A Latin word for : "to speak without notes"

ex tempore

Explanation:

The English word for "to speak without notes" is Extemporaneous. The origin of the Extemporaneous comes from the mid-17th century Latin word ex tempore. Ex tempore literally means out of time.

Impromptu is a similar word in which means to talk spontaneously without preparation while Extemporaneous involves preperation but the speech is delivered without notes.