A particle is a body (or portion of a body) with negligible dimensions. Its dimensions are negligible if they are sufficiently small in comparison with other distances employed in the particular problem under consideration. The decision as to when some particular quantity is to be considered negligible in comparison with another depends upon the desired, or the possible, accuracy of the reslt or "answer" to the problem. While we speak of exact sciences, no measurement can be known to be truly exact (unless we extend "measurement" to include such a simple act as counting the number of acute angles in an equilateral triangle) and the limits or probable limits of accuracy need to be kept in mind in dealing practically with any problem. In certain astronomical problems the earth may be treated as a particle, while in other problems it may be treated as an infinite mass constituting a uniform slab with an infinite plane surface and finite thickness. In applying the methods of calculus to the study of supposedly continuous bodies, the material within an infinitesimal element of the volume of the body may be considered to constitute a particle.
Through no body and hence no particle (not even a proton) can actually have zero dimensions, and no finite mass can be concentrated at a point and thus provide infinite density, it is often convenient to consider a particle to be located at a point. The point in question may be any point within the particle, since its dimensions are negligible in comparison with all others involved in the problem. All the forces acting upon the particle may then be regarded as having their lines of action passing through a common point, and so they are called concurrent forces.
- Broxon, James W. "Mechanics", Appleton-Century-Crofts, INC., New York, 1956.