Quicquid premit vel trahit alterum, tantundem ab eo premitur vel trahitur ... Si corpus aliquod in corpus aliud impingens motum ejus vi suâ quomodocunque mutaverit, idem quoque vicissim in motu proprio eandem mutationem in partem contrariam vi alterius (ob æqualitatem pressionis, mutuæ) subibit ... Obtinet etiam hæc Lex in attractionibus. NEWTON, _Princip._ ad init. {{171}} BOOK III. THE PHILOSOPHY OF THE MECHANICAL SCIENCES. CHAPTER I. OF THE MECHANICAL SCIENCES. IN the History of the Sciences, that class of which we here speak occupies a conspicuous and important place; coming into notice immediately after those parts of Astronomy which require for their cultivation merely the ideas of space, time, motion, and number. It appears from our History, that certain truths concerning the _equilibrium_ of bodies were established by Archimedes;--that, after a long interval of inactivity, his principles were extended and pursued further in modern times:--and that to these doctrines concerning equilibrium and the forces which produce it, (which constitute the science _Statics_,) were added many other doctrines concerning the _motions_ of bodies, considered also as produced by forces, and thus the science of _Dynamics_ was produced. The assemblage of these sciences composes the province of _Mechanics_. Moreover, philosophers have laboured to make out the laws of the equilibrium of _fluid_ as well as solid bodies; and hence has arisen the science of _Hydrostatics_. And the doctrines of Mechanics have been found to have a most remarkable bearing upon the motions of the heavenly bodies; with reference to which, indeed, they were at first principally studied. The explanation of those cosmical facts by means of mechanical {172} principles and their consequences, forms the science of _Physical Astronomy_. These are the principal examples of mechanical science; although some other portions of Physics, as Magnetism and Electrodynamics, introduce mechanical doctrines very largely into their speculations. Now in all these sciences we have to consider _Forces_. In all mechanical reasonings forces enter, either as producing motion, or as prevented from doing so by other forces. Thus force, in its most general sense, is the _cause_ of motion, or of tendency to motion; and in order to discover the principles on which the mechanical sciences truly rest, we must examine the nature and origin of our knowledge of Causes. In these sciences, however, we have not to deal with Cause in its more general acceptation, in which it applies to all kinds of agency, material or immaterial;--to the influence of thought and will, as well as of bodily pressure and attractive force. Our business at present is only with such causes as immediately operate upon matter. We shall nevertheless, in the first place, consider the nature of Cause in its most general form; and afterwards narrow our speculations so as to direct them specially to the mechanical sciences.