draws amorphous pictures, quite unrecognisable without assistance, and then writes underneath "This is a man," or "This is a satyr," or "This is a lion," or the like. Hence it happens that the very same geometrical method served Proclus to demonstrate the principles of Aristotelian science, and Descartes to demonstrate his own, though totally distinct from, if not diametrically opposed to them. Yet each was a great geometrician, whom no one could accuse of inability to use the method. What ought to be introduced into natural science is not the method of geometry, but its conclusiveness; which is precisely what can never be done. Still less is it possible in other sciences, in proportion as they are more material and concrete; least of all in ethical science. For this reason, where the reality cannot be used, the name is misused instead; till, just as the title "Master," which Tiberius once refused as too haughty, is given to-day to the humblest man, so the name "demonstration," applied as it is to arguments at best probable, sometimes patently fallacious, has impaired the respect due to truth. Even for mathematics itself Vico apprehends danger from the substitution of analytic for geometrical or synthetic methods. He doubts whether modern mechanics is really a product of analysis; for analysis blunts the inventive faculty or talent, and though infallible in, its results (_opere_) is confused in its processes (_opera_); while the synthetic method is _turn opere cum opera_ infallible. Analysis presents its grounds by inquiring whether the equations of which it is in search happen to be present; it appears to be an art of guessing, a kind of mechanism rather than thought. For similar reasons Vico attached no value, to the more or less mechanical topics and arts of discovery and memory invented by Lulle and Kircher.