Date of publication: 2017-08-27 17:32
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He was clear, in his own mind at least, that the model had hardly be given a demonstration in the sense in which one could give in geometry the sort of demonstration given by Euclid. He wrote to Mersenne:
I am writing a Paper on Rene Descartes and i just was wondering how accurate everything is because on othe cites it says that he attened the Jesuite college at the age of 6 not 8.
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Descartes’ own contributions to physics, both in optics and mechanics, were considerable. In mechanics, his work was definitely blocked by his failure to even think that a notion of mass was essential to any mechanics that was to move from kinematics to dynamics. In optics, his mechanistic ideas clearly interfered with his attempts to understand colors. These problems, in both mechanics and optics, awaited Newton for their solution.
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As for the analytic method, Descartes was to use the first of the treatises appended to the Discourse on Method to illustrate the power of this method. This was the treatise on Geometry. This work in mathematics is remarkable, and it too was to revolutionize the way people thought about both algebra and geometry.
Descartes’ idea of God will be discussed momentarily, but let’s consider his claim that the mind is better known than the body. This is the main point of the wax example found in the Second Meditation. Here, Descartes pauses from his methodological doubt to examine a particular piece of wax fresh from the honeycomb:
From what has already been said we have established that all the bodies in the universe are composed of one and the same matter, which is divisible into indefinitely many parts, and is in fact divided into a large number of parts which move in different directions and have a sort of circular motion moreover, the same quantity of motion is always preserved in the universe. (AT VIIIA 655: CSM I 756)
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From the simple fact that I consider two halves of a part of matter, however small it may be, as two complete substances... I conclude with certainty that they are really divisible. (AT III 977: CSMK 757-758
To observe, however, is not to explain, and the new science seeks also to explain. Descartes has prepared the way for this. In earlier Discourses in the Optics , he presented the laws of geometrical optics for reflection and refraction. The former was already well known, but the sine law for refraction was newly discovered. (Huygens was later to complain that Descartes had not referred to Snell, who is now generally credited with the discovery of this law.) Descartes carefully shows how the lens of the eyeball, in conformity with the law of refraction, focuses light arriving from the object to form the image on the retina. The more particular biological facts of sight can be explained by the more general laws of geometrical optics.
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