Converge
Meaning
to tend to meet in a point or line; incline toward each other, as lines that are not parallel.
to tend to a common result, conclusion, etc.

Origin
1685–95; < LL convergere to incline together.

Etymology
1691, from L.L. convergere "to incline together" from com- "together" + vergere "to bend"

Diverge
Meaning
to move, lie, or extend in different directions from a common point; branch off.
to differ in opinion, character, form, etc.; deviate.

Origin
1655–65; ML dīvergere, equiv. to L dī- + vergere to incline

Etymology
1665, from L. divergere "go in different directions," from dis- "apart" + vergere "to bend, turn". Originally a term in optics; the fig. sense is 19c.