Cartesian

Definitions

  • WordNet 3.6
    • adj Cartesian of or relating to Rene Descartes or his works "Cartesian linguistics"
    • n Cartesian a follower of Cartesian thought
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Webster's Revised Unabridged Dictionary
    • n Cartesian An adherent of Descartes.
    • a Cartesian Of or pertaining to the French philosopher René Descartes, or his philosophy. "The Cartesion argument for reality of matter."
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Century Dictionary and Cyclopedia
    • Cartesian Pertaining to the French philosopher René Descartes (1596-1650), to his philosophy, or to his geometrical method. In order to put philosophy on a sound basis, Descartes professed to begin by doubting all things. But the doubt, the thought, could not be doubted; hence the fundamental proposition of his philosophy, Cogito, ergo sum (I think, therefore I am). This proposition (which is not a syllogism nor any formal mode of inference) means that, recognizing the fact that I think, I am irresistibly led to believe and clearly to discern that I exist, without being able to account for the inference. According to Descartes, the consideration that the conception of a deity involves the conception of a reality surpassing my own leads to the irresistible belief and clear perception of the existence of a God. Also, since veracity is an attribute of God, all that is clearly and distinctly apprehended must be true. This is the so-called Cartesian criterion of truth. Substances, he taught, are of two radically different kinds: the material, which are extended and not conscious, and the spiritual, which are conscious and not extended—a doctrine which is called Cartesian dualism. The Cartesian doctrine of divine assistance, or occasionalism, which was not fully developed by Descartes himself, is that whenever the soul makes a volition God intervenes to cause the corresponding motion of the body. He also taught that brutes are mere machines without consciousness (the Cartesian automatism.), and that all space is filled with matter, which turns about in vortices, and so produces the motions of the heavenly bodies.
    • n Cartesian One who adopts the philosophy of Descartes; a follower of Descartes.
    • n Cartesian Any curve of the fourth order having two cusps on the absolute. There are three genera of Cartesians. The first consists of curves of the sixth class, composed of a pair of Cartesian ovals, one inside the other. The second genus consists of curves of the fourth class, which are limaçons. Curves of this kind generally have an acnode which may become a crunode. The third genus consists of the cardioid, which is a curve of the third class with and a real cusp. Every Cartesian has a single bitangent.
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Chambers's Twentieth Century Dictionary
    • adj Cartesian kar-tē′zhi-an relating to the French philosopher René Descartes (1596-1650), or his philosophy
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Etymology

Webster's Revised Unabridged Dictionary
From Renatus Cartesius, Latinized from of René Descartes,: cf. F. cartésien,

Usage

In literature:

Lamont is not unhappy: he keeps his mind active by solving stiff quadratic equations and fiddling with Cartesian co-ordinates.
"Literary Tours in The Highlands and Islands of Scotland" by Daniel Turner Holmes
There can be little doubt that Newton himself aimed his rule at the Cartesian hypothesis of Vortices.
"Logic, Inductive and Deductive" by William Minto
Cartesianism, which gave it an impulse, became inactive and contemplative in Mallebranche (1674).
"Priests, Women, and Families" by J. Michelet
After this he resided for some time in Switzerland, studying Cartesianism.
"A Short History of French Literature" by George Saintsbury
The general approval of the Cartesian school proved that this was a legitimate development of doctrine.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 4" by Various
I do not mean to identify the epistemological situation with the Cartesian disjunction.
"Creative Intelligence" by John Dewey, Addison W. Moore, Harold Chapman Brown, George H. Mead, Boyd H. Bode, Henry Waldgrave, Stuart James, Hayden Tufts, Horace M. Kallen
His principal work is a History of the Cartesian Philosophy.
"A Biographical Dictionary of Freethinkers of All Ages and Nations" by Joseph Mazzini Wheeler
It was to get over this very difficulty that the Cartesians invented the system of Occasional Causes.
"A System of Logic: Ratiocinative and Inductive" by John Stuart Mill
To pretend that they are atheists would be like saying they are anti-Cartesians.
"A Philosophical Dictionary, Volume 2 (of 10)" by François-Marie Arouet (AKA Voltaire)
Cartesian-Copernicans, 85-86, 91, 95, 98, 106.
"The gradual acceptance of the Copernican theory of the universe" by Dorothy Stimson
Its cartesian equation is x^3 + y^3 = 3axy.
"Encyclopaedia Britannica, 11th Edition, Volume 10, Slice 5" by Various
The Cartesian philosophy, in spite of its profound originality, and its wholly French character, is full of the Platonic spirit.
"Lectures on the true, the beautiful and the good" by Victor Cousin
There were two reasons why the older or Pre-Cartesian view of this question should give place to the modern doctrine.
"International Congress of Arts and Science, Volume I" by Various
It is convenient to use these rather than Cartesian co-ordinates.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8" by Various
Amongst these we find the Cartesians, Boyle, Hoffmann, and Haller.
"Curiosities of Medical Experience" by J. G. (John Gideon) Millingen
This is the question, and I need not say it is a question not answerable on the Cartesian principle or method.
"The Catholic World. Volume II; Numbers 7, 8, 9, 10, 11, 12." by E. Rameur
Pascal also expresses the like displeasure against the Cartesian theory of the vortices.
"Plato and the Other Companions of Sokrates, 3rd ed. Volume II (of 4)" by George Grote
Monboddo, on Cartesian and Newtonian theories, ii.
"Plato and the Other Companions of Sokrates, 3rd ed. Volume IV (of 4)" by George Grote
To assert that they are atheists would be very much the same thing as to assert that they are anti-Cartesians.
"Expositor's Bible: The Epistles of St. John" by William Alexander
The chief content of the Cartesian system may be seen condensed in the following epitome.
"A History of Philosophy in Epitome" by Albert Schwegler
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In news:

Many manufacturers of plastic components use inflexible linear gantries restricted to Cartesian motions for loading and unloading plastic parts on injection molding machines.
Cartesian , Russia's Private Equity Fund to Buy Part of Moscow Stock Exchange.
New-Generation Cartesian -Loop Transmitters for Software-Defined Radio.
Cartesian Coordinates can be used to specify the position of any point in three-dimensional space by measuring its distances from three mutually perpendicular planes.
The XR-Series four-axis, compact gantry robots feature a ceiling mounted, flexible SCARA robot combined with a long-stroke Cartesian robot.
Mr Gore referred to "the Cartesian revolution," Reinhold Neibuhr's work and Thomas Kuhn's theory of paradigms.
The XR-Series four-axis, compact gantry robots feature a ceiling mounted, flexible SCARA robot combined with a long-stroke Cartesian robot .
The system is based on a Cartesian machine with a range of 39.37 in.
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In science:

Go back to the transformation (10) and pass there from the polar coordinates (r, φ) to the Cartesian ones (x1 , x2).
Dyon-Oscillator Duality
Savage, Symmetric measures on Cartesian products, Trans.
Invariant subspaces of Voiculescu's circular operator
First, one has to cut a hole in the computational domain that has a spherical topology and is therefore not well adapted to the Cartesian coordinates typically used.
Simple excision of a black hole in 3+1 numerical relativity
Excise a region adapted to Cartesian coordinates, i.e. excise a cube contained inside the horizon.
Simple excision of a black hole in 3+1 numerical relativity
For these terms use upwind along the shift direction (we use the standard 1D second-order upwind stencil in each of the Cartesian coordinate directions based on the sign of the corresponding shift component at each point).
Simple excision of a black hole in 3+1 numerical relativity
In our case this means: 1) excising a cube naturally adapted to the underlying Cartesian coordinates, 2) imposing a simple but stable boundary condition on the sides of this cube, and 3) using an upwind scheme instead of causal differencing.
Simple excision of a black hole in 3+1 numerical relativity
Also studied are certain tilings of the hyperbolic plane (see Section 4), and further examples can be obtained, e.g., by taking Cartesian products of other Cayley graphs (such as Tn × Z, the muchstudied example of Grimmett and Newman ).
Explicit isoperimetric constants and phase transitions in the random-cluster model
It is well known that canonical quantization leads to a theory consistent with experiment only if it is performed in terms of Cartesian coordinates and momenta.
Quantum Theory within the Framework of General Relativity
In Euclidean space this restriction does not present any problem since in this space the set of Cartesian coordinates is preferred (it can be selected unambiguously and equivalence within the set is ensured).
Quantum Theory within the Framework of General Relativity
Cartesian and the fibers of the vertical maps are discs.
Ramification of local fields with imperfect residue fields
Cartesian, where the superscript log indicates the valued points as log schemes.
Ramification of local fields with imperfect residue fields
Cartesian basis vector e is the direction of displacement.
Gravitational radiation, energy and reaction on quasi-spherical black holes
To perform an actual sprinkling in a computer simuation is very easy if the geometry is flat, since then coordinate values can be chosen uniformly at random in a Cartesian chart; if the geometry is curved, other well-known techniques can be applied (see, e.g., Ref. ).
Statistical geometry of random weave states
It can also be regarded as the Cartesian product of two complex planes, or C2 .
Bicomplex algebra and function theory
In our previous paper we developed adaptive mesh refinement approach to the construction of initial data for black hole collisions on high resolution Cartesian meshes .
Local and global properties of conformally flat initial data for black hole collisions
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