Choosing a Cartesian coordinate system for a one-dimensional space — that is, for a straight line — means choosing a point O of the line ( the origin ), a unit of length, and an orientation for the line.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines ( axes ), any two of them being perpendicular ; a single unit of length for all three axes ; and an orientation for each axis.

In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc.

The symmetric product of n copies of X means the quotient of X < sup > n </ sup >, the n-fold Cartesian product of X with itself, by the permutation action of the symmetric group on n letters operating on the indices of coordinates.

The great circle chord length,, may be calculated as follows for the corresponding unit sphere, by means of Cartesian subtraction:

Orthogonality here means that every pair ( s, t ) from the Cartesian product S × T occurs exactly once.

It does not dismiss the Cartesian first-person perspective, but rather brackets it so that it can be intersubjectively verified by empirical means, allowing it to be submitted as scientific evidence.

This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back.

Charles Bettelheim complained that Mandel lacked a " dialectical synthesis ", because, in a somewhat Cartesian way, Mandel tried " to deal with the complex reality of the transitional society by means of the simplest and most abstract categories of " pure " and fully developed socialist society.

The adjective Cartesian refers to the French mathematician and philosopher René Descartes ( who used the name Cartesius in Latin ).

Nicole Oresme, a French cleric and friend of the dauphin ( later to become King Charles V ) of the 14th Century, used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat.

In response to Hobbes, the French Philosopher Rene Descartes ( 1596 – 1650 ) developed Cartesian Dualism, which posits that there is a divisible, mechanical body and an indivisible, immaterial mind which interact with one another.

In his Phenomenology of Perception ( first published in French in 1945 ), Merleau-Ponty developed the concept of the body-subject as an alternative to the Cartesian " cogito.

René Descartes (; Latinized form: Renatus Cartesius ; adjectival form: " Cartesian "; 31 March 1596 – 11 February 1650 ) was a French philosopher, mathematician, and writer who spent most of his adult life in the Dutch Republic.

A uniform space ( X, Φ ) is a set X equipped with a nonempty family Φ of subsets of the Cartesian product X × X ( Φ is called the uniform structure or uniformity of X and its elements entourages ( French: neighborhoods or surroundings )) that satisfies the following axioms:

The English notation corresponds to the one universally used for matrices, while the French notation is closer to the convention of Cartesian coordinates ; however, French notation differs from that convention by placing the vertical coordinate first.

The first influential philosopher to discuss this question specifically was Descartes, and the answer he gave is known as Cartesian dualism.

The book was attacked by fellow Cartesian philosopher, Antoine Arnauld, and, although Arnauld's initial concerns were theological ones, the bitter dispute which ensued very quickly branched out into most other areas of their respective systems.

Gilbert Ryle ( 19 August 1900, Brighton – 6 October 1976, Oxford ), was a British philosopher, a representative of the generation of British ordinary language philosophers who shared Wittgenstein's approach to philosophical problems, and is principally known for his critique of Cartesian dualism, for which he coined the phrase " the ghost in the machine.

The philosopher Gilbert Ryle was concerned with what he called the intellectualist legend ( also known as the " Dogma of the ghost in the machine ," the " Two-Lives Legend ," the " Two-Worlds Story ," or the " Double-Life Legend ") which requires intelligent acts to be the product of the conscious application of mental rules ( in other words Ryle was attempting to combat Cartesian dualism ).

The title is a phrase coined by the Oxford philosopher Gilbert Ryle to describe the Cartesian dualist account of the mind / body relationship.

The Cartesian theater is a derisive term coined by philosopher Daniel Dennett to pointedly refer to a defining aspect of what he calls Cartesian materialism, which he considers to be the often unacknowledged remnants of Cartesian dualism in modern materialistic theories of the mind.

* May 29-Frans van Schooten, Dutch Cartesian mathematician ( born 1615 )

* Cartesian dualism, the philosophy of the distinction between mind and body developed by René Descartes

The invention of Cartesian coordinates in the 17th century by René Descartes ( Latinized name: Cartesius ) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra.

Amidst this turmoil, René Descartes sought answers to philosophical questions through the use of logic and reason and formulated what would be called Cartesian Dualism in 1641.

With regard to René Descartes, he is popularly said to have recorded the three dreams leading up to the Cartesian Cogito.

A Cartesian diver or Cartesian devil is a classic science experiment, named for René Descartes, which demonstrates the principle of buoyancy ( Archimedes ’ principle ) and the ideal gas law.

* René Descartes introduces the Cartesian coordinate system in his work La Géométrie and promotes intellectual rigour in Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences ( published in Leiden ).

This drastic distinction between inner world and outer world was most popularized by René Descartes when he solidified his principle of Cartesian dualism.

He was one of the followers of René Descartes who tried to work out more detailed versions of a generally Cartesian philosophy.

After finishing his military service, during which he began to read René Descartes, he studied for his licence ( bachelor's degree ), focusing on the influence of scholasticism on Cartesian thought.

Res extensa ( often translated " corporeal substance " by Descartes ) is one of the three substances described by René Descartes in his Cartesian ontology, alongside res cogitans and God.

The Cartesian coordinate system developed by René Descartes explicitly assumes this axiom by blending the distinct concepts of real number system with the geometric line or plane into a conceptual metaphor.

Cartesian anxiety refers to the notion that, ever since René Descartes promulgated his influential form of body-mind dualism, Western civilization has suffered from a longing for ontological certainty, or feeling that scientific methods, and especially the study of the world as a thing separate from ourselves, should be able to lead us to a firm and unchanging knowledge of ourselves and the world around us.

The Cartesian circle is a potential mistake in reasoning attributed to René Descartes.

Descartes ' influence in mathematics is equally apparent ; the Cartesian coordinate system — allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system ( and conversely, shapes to be described as equations ) — was named after him.

In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes began his long correspondence with Princess Elisabeth of Bohemia, devoted mainly to moral and psychological subjects.

One of Descartes ' most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry.

The evil demon is omnipotent, Christian doctrine notwithstanding, and is seen as a key requirement for Descartes ' argument by Cartesian scholars such as Alguié, Beck, Émile Bréhier, Chevalier, Frankfurt, Étienne Gilson, Anthony Kenny, Laporte, Kemp-Smith, and Wilson.

Although better known for his philosophical work, Malebranche made some notable contributions to physics, working within a broadly Cartesian framework but nevertheless prepared to depart from Descartes where necessary.

The central claim of what is often called Cartesian dualism, in honor of Descartes, is that the immaterial mind and the material body, while being ontologically distinct substances, causally interact.

La Géométrie contains Descartes ' first introduction of the Cartesian coordinate system.

Descartes unified geometry and algebra ( see: Cartesian coordinate system ).

As it was written in the vernacular, it became quite popular and was in use, as a paradigm of traditional term logic, into the twentieth century, introducing the reader to logic, and exhibiting strong Cartesian elements in its metaphysics and epistemology ( Arnauld having been one of the main philosophers whose objections were published, with replies, in Descartes ' Meditations on First Philosophy.

Descartes employed Cartesian doubt as a pre-eminent methodological tool in his fundamental philosophical investigations.

In the 17th century Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry.