Let us return now to our special subject, and examine in a more strictly historical way what has been done hitherto for theoretical Kinematics. The reader need not fear that I shall disturb the dust on old parchments in order to build up from dry dates the foundations of a science. We look now for the beginnings of the idea of our subject, and this delicate material can be taken from the ancient volumes without disturbing the moths.
In earlier times men considered every machine as a separate whole, consisting of parts peculiar to it; they missed entirely or saw but seldom the separate groups of parts which we call mechanisms. A mill was a mill, a stamp a stamp and nothing else, and thus we find the older books describing each machine separately from beginning to end. So for example Ramelli (1588), in speaking of various pumps driven by water-wheels, describes each afresh from the wheel, or even from the water driving it, to the delivery pipe of the pump. The concept "waterwheel" certainly seems tolerably familiar to him, such wheels were continually to be met with, only the idea "pump"—and therefore also the word for it—seems to be absolutely wanting.2 Thought upon any subject has made considerable progress when general identity is seen through the special variety;—this is the first point of divergence between popular and scientific modes of thinking. Leupold (1724) seems to be the first writer who separates single mechanisms from machines, but he examines these for their own sakes, and only accidentally in reference to their manifold applications. The idea was certainly not yet very much developed. This is explained by the fact that so far machinery had not been formed into a separate subject of study, but was included, generally, under physics in its wider sense. So soon, however, as the first Polytechnic School was founded, in Paris in 1794, we see the separation between the study of mechanisms and the general study of machinery, for which the way had thus been prepared, systematically carried out.
The completion of this separation connects itself with the honoured names of Monge and Carnot. The new line of study appeared first as a subdivision of descriptive geometry, from which it has only by degrees released itself. It fell to Hâchette to give instruction in it, and he, working upon outlines given by Monge, constructed (1806) a programme of which Lanz and
