Simple: I acknowlege Netwons second law of motion as well, and all works out.
Certainly, though he doesnt have a single law, it is more of applying his laws to the scenario you created.
The net force is defined as the sum of all forces acting upon an object, which is how we get z=x+y, assuming we keep our system simple (only taking the gravitation of the two bodies into account.) From here, it is all mathmatics (using Newtons law of universal gravitation to find out values for x and y)
Z=0 if the location of our particle happens to resault in an x value of equal magnitude as the y value, but in an opposite direction.
So, let's model the apple between the earth and moon, using newtons equations.
The scenario to be modeled: earth and moon and apple are in a line, apple is some distance d, from earth and moon, determin acceleration, y, on apple at given distance d.
Assume the moon has distance 5 from earth.
Let d be the distance of the apple to earth, where 5<d<0.
Let y be the net acceleration of the apple towards earth. (Negative meaning towards moon, force is a vector, so a negativ simply denotes opposite direction.)
Using Newtons law of universal gravitation:
If we say Fearth=G*Earth*Apple/d^2
Let G*earth*apple=4
Fearth=4/d^2
Fmoon=G*moon*apple/(5-d)^2
where G*moon*apple=1 (moon's mass is roughly 1/4 of the earth's)
Fmoon=-1/(5-d)^2
(5-d) meaning, the distance of the moon to earth minus the distance of the apple to earth give us the distance of the apple to the moon, -1 because the moon is pulling the apple away from the earth.
Now, we know that Fnet equals the sum of all forces, so assume the two above are the only forces in the system:
Fnet=Fearth+Fmoon
Newtons second law states that Fnet=ma, where y=a, and the mass of apple is 1:
ma=Fearth+Fmoon
my=Fearth+Fmoon
y=(Fearth+Fmoon)/m
y=(Fearth+Fmoon)/1
y=Fearth+Fmoon
y=4/d^2 + -1/(5-d)^2
So we have 3 functions, the acceleration on the apple due to the earth, Fearth (okay thats the force but deviding by the 1 mass of apple keeps the function the same)
the acceleration on the apple due to the moon Fmoon, and the aceleration on the apple due to both, y.
Now punch those into a graphing calculator such as this one:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
And we see that, according to newton, the acceleration of the apple is indeed 0 at one point, because the function y intersects the d-axis (near 3.3)
We can also note that at that value of d, the forces due to the gravity of the earth and the moon have non-zero magnitudes, furthurmore they have equal magnitudes, and are opposite, fullfilling newtons first law; as they are balanced, and causing there to be no acceleration on the apple.
-Andrew