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How is Euclid's first common notion related to the equivalence properties of equality?
αʹ. Τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα.
Translation from ( Euclid'S ELEMENTS OF GEOMETRY
The Greek text of J.L. Heiberg (1883-1885) )
1. Things equal to the same thing are also equal to one another.
Algebraicly stated: If a = c and b = c then a= b, a,b,c things that Euclid talks about in his book. (Figures, magnitudes etc)
This relates to the Transitive property of equality that states the exact same thing for the set of Real numbers(superset).
If a = c and b = c then a = b, a,b,c belong to R.
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