## Cartesian Sentence Examples

- It is to her that the Principles of Philosophy were dedicated; and in her alone, according to Descartes, were united those generally separated talents for metaphysics and for mathematics which are so characteristically co-operative in the
**Cartesian**system. - The contempt of aesthetics and erudition is characteristic of the most typical members of what is known as the
**Cartesian**school, especially Malebranche. - The first public teacher of
**Cartesian**views was Henri Renery, a Belgian, who at Deventer and afterwards at Utrecht had introduced the new philosophy which he had learned Spread of from personal intercourse with Descartes. - In 1639 he published a series of arguments against atheism, in which the
**Cartesian**views were not obscurely indicated as perilous for the faith, though no name was mentioned. - There the
**Cartesian**innovations had found a patron in Adrian Heerebord, and were openly discussed in theses and lectures. - Such are the four points of
**Cartesian**method: (1) Truth requires a clear and distinct conception of its object, excluding all doubt; (2) the objects of knowledge naturally fall into series or groups; (3) in these groups investigation must begin with a simple and indecomposable element, and pass from it to the more complex and relative elements; (4) an exhaustive and immediate grasp of the relations and interconnexion of these elements is necessary for knowledge in the fullest sense of that word.4 " There is no question," he says in anticipation of Locke and Kant, " more important to solve than that of knowing what human knowledge is and how far it extends." - To attach a clear and definite meaning to the
**Cartesian**doctrine of God, to show how much of it comes from the Christian theology and how much from the logic of idealism, how far the conception of a personal being as creator and preserver mingles with the pantheistic conception of an infinite and perfect something which is all in all, would be to go beyond Descartes and to ask for a solution of difficulties of which he was 1 Ouvres, vi. - In both these doctrines of a priori science Descartes has not been subverted, but, if anything, corroborated by the results of experimental physics; for the so-called atoms of chemical theory already presuppose, from the
**Cartesian**point of view, certain aggregations of the primitive particles of matter. - But the
**Cartesian**theory, like the later speculations of Kant and Laplace, proposes to give a hypothetical explanation of the circumstances and motions which in the normal course of things led to the state of things required by the law of attraction. - It should be added that the modern theory of vortex-atoms (Lord Kelvin's) to explain the constitution of matter has but slight analogy with
**Cartesian**doctrine, and finds a parellel, if anywhere, in a modification of that doctrine by Malebranche. **Cartesian**professoriate, - Wittich, Clauberg and Geulincx.- The chief names in this advanced theology connected with
**Cartesian**doctrines are Ludwig Meyer, the friend and editor of Spinoza, author of a work termed Philosophia scripturae interpres (1666); Balthasar Bekker, whose World Bewitched helped to discredit the superstitious fancies about the devil; and Spinoza, whose Tractatus theologico-politicus is in some respects the classical type of rational criticism up to the present day. - The Chateau of the duc de Luynes, the translator of the Meditations, was the home of a
**Cartesian**club, that discussed the questions of automatism and of the composition of the sun from filings and parings, and rivalled Port Royal in its vivisections. - On his visit to Toulouse in 1665, with a mission from the
**Cartesian**chiefs, his lectures excited boundless interest; ladies threw themselves with zeal and ability into the study of philosophy; and Regis himself .was made the guest of the civic corporation. - In 1673 a decree of the parlement against
**Cartesian**and other unlicensed theories was on the point of being issued, and was only checked in[time by the appearance of a burlesque mandamus against the intruder Reason, composed by Boileau and some of his brother-poets. - From the real or fancied rapprochements between
**Cartesianism**and Jansenism, it became for a while impolitic, if not dangerous, to avow too loudly a preference for**Cartesian**theories. - Pascal and other members of Port Royal openly expressed their doubts about the place allowed to God in the system; the adherents of Gassendi met it by resuscitating atoms; and the Aristotelians maintained their substantial forms as of old; the Jesuits argued against the arguments for the being of God, and against the theory of innate ideas; whilst Pierre Daniel Huet (1630-1721), bishop of Avranches, once a
**Cartesian**himself, made a vigorous onslaught on the contempt in which his former comrades held literature and history, and enlarged on the vanity of all human aspirations after rational truth. - But this doctrine was a criticism and a divergence, no less than a consequence, from the principles in Descartes; and it brought upon Malebranche the opposition, not merely of the
**Cartesian**physicists, but also of Arnauld, Fenelon and Bossuet, who found, or hoped to find, in the Meditations, as properly understood, an ally for theology. - And before 1725, readings, both public and private, were given from
**Cartesian**texts in some of the Parisian colleges. - Fortunately the
**Cartesian**method had already done its service, even where the theories were rejected. - In Germany a few
**Cartesian**lecturers taught at Leipzig and Halle, but the system took no root, any more than in Switzerland, where it had a brief reign at Geneva after 1669. - At Naples there grew up a
**Cartesian**school, of which the best known members are Michel Angelo Fardella (1650-1708) and Cardinal Gerdil (1718-1802), both of whom, however, attached themselves to the characteristic views of Malebranche. - He is the author of several works, amongst others a system of
**Cartesian**philosophy, where a chapter on " Angels " revives the methods of the schoolmen. - His chief opponent was Samuel Parker (1640-1688), bishop of Oxford, who, in his attack on the irreligious novelties of the
**Cartesian**, treats Descartes as a fellow-criminal in infidelity with Hobbes and Gassendi. - Rohault's version of the
**Cartesian**physics was translated into English; and Malebranche found an ardent follower in John Norris (1667-171 I). - Fouillee, Descartes (Paris, 1893); Revue de metaphysique et de morale (July, 1896, Descartes number); Norman Smith, Studies in the
**Cartesian**Philosophy (1902); R. - Geulincx carried out to their extreme consequences the irreconcilable elements in the
**Cartesian**metaphysics, and his works have the peculiar value attaching to the vigorous development of a one-sided principle. - Forbes communicated to the Royal Society of Edinburgh a short paper of his on a mechanical method of tracing
**Cartesian**ovals. - Embracing the whole philosophic movement under the name of "the
**Cartesian**system," Reid detects its fundamental error in the unproved assumption shared by these thinkers "that all the objects of my knowledge are ideas in my own mind." - After travelling in France and England, he studied the
**Cartesian**philosophy under John Racy at Leiden. - Its
**cartesian**equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20. - Also, as the
**Cartesian**geometry shows, all the relations between points are expressible in terms of geometric quantities. - Restricted Substitutions We may regard the factors of a binary n ip equated to zero as denoting n straight lines through the origin, the co-ordinates being
**Cartesian**and the axes inclined at any angle. - Glanvill's first work (a passage in which suggested the theme of Matthew Arnold's Scholar Gipsy), The Vanity of Dogmatizing, or Confidence in Opinions, manifested in a Discourse of the shortness and uncertainty of our Knowledge, and its Causes, with Reflexions on Peripateticism, and an Apology for Philosophy (1661), is interesting as showing one special direction in which the new method of the
**Cartesian**philosophy might be developed. - But this example, combined with the
**Cartesian**principles, set many active and ingenious spirits to work to reconstruct the whole of medicine on a physiological or even a mechanical basis - to endeavour to form what we should now call physiological or scientific medicine. - The
**cartesian**equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '. - The
**cartesian**equation is x = ti' (c2-y'")+ 2c log [{c-?/ (c.2- y2)}/{c+?i (c2+y2)il, and the curve has the geometrical property that the length of its tangent is constant. - At a time when the
**Cartesian**system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it. - The
**cartesian**equation is y=a cos /2a. - It is less comprehensible how the
**Cartesian**philosophy from: the starting-point of thought allied itself with a similar point of view. - This involves the use of
**Cartesian**co-ordinates, and leads to important general formulae, such as Simpson's formula. - The most important formulae are those which correspond to the use of rectangular
**Cartesian**co-ordinates. - In analytical geometry, the equation to the sphere takes the forms x 2 +y 2 +z 2 =a 2, and r=a, the first applying to rectangular
**Cartesian**co-ordinates, the second to polar, the origin being in both cases at the centre of the sphere. - If the centre be (a, a, y), the
**Cartesian**equation becomes (x - a) 2 l3)2 + (z - y)2 = a2; consequently the general equation is x2+y2 -}- z 2 + 2Ax+ 2By+2Cz+D =o, and it is readily shown that the co-ordinates of the centre are (-A, -B, -C), and the radius A2+B2+C2-D. - Yet he would not avow himself a follower of Bacon or indeed of any other teacher: on several occasions he mentions that in order to keep his judgment as unprepossessed as' might be with any of the modern theories of philosophy, till he was "provided of experiments" to help him judge of them, he refrained from any study of the Atomical and the
**Cartesian**systems, and even of the Novum Organum itself, though he admits to "transiently consulting" them about a few particulars. - In the article Geometry: Analytical, it is shown that the general equation to a circle in rectangular
**Cartesian**co-ordinates is x 2 - { - y 2 + 2gx-}-2fy+c= o, i.e. **Cartesian**co=ordinates.- Analytically, the
**Cartesian**equation to a coaxal system can be written in the form x 2 + y 2 + tax k 2 = o, where a varies from member to member, while k is a constant. - Essentially, therefore, Descartes's process is that known later as the process of isoperimeters, and often attributed wholly to Schwab.2 In 16J5 appeared the Arithmetica Infinitorum of John Wallis, where numerous problems of quadrature are dealt with, the curves being now represented in
**Cartesian**co-ordinates, and algebra playing an important part. - The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the
**Cartesian**equation referred to oblique axes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity.