(? need introduction here ?)

Newton's First Law -- The Law of Inertia
      Newton's first law of motion is based on Galileo's observation that bodies which roll down one inclined plane, and then up another, tend to reach the same height they originally had. While the bodies roll down the first plane, they accelerate at a constant rate; and while they roll up the second plane, they decelerate at a constant rate; and the two rates are proportional to the relative slopes of the planes, being greater the steeper the slope, and lesser the shallower the slope.
      In the extreme case where the planes have no slope at all, and are absolutely horizontal, the acceleration and deceleration should be equal, and equal to zero; that is, bodies moving along horizontal planes should move with constant speed. Of course friction or other forces always prevent this from happening, but by Newton's time it seemed reasonably obvious that in an ideal, theoretical situation, bodies might indeed move with constant speed, which led him to propose his First Law of Motion:

     At this point, the average reader might be tempted to say "huh?" or some more forceful expression of dismay or discontent, as nowadays Latin is not used much, even in liturgical services; but in Newton's day, all "educated" individuals knew Latin, which served as the universal language of science, transcending the barriers raised by the diverse languages of different countries. Still, it is undoubtedly better, for the purposes of understanding, to provide a rough translation:

     Now, it might be noted that there is no mention in this statement of anything called inertia, and as a result, the name usually given to Newton's First Law of Motion -- the Law of Inertia -- may seem a bit odd. So just what is inertia, and why is its name attached to Newton's First Law?
     In ancient times, it was presumed that things had a natural desire to be in their "natural" place. Any effort to move them from that place required a force, larger for some objects, and smaller for others; and in the absence of such a force, they would tend to remain at rest. The desire of an object to not move, and the measure of how hard it was to move it, was referred to as its inertia. Large things, which were hard to move, had large inertias; while smaller things, which were easy to move, had small inertias. Kepler's discovery of the laws of planetary motion, and Galileo's experimental and theoretical exploration of the laws of Earthly motion destroyed the concept of inertia as a resistance to a change of position, but did not change the fact that objects do resist a change in what they are doing. It is just that what they resist is not a change in their position, but in their motion, and since Newton's First Law is a statement of that tendency for objects to resist a change in their motion, it seems reasonable to call it the Law of Inertia, particularly if paraphrased thusly:

Newton's Second Law -- The Force Law
     Newton's First Law of Motion says that if an object does not have a force acting on it, it will maintain a constant motion. But what if it does have a force acting on it? Then, obviously, it cannot maintain a constant motion, but must be accelerated (or decelerated), by an amount which is given by Newton's Second Law of Motion, also known as the Force Law:

(lots more to follow)

(proceed to inertial / noninertial frames of reference?)