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The sight of a line of battle of twenty thousand Isosceles suddenly facing about, and exchanging the sombre black of their bases for the orange of the two sides including their acute angle; the militia of the Equilateral Triangles tricoloured in red, white, and blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square artillerymen rapidly rotating near their vermillion guns; the dashing and flashing of the five-coloured and six-coloured Pentagons and Hexagons careering across the field in their offices of surgeons, geometricians and aides-de-camp all these may well have been sufficient to render credible the famous story how an illustrious Circle, overcome by the artistic beauty of the forces under his command, threw aside his marshal's baton and his royal crown, exclaiming that he henceforth exchanged them for the artist's pencil.
You tell me they acquire some rudiments of geometry, and you think you prove your case; not so, it is mine you prove; you show that far from being able to reason themselves, children are unable to retain the reasoning of others; for if you follow the method of these little geometricians you will see they only retain the exact impression of the figure and the terms of the demonstration.
Yet there have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of being, was only created in Euclid’s geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity.
If forms appear divisible in matter, it is only in considering them by abstraction, after the method, of geometricians; but this divisibility of form exists not in Nature, in which there is neither a point, an atom, nor form perfectly regular; it must therefore be concluded, that the forms of matter are not less indivisible than thought.
This may be shown also from the intimate connection subsisting between each Pleasure and the Working which it perfects: I mean, that the Pleasure proper to any Working increases that Working; for they who work with Pleasure sift all things more closely and carry them out to a greater degree of nicety; for instance, those men become geometricians who take Pleasure in geometry, and they apprehend particular points more completely: in like manner men who are fond of music, or architecture, or anything else, improve each on his own pursuit, because they feel Pleasure in them.
For when the geometricians teach anything, if what they have before taught relates to their present subject, they take that for granted which has been already proved, and explain only what they had not written on before. But the philosophers, whatever subject they have in hand, get together everything that relates to it, notwithstanding they may have dilated on it somewhere else.
It is not only the geometricians of the Republic that find him a good subject: the chemists have bespoke him, after the geometricians have done with him. As the first set have an eye on his Grace's lands, the chemists are not less taken with his buildings.
There were many that studied that Science to the great advantage of mankind: but there is no mention of their Schools; nor was there any Sect of Geometricians; nor did they then passe under the name of Philosophers. Their Morall Philosophy is but a description of their own Passions.
He examined the whole system of the geometricians, and after having constructed his demonstration he scrutinized it from every imaginable angle, he endeavoured to find its weak spot and was never able to discover any means of destroying it, or even of weakening it.
The time would fail me if I attempted to do justice to the memory of all the illustrious men who, during that period, taught or learned wisdom within these ancient walls; geometricians, anatomists, jurists, philologists, metaphysicians, poets: Simpson and Hunter, Millar and Young, Reid and Stewart; Campbell, whose coffin was lately borne to a grave in that renowned transept which contains the dust of Chaucer, of Spenser, and of Dryden; Black, whose discoveries form an era in the history of chemical science; Adam Smith, the greatest of all the masters of political science; James Watt, who perhaps did more than any single man has done, since the New Atlantis of Bacon was written, to accomplish that glorious prophecy.
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