Learn English – Coterminous vs. Conterminous

Yes, conterminous and coterminous both mean "to share a boundary".

According to the entries for co- and con-, below, co- is an Anglicising of con-, which is possibly why Latin purists prefer con-

In this instance co- and con- both mean together or with.

Etymology of co-

in Latin, the form of com- in compounds with stems beginning in vowels and h- and gn- (see com-). Taken in English from 17c. as a living prefix meaning “together, mutually, in common,” and used promiscuously with native words and Latin-derived words not beginning with vowels, sometimes even with words already having it (e.g. co-conspiritor).

Etymology of con-

prefix meaning "together, with," sometimes merely intensive; the form of com- used in Latin before consonants except -b-, -p-, -l-, -m-, or -r-. In native English formations, co- tends to be used where Latin would use con- (e.g. costar).

coöriginal or cooriginal (not comparable)

(philosophy) Existing together ab initio; equiprimordial.  

(geometry, of a line) Originating from the same point in space.

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