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In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles.
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
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Descartes describes philosophy as like a tree, whose roots are metaphysics, its trunk physics, and the branches are the rest of the sciences, mainly medicine, mechanics, and morals that is the last level of wisdom. In the same way that trees have fruits in their outer parts, the usefulness of philosophy is also contained in the areas that stem ...
Fig. 1: Fermat's principle in the case of refraction of light at a flat surface between (say) air and water. Given an object-point A in the air, and an observation point B in the water, the refraction point P is that which minimizes the time taken by the light to travel the path APB.
Squaring the circle is a problem in geometry first proposed in Greek mathematics.It is the challenge of constructing a square with the area of a given circle by using only a finite number of steps with a compass and straightedge.
In Definition III, he defined the force that resists a change in motion as the vis inertia of Descartes. Newton’s Third Law of Motion (for every action there is an equal and opposite reaction) is also equivalent to the principle of conservation of momentum .
Meditations on First Philosophy, in which the existence of God and the immortality of the soul are demonstrated (Latin: Meditationes de Prima Philosophia, in qua Dei existentia et animæ immortalitas demonstratur) is a philosophical treatise by René Descartes first published in Latin in 1641.