Yesterday I encountered this passage in a book (The Notation of Western Music, by Richard Rastall), and, well...
To the dot of division, two more types of dot were added in the early fourteenth century.
1. The 'dot of addition' (punctum additionis). In duple mensuration, a dot after a note adds half the length of the note to its duration: e.g. a dotted S lasts for the duration of one-and-a-half Ss. 2. The 'dot of syncopation' (punctum demonstrationis - the dot which points out). It is impossible to give rules for the use of this dot, or to tell a student what to look for: but (i) if a dot cannot be read as a normal dot of division or addition, and it is not a blemish on the paper or a worm-hole, then it must be a dot of syncopation or a scribal error; and (ii) the dot of syncopation is really a misplaced dot of division - that is, a dot of division that forces a perfection to start in the 'wrong' place.
amused