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I have been learning Newton's laws, and I am confused about the different formulations of the laws, the definitions of the quantities in the modern version, and the definitions of the quantities Newton used.

Nowadays, mass is defined to be an object's resistance to change in acceleration. But that presupposes Newton's second law.

I previously assumed that forces are and were a push or pull, and at Newton's times could be measured and represented as vectors; accelerations are and were second derivatives of displacement vectors. And Newton, with the exact previous definitions, found a relationship between the vector sum of the force vectors on a body and the acceleration vector of the body, and the constant for scalar multiplication is given the name mass, a measure of a body's resistance to change in acceleration.

However, it seems that was not the case, and mass was a pre-existing concept. But how could mass have existed when there was no Newton's second law?

Can someone give a brief explanation of the definitions of the quantities in Newton's laws? And, if the definitions changed overtime, can someone explain that change?

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The American Journal of Physics article The pre-Newtonian Meaning of the Word Weight notes that Newton used the Latin term pondus, which translates as weight, though he clearly meant mass, writing in an unfinished manuscript of the Principia:

By weight I mean the quantity or amount of matter (quantitas seu copia materiae) being moved, apart from considerations of gravity, so long as there is no question of gravitating bodies.

The article notes that:

Nor, until the time of Hooke and Newton, was there any known method of measuring what we now call weight or force of gravity on the mass.

Prior to Newton, Kepler, for example, also used the term weight (pondus) for what we now call mass. Quoting the article:

Kepler, [...] when discussing the causes of periods of planetary motion in his Epitome where he states: “secunda pondus seu copia materiae transportandae” (“the second [cause] is the weight or the amount of matter (copia materiae) to be transported”) and “pondera vero, seu copia materiae in diversis Planetis” (“weights in truth, or the amount of matter in the different planets”) which means that Kepler defined the amount of matter in the planet as its “weight”—which we now call mass.

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    $\begingroup$ Heck, even physicists mix weight and mass in casual conversation, particularly with non-technical folks. $\endgroup$
    – Jon Custer
    Mar 9, 2022 at 14:23

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