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I suspect Isaac newton worked out his laws by calculus. Newton invented calculus and he used calculus to derive the force laws from the Energy law W=-mGM/r. Newton also added a little creativity in adding the Momentum Law , F= dP/dt, a vector.

Newton's law of Gravity needs to be corrected W = -mGM/r + cP = -mGM/r+ cmV

All NEWTON'S force Laws result from the Derivative of Energy.

Force F = XW = [d/dr,DEL][-mGm/r, cP]= [mGm/r2 -cDEL.P, cdP/dr - DEL mGM/r + cDELxP]

F = [vp/r -cp/r cos(P), -cp/r 1P + vp/r 1R + cp/r sin(P) 1RxP]

F = cp/r[ v/c -cos(P), -1P + v/c 1R + sin(P) 1RxP] where cp/r =cp/ct = p/t = mv/t = ma.

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