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My off-the-cuff quick-and-dirty shot at this (literally too lazy to
pick up Feynman down the hall) follows. Ps and Fs below should have
vector symbols over them; read F_12 as "force of object one on object
two" etc.
start with (only) two objects interacting
N3: F_12 = - F_21
recall N2 and P defns:
F_net = ma = d (mv) / dt = dP / dt
assume net forces are the interacting forces (only)
therefore F_12 = dP_2 / dt and F_21 = dP_1 / dt
substitute back into N3 above:
dP_2 / dt = - dP_1 / dt
regroup, et voila:
dP_1 / dt + dP_2 / dt = 0 = d(P total) / dt
conservation of linear momentum for the two interacting objects
...so conservation of linear momentum seems a direct implication from
N2 and N3 (and definitions which probably ropes N1 into the game as
well). That'd seem to me to make Newton's Laws a consequence of the
conservation of linear momentum (or vice versa).