How would you translate: "quae sunt eadem uni tertio sunt idem inter se" Here "uni tertio" means "one third thing" and not "unite with a third", no?
first of all the syllogism "Quae sunt eadem uni tertio sunt idem inter se” means:"Those things which are equal to a third one are each other equal”.
Please note that in this syllogism the expression “uni tertio” cannot mean “unite with a third”, as you say, simply because “uni “is without any doubt the dative case of the cardinal number “unus”(= one) which agrees with “tertio” which is the dative of the ordinal adjective “tertius”(= third).
In short, “uni tertio” absolutely must be a dative case depending on the nominative neuter plural “eădem”, which as a word of comparison takes the dative case.
Therefore here's the literal translation for “Quae sunt eadem uni tertio sunt idem inter se”:
”Those things that (quae) are (sunt) the same as (eadem) a third one (uni tertio) are (sunt) identical (idem) each other (inter se)”, i.e. :“Those things which are equal to a third one are each other equal”.
Hope all is clear enough, since grammatically “uni tertio” absolutely cannot be anything but a dative case, so that it absolutely cannot mean “unite with a third".