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Updated: May 15, 2025
I believe that able geometricians will scarce be troubled by the objections of Joseph Scaliger against Archimedes, or by those of Mr. Hobbes against Euclid; but that is because they have fully understood and are sure of the proofs. Nevertheless it is sometimes well to show oneself ready to examine certain objections.
By this characteristic we recognize the 'logarithmic spiral. Geometricians give this name to the curve which intersects obliquely, at angles of unvarying value, all the straight lines or 'radii vectores' radiating from a centre called the 'Pole. The Epeira's construction, therefore, is a series of chords joining the intersections of a logarithmic spiral with a series of radii.
But what has been the Utility of those Schools? what Science is there at this day acquired by their Readings and Disputings? That wee have of Geometry, which is the Mother of all Naturall Science, wee are not indebted for it to the Schools. Plato that was the best Philosopher of the Greeks, forbad entrance into his Schoole, to all that were not already in some measure Geometricians.
I had a little studyed, being young, of the parts of Philosophy, Logick, and of the Mathematicks, the Analysis of the Geometricians, and Algebra: Three arts or sciences which seem'd to contribute somewhat conducing to my designe: But examining them, I observ'd, That as for Logick, its Sylogisms, and the greatest part of its other Rules, serve rather to expound to another the things they know, or even as Lullies art, to speak with judgment of the things we are ignorant of, then to learn them.
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