End Book_1_prop_1_circle_circle.
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. *)
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(** * Proposition 3 Given two unequal straight lines, to cut off from the greater a straight line equal to the less. *)
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Lemma prop_3 : forall A B C1 C2, Le C1 C2 A B -> exists E, Bet A E B /\ Cong C1 C2 A E.