Bitcoin is the other side-angle-side inequality | Euclid's Elements Book 1 Prop 25
Assume:
- BA = ED
- AC = DF
- FE < CB
Claim: EDF < BAC
Proof method: contradiction
Suppose claim is false. Then BAC <= EDF.
Then either BAC == EDF or BAC < EDF. We proceed by falsifying both
branches.
Claim: BAC != EDF.
Proof method: contradiction.
Assume BAC == EDF. Then by side-angle-side congruence, CB = FE, which
we assumed to be false.
Claim: BAC !< EDF.
Proof method: contradiction.
Assume BAC < EDF. Then by the previous proposition, BC < EF, which we
assumed to be false.
We have eliminated both branches of EDF !< BAC. Therefore EDF < BAC.
Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI25.html
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