Descartes

Once Galileo had demonstrated the inconsistencies in Aristotle s theory of motion and Kepler had formulated the laws of planetary motion, the only remaining obstacle to the development of a mathematical model of the solar system was the law of inertia, still based on uniform circular motion. This final problem was removed by the French mathematician and philosopher, Descartes. 

Rene Descartes (1596 - 1650), who also published under the latinized name Renatus Cartesius, operated on the assumption that understanding of the physical world was contingent on the formulation of a sound metaphysical model or logical framework, drawing its first principles from reason. As the most fundamental principle he accepted a conservation law that demands the quantity of motion in the universe to remain constant. He equated matter with extension, which must therefore fill all space. 

Under these conditions any movement tends to create a vortex. The solar system is such an aetherial vortex with the sun at its centre. The planets are swirled around the sun by the aether. A planet, in turn, is at the centre of a subsidiary vortex, which may carry satellites, like the moon, around. On a larger scale the universe is made up of solar vortices centred on stars, like the sun, and fitting together like a foam, to fill all space. 

The aether of a rotating vortex tends to recede from the central star under centrifugal pressure which becomes visible as light, emitted by the star and reflected by the planets. Because of its confinement in the foam-like structure the aether exerts an inward pressure on the planets. The reason why planets are not pushed into the central star is because they are in a state of uniform linear motion. Under aetherial pressure the direction of this motion changes continually and in the state of balance the planet stays on a closed characteristic orbit around the sun. Although Newton scoffed at the Cartesian model he gave the law of inertia in this exact same form. 

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The phase velocity is directly linked to the angles of incidence by the Snell-Descartes law ... 

The simpler model can be derived to describe a shallow shell which is characterized by the closeness of the mid-surface to the plane. In other words, it is assumed that a = b = 1 and the coordinate system a, (5) coincides with the Descartes system X, X2- Then differentiating the fourth and the fifth equilibrium equations with respect to Xi and X2, respectively, and combining with the third equilibrium equation give... 

Let a punch shape be described by the equation z = ip(x), and xi,X2,z be the Descartes coordinate system, x = xi,X2). We assume that the mid-surface of a plate occupies the domain fl of the plane = 0 in its non-deformable state. Then the nonpenetration condition for the plate vertical displacements w is expressed by the inequalities... 

Let the mid-surface of the Kirchhoff-Love plate occupy a domain flc = fl Tc, where C is a bounded domain with the smooth boundary T, and Tc is the smooth curve without self-intersections recumbent in fl (see Fig.3.4). The mid-surface of the plate is in the plane z = 0. Coordinate system (xi,X2,z) is assumed to be Descartes and orthogonal, x = xi,X2)-... 

The concept of a contact lens device for modifying the optical power of the eye was described by Leonardo da Vinci and later by Rene Descartes and Thomas Young. In 1823, Sir John Herschel described the appHcation of a contact lens device specifically for the purpose of correcting vision. The first contact lens was fitted to a human eye for correction of vision in 1888. The early lenses were made of blown or molded glass and were difficult to wear. 

Descartes Rule of Signs The number of positive real roots of a polynomial equation with real coefficients either is equal to the number V of its variations in sign or is less than i by a positive even integer. The number of negative roots of P(x) = 0 either is equal to the number of variations of sign of P - ) or is less than that number by a positive even integer. 

Simple terms can be a trap and a delusion. In the study of materials, we must be prepared to face complexity and we must distrust elaborate theoretical systems advanced too early, as Bridgman did. As White (1970) remarked with regard to Descartes Regarding the celebrated vorticist physics which took the 1600s by storm... it had all the qualities of a perfect work of art. Everything was accounted for. It left no loose ends. It answered all the questions. Its only defect was that it was not true . 

Early in the 17th century, there was still vigorous disagreement as to the feasibility of empty space Descartes denied the possibility of a vacuum. The matter was put to the test for the first time by Otto von Guericke (1602-1686), a German politician who devoted his brief leisure to scientific experimentation (Krafft 1970-1980). He designed a crude suction pump using a cylinder and piston and two flap valves, and... 

Tor the purpose of this brief account we will provide only a notional definition of optical aberrations. In an optical system, the angular coordinates of incident rays are transformed according to sequential applications of Descarte s law from one optical surface to the next. Aberrations are essentially the non-linear terms of the transformation, the angular coordinates of emerging rays not being strictly proportional to those of the incident ones -thereby generating distorted and/or blurred images. 

Universite Louis Pasteur Strasbourg 15, rue Descartes 67084 Strasbourg Cedex France... 

Davis, P. J. and Hersh, R. Descartes Dream The World According to Mathematics. Harcourt Brace Jovanovich, San Diego, CA, 1986. 

Descartes de Garcia, Paula R., Alkaloids in Brazilian mate (Ilex paraguarieneis). Rev Brasil Quim 54, 492, 1962. 

Thorndike, Lynn. "The attitude of Francis Bacon and Descartes towards magic and occult science." In Science medicine and history, ed. E. Ashworth Underwood, i, 451-454. Oxford OUP, 1953. 

G. Bruno, Descartes, Galileo, Gilbert, Kepler, Spinoza. Precious editions of classical and Italian literature. Rare musical items. Illustrated works by Paracelsus, Vesalius, Coiter. Remarkable items on America and geography, comprising the first national atlas of France, etc. Lugano L Art ancien, 1936. 112p. 

Keefer, Michael H. The dreamer s path Descartes and the 16th century. Renaissance Q 49 (1996) 30-76. 

On the influence of Renaissance hermetism and Calvinist theology on Descartes... 

Descartes based his thesis for the existence of God on the premise that man could not conceive of anything greater than himself unless that thing existed. The correctness of this has been debated for years. However, one statement, that is beyond debate is that computers cannot be greater than the men who build and program them. A computer can do only what a man has told it to do. It cannot be any more accurate than the information that has been supplied to it. It cannot do anything that it has not been told to do. 

Oliver Heaviside, British mathematician (1850-1925). tReod Descartes, French philosopher, mathematician (1596-1650). 

De Moivre, Abraham 13n deBroglie, Louis 97n Debye, Petrus 344n Descartes, Rend 63n Dewar, Sir James 316n Dirac, PAM 264n... 

Laboratoire de Pharmacochimie MoUculaire et Cellulaire, U648 INSERM, UFR Biomedicale, University Reny-Descartes, 45, rue des Saints-Pyres, 75006 Paris, France... 

Damasio, A. (1994), Descartes Error Emotion, Reason and the Human Brain, Grosset/Putnam, New York. 

Calvin, W.H. (1996). How Brains Think. Weidenfeld and Nicholson, London Chomsky, N. (1975). Reflections on Language. Pantheon, New York Cox, P.A. (1995). The Elements of Earth. Oxford University Press, Oxford Damasio, A.R. (1995). Descartes Error. Picador, London Dawkins, R. (1998). Unweaving the Rainbow, Penguin, London... 

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