists E, Bet A E B /\ Cong C1 C2 A E.