Why variables in directly proportinality are multipiled

Newton's law actually said that FORCE was directly proportional to RATE OF CHANGE OF MOMENTUM.
i.e. F=k mv/t.
We extrapolate to F=k ma by using a=v/t and this usually assumes that the mass remains constant. Mass may not be considered constant when approaching light speeds, or perhaps when a rocket loses mass by burning fuel.

The more general answer is that if x is directly proportional both to a and to b, then holding a constant, varying b produces a straight line graph for x against b (and vice versa). This would not be the case if a and b were added, only if a and b were multiplied.

@fresco I think you are right I read something like this in high school. But now I've forgotten, Can you refer me any text.

Try
http://en.wikipedia.org/wiki/Momentum

In reality it was

F=d/dt(mv)

which becomes

F=md/dt(v)+vd/dt(m)

and if the mass is constant d/dt(m)=0

then

F=md/dt(v)

and as d/dt(v)=a

this becomes

F=ma

the rocket ship or relativistic force cases would be those conditions where d/dt(m)<>0

Remember that Newton (Leibniz) invented (discovered?) the calculus necessary to differentiate momentum (mv)

Rap

Yes. I deliberately used "rate of change" rather than the notation of calculus for pedagogical reasons. The request for a further reference, which I gave, allowed for that further analysis. Note that the focus for this respondent was "direct proportion" rather than Newton per se