THREE:Patterns that are deep, and for castings that require to be parallel or square when finished, are made with the least possible amount of draught. If a pattern is a plain form, that affords [99] facilities for lifting or drawing, it may be drawn without taper if its sides are smooth and well finished. Pieces that are shallow and moulded often should, as a matter of convenience, have as much taper as possible; and as the quantity of draught can be as the depth of a pattern, we frequently see them made with a taper that exceeds one inch to the foot of depth.To understand Descartes aright, we must provisionally disregard the account given in his work on Method of the process by which he arrived at a new theory of the world; for, in truth, there was nothing new about it except the pro388portion in which fragments taken from older systems were selected and recombined. As we have already noticed, there is no such thing as spinning philosophies out of ones own head; and, in the case of Descartes, even the belief that he was so doing came to him from Plato; for, along with Aristotles dogmatic errors, his sound teaching with regard to the derivation of knowledge had fallen into oblivion. The initial doubt of the Discourse on Method and the Meditations is also Platonic; only it is manifested under an individual and subjective, instead of a universal and objective form. But to find the real starting-point of Descartes enquiries we must look for it in his mathematical studies. A geometrician naturally conceives the visible world under the aspect of figured extension; and if he thinks the figures away, nothing will remain but extension as the ultimate material out of which all determinate bodies are shaped. Such was the result reached by Plato in his Timaeus. He identified matter with space, viewing this as the receptacle for his eternal and self-existent Ideas, or rather the plastic medium on which their images are impressed. The simplest spatial elements are triangles; accordingly it is with these that he constructs his solid bodies. The theory of triangular elements was probably suggested by Atomism; it is, in fact, a compromise between the purely mathematical and the materialistic methods. Like all Platos fancies, this theory of matter was attacked with such convincing arguments by Aristotle that, so long as his physics remained in the ascendent, it did not find a single supporter; although, as we saw in the last chapter, Plotinus very nearly worked his way back to it from the Peripatetic definition. Even now, at the moment of Aristotles fall, it might have failed to attract attention, had not the conditions under which it first arose been almost exactly repeated. Geometrical demonstration had again become the type of all reasoning; there was again a sceptical spirit abroad, forcing men to fall back on the most elementary and universal con389ceptions; an atomistic materialism again threatened to claim at least the whole field of physical enquiry for its own. That Descartes followed the Timaeus in identifying matter with extension cannot be doubted; especially when we see that he adopts Platos analysis of body into elementary triangles; but the theory agreed so well with his intellectual predispositions that he may easily have imagined it to be a necessary deduction from his own priori ideas. Moreover, after the first two steps, he parts company with Plato, and gives himself up, so far as his rejection of a vacuum will permit, to the mechanical physics of Democritus. Much praise has recently been bestowed on his attempt to interpret all physical phenomena in terms of matter and motion, and to deduce them from the unaided operation of natural causes; but this is no more than had been done by the early Greek thinkers, from whom, we may observe, his hypothesis of an initial vortex was also derived. His cosmogony is better than theirs, only in so far as it is adapted to scientific discoveries in astronomy and physiology not made by Descartes himself; for where his conjectures go beyond these they are entirely at fault.
