Quoting Leibniz, on types of geometry

a little Leibniz and I do mean 'a little'... I found this an interesting and nicely put way of examining the early geometers.. and linking them for later research.

Quote:

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Since theorems serve only to abbreviate or guide the solution of problems and since all theory should assist practise, all we need to do in order to judge the variety of kinds of geometry is to consider its problems.

The problems of geometery are about straight lines or curves, and presuppose only the magnitude of some lines or figures, straight or curved. To the latter sort belong the problems of finding centers of gravity, and consequently, a good many problems of mechanics.

Thus we may say that there are two kinds of geometry, an Apollonian and an Archimedian; the first was revived by Viète and Descartes, the second by Galileo and Cavalieri.

From a 1951 version of 'Leibniz' selections, Ch 1, pg 5. : cited there from 'General Geometry and the Method of Universals, (1674)

some neat links:
six species of information architect

oh what a cool blog! --> Space from the inside, and outside at A Kind of Bastard Reasoning. Just read the top header and you'll know why I am reeling with curiosity and awe that this exists in the blogosphere!