Definitions, and the only rule of counterpoint...

This is the only background information Fux expects.

Intervals

Perfect consonances: Unison, fifth, and octave.

Imperfect consonances: Six and third.

Dissonances: Second, fourth, diminished fifth, tritone, and seventh.

I have a question: What's a tritone, if neither a fourth nor a diminished fifth?

Motion

"Direct motion results when two or more parts ascend or descend in the same direction by step or skip."

"Contrary motion results when one part ascends by step or skip and the other descends-- or vice versa."

"Oblique motion results when one part moves by step or skip while the other remains stationary."

The four rules of counterpoint

1. From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion.
2. From a perfect consonance to an imperfect consonance one may proceed in any of the three motions.
3. From an imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion.
4. From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions.

It seems to me the four rules are a roundabout way of saying one thing: never use direct motion to enter a perfect consonance.

It is necessary for you to know that in earlier times, instead of our modern notes, dots or points were used. Thus one used to call a composition in which point was set against or counter to point, counterpoint; this usage is still followed today, even though the form of the notes has been changed. By the term counterpoint therefore is understood a composition which is written strictly according to technical rules.