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infinite

infinite

infinite Sentence Examples

  • The true physical conception is motion, the ultimate ground of which is to be sought in God's infinite power.

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  • All is vanity, all falsehood, except that infinite sky.

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  • (2) Time is infinite motion without a moment of rest and is unthinkable otherwise.

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  • Each day Miss Sullivan went to the classes with me and spelled into my hand with infinite patience all that the teachers said.

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  • Bruno looked on our solar system as but one out of an infinite number of worlds.

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  • We are a tiny dot of life suspended in a nearly infinite universe.

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  • The group left the Jeep and spent more than an hour on foot with Cynthia taking infinite care with each of her photos.

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  • The particular laws are as our points of view, as, to the traveller, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form.

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  • Who can say what may emerge from an infinite background ?

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  • Cynthia, in her infinite wisdom, arranged a generous monetary scale of chores-for-bucks that seemed to take care of the problem.

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  • These relation-numbers are the infinite ordinal numbers.

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  • But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.

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  • The process is conceived as an infinite series of variations or specifications of one primitive and common type.

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  • She responds quickly to the gentle pressure of affection, the pat of approval, the jerk of impatience, the firm motion of command, and to the many other variations of the almost infinite language of the feelings; and she has become so expert in interpreting this unconscious language of the emotions that she is often able to divine our very thoughts.

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  • His extreme sensitiveness and hatred of pain constrained Mill to hold that, if a good God exists, he cannot possess infinite power.

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  • I hung about the dangerous frontier of "guess," avoiding with infinite trouble to myself and others the broad valley of reason.

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  • Would a college at Havana not be the noblest and most enduring monument that could be raised to the brave men of the "Maine," as well as a source of infinite good to all concerned?

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  • And His will is governed only by infinite love for us, and so whatever befalls us is for our good.

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  • They are infinite and perfect when the En Soph imparts his fullness to them, and finite and imperfect when that fullness is withdrawn from them.

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  • He put infinite trouble and time into the work, and many portions of it are exceedingly well done.

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  • We have already seen that the Sephiric decade or the archetypal man, like Christ, is considered to be of a double nature, both infinite and finite, perfect and imperfect.

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  • Today we have the Internet and all its associated technologies, vastly more versatile, almost infinite in possibility.

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  • When such a tube is inserted in series with a single voltaic cell and galvanometer it is found that the resistance of the tube is nearly infinite, provided the filings are not too tightly squeezed.

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  • Knowledge is nothing to these men if it does not show them the infinite reality which is able to fill the aching void within.

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  • I would fain keep sober always; and there are infinite degrees of drunkenness.

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  • The forms of the dry land are of infinite variety, and have been studied in great detail.'

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  • Before Lightfoot's time commentaries, especially on the epistles, had not infrequently consisted either of short homilies on particular portions of the text, or of endeavours to enforce foregone conclusions, or of attempts to decide with infinite industry and ingenuity between the interpretations of former commentators.

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  • The soul's destiny upon earth is to develop those perfections the germs of which are eternally implanted in it, and it ultimately must return to the infinite source from which it emanated.

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  • While men believe in the infinite some ponds will be thought to be bottomless.

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  • "How quiet, peaceful, and solemn; not at all as I ran," thought Prince Andrew--"not as we ran, shouting and fighting, not at all as the gunner and the Frenchman with frightened and angry faces struggled for the mop: how differently do those clouds glide across that lofty infinite sky!

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  • Five years have passed since then, and already I, with my petty understanding, begin to see clearly why she had to die, and in what way that death was but an expression of the infinite goodness of the Creator, whose every action, though generally incomprehensible to us, is but a manifestation of His infinite love for His creatures.

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  • He had equipped himself with a mental telescope and looked into remote space, where petty worldliness hiding itself in misty distance had seemed to him great and infinite merely because it was not clearly seen.

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  • Countess Mary's soul always strove toward the infinite, the eternal, and the absolute, and could therefore never be at peace.

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  • For the world as a whole, however, he postulated a beginning in time (whence his use of the word creation), and further supposed that the impulse of organization which was conveyed to chaotic matter by the Creator issued from a central point in the infinite space spreading gradually outwards.

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  • 3 Leibnitz's doctrine of continuity necessarily led him in the same direction; and, of the infinite multitude of monads with which he peopled the world, each is supposed to be the focus of an endless process of evolution and involution.

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  • That first discovered is known as Burali-Forti's contradiction,' and consists in the proof that there both is and is not a greatest infinite ordinal number.

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  • For the world as a whole, however, he postulated a beginning in time (whence his use of the word creation), and further supposed that the impulse of organization which was conveyed to chaotic matter by the Creator issued from a central point in the infinite space spreading gradually outwards.

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  • But he could not always control his followers when their blood was up, and infinite damage was done before he could stop it.

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  • Matter and force (or energy) are infinite; the conservation of force follows from the imperishability of matter, the ultimate basis of all science.

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  • His argument for the Being of God is based on the hypothesis that thought - not individual but universal - is the reality of all things, the existence of this Infinite Thought being demonstrated by the limitations of finite thought.

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  • Materials for forming such an estimate no doubt exist, but before doing so we have to study in infinite detail a vast number of separate manors, municipalities or other separate economic areas.

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  • There are other infinite singularities of detail; but the above are more than sufficient to establish the point.

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  • Religion therefore is "nothing else than the consciousness of the infinity of the consciousness; or, in the consciousness of the infinite, the conscious subject has for his object the infinity of his own.

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  • Friends have always held that war is contrary to the precepts and spirit of the Gospel, believing that it springs from the lower impulses of human nature, and not from the seed of divine life with its infinite capacity of response to the Spirit of God.

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  • When the whole pleroma of preexistent souls in the world of the Sephiroth shall have descended and occupied human bodies and have passed their period of probation and have returned purified to the bosom of the infinite Source, then the soul of Messiah will descend from the region of souls; then the great Jubilee will commence.

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  • He may be said to furnish a further contribution to a metaphysical conception of evolution in his view of all finite individual things as the infinite variety to which the unlimited productive power of the universal substance gives birth.

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  • The worlds, or systems of worlds, which fill infinite space are continually being formed and destroyed.

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  • " The majority of men," he says himself, " do not think of God as an infinite and incomprehensible being, and as the sole author from whom all things depend; they go no further than the letters of his name."

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  • God, he says, is to be regarded not as an absolute but as an Infinite Person, whose nature it is that he should realize himself in finite persons.

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  • Similar principles apply in infinite detail to the treatment of wind instruments, and we must never lose sight of them in speculating as to the reasons why the genius of Beethoven was able to carry instrumentation into worlds of which Haydn and Mozart never dreamt, or why, having gone so far, it left anything unexplored.

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  • " The majority of men," he says himself, " do not think of God as an infinite and incomprehensible being, and as the sole author from whom all things depend; they go no further than the letters of his name."

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  • Its charm lies in its exquisite accent and its infinite tenderness.

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  • This is the typical river of which there are infinite varieties, yet every variety would, if time were given, and the land remained unchanged in level relatively to the sea, ultimately approach to the type.

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  • Thus the direction of true scientific progress was for many ages towards the recognition of the infinite divisibility of space and time.

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  • and which, he thinks, must be posited as necessarily coexisting with the Infinite Spirit or God.

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  • Having the color chart is like having an infinite box of crayons at your desk to color the web.

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  • In the limiting case in which the medium is regarded as absolutely incompressible S vanishes; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new function of the co-ordinates.

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  • As he foresaw, the shrinkage of the great empire into the realm of old France caused infinite disgust, a feeling fed every day by stories of the tactless way in which the Bourbon princes treated veterans of the Grand Army.

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  • Vessels for culinary, table, and luxurious uses show an infinite variety of form and purpose.

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  • According to the electromagnetic theory of light K = N2, where N is the refractive index for rays of infinite wave-length.

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  • We cannot here enter into the infinite details of the other subdivisions imagined by Joachim, or into his system of perpetual concordances between the New and the Old Testaments, which, according to him, furnish the prefiguration of the third age.

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  • In this all-important doctrine of the Sephiroth, the Kabbalah insists upon the fact that these potencies are not creations of the En Soph, which would be a diminution of strength; that they form among themselves and with the En Soph a strict unity, and simply represent different aspects of the same being, just as the different rays which proceed from the light, and which appear different things to the eye, are only different manifestations of one and the same light; that for this reason they all alike partake of the perfections of the En Soph; and that as emanations from the Infinite, the Sephiroth are infinite and perfect like the En Soph, and yet constitute the first finite things.

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  • He knew it was Napoleon--his hero--but at that moment Napoleon seemed to him such a small, insignificant creature compared with what was passing now between himself and that lofty infinite sky with the clouds flying over it.

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  • This substance is endowed with a generative or transmutative force by virtue of which it passes into a succession of forms. They thus resemble modern evolutionists, since they regard the world with its infinite variety of forms as issuing from a simple mode of matter.

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  • Our world is but one of an infinite number of others, and all the harmonies and adaptations of the universe are regarded as a special case of the infinite possibilities of mechanical events.

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  • Schelling conceives of the gradual self-evolution of nature in a succession of higher and higher forms as brought about by a limitation of her infinite productivity, showing itself in a series of points of arrest.

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  • We find that all our ideas of limits, sorrows and weaknesses presuppose an infinite, perfect and ever-blessed something beyond them and including them, - that all our ideas, in all their series, converge to one central idea, in which they find their explanation.

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  • We have therefore the idea of an infinite, perfect and all-powerful being - an idea which cannot be the creation of ourselves, and must be given by some being who really possesses all that we in idea attribute to him.

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  • 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.

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  • The relations between the new emperor and the pope were ill defined; and this proved the source of infinite disasters to Italy and Europe in the sequel.

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  • Muller tried to show that even sense experience throws us on the Infinite - which for him was the kernel of the idea of God.

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  • The relations between the new emperor and the pope were ill defined; and this proved the source of infinite disasters to Italy and Europe in the sequel.

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  • Religion is consciousness of the infinite.

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  • The selection of the topics of mathematical inquiry among the infinite variety open to it has been guided by the useful applications, and indeed the abstract theory has only recently been disentangled from the empirical elements connected with these applications.

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  • Indeed, mathematicians now reserve "continuity" as the term for the latter kind of continuity; the mere property of having an infinite number of terms between any two terms is called "compactness."

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  • Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations.

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  • Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.

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  • If µ be the molecular conductivity, and its value at infinite dilution, the fractional number of molecules dissociated is k /µop, which we may write as a.

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  • pp. 8 0 -94, 95112) showed by his calculus of hyper-determinants that an infinite series of such functions might be obtained systematically.

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  • Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry.

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  • If m be infinite and 1 + b i x + b 2 x 2 +...

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  • Single binary forms of higher and finite order have not been studied with complete success, but the system of the binary form of infinite order has been completely determined by Sylvester, Cayley, MacMahon and Stroh, each of whom contributed to the theory.

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  • Perpetuants.-Many difficulties, connected with binary forms of finite order, disappear altogether when we come to consider the (p1p2p3...) to where form of infinite order.

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  • The Complete Theory Of The Perpetuants Appertaining To Two Or More Forms Of Infinite Order Has Not Yet Been Established.

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  • The main objections to this are that it does not explain the infinite variety of phenomena, and that it disregards the distinction which most philosophers admit between higher and lower pleasures.

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  • For a point in the line OY bisecting the magnet perpendicularly, 0 =42 therefore cos 0 =0, and the point D is at an infinite distance.

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  • A magnet may be regarded as consisting of an infinite number of elementary magnets, each having a pair of poles and a definite magnetic moment.

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  • Since p can never be infinite, complete shielding is not possible.

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  • This corresponds to the second stage of magnetization, in which the susceptibility is large and permanent magnetization is set up. A still stronger magnetizing force has little effect except in causing the direction of the needles to approach still more nearly to that of the field; if the force were infinite, every member of the group ‘ would have exactly the same direction and the greatest possible resultant moment would be reached; this illustrates " magnetic saturation " - the condition approached in the third stage of magnetization.

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  • The leading idea of this work was contained in a paper published in the Berlin Memoirs for 1772.5 Its object was the elimination of the, to some minds, unsatisfactory conception of the infinite from the metaphysics of the higher mathematics, and the substitution for the differential and integral calculus of an analogous method depending wholly on the serial development of algebraical functions.

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  • In the first group are found Infinite Time, or Cronus; Tellus and Atlas supporting the globe, representing the union of Earth and Heaven; Oceanus; the Fates; Infinite Time giving into the hand of his successor Ormazd the thunderbolt, the symbol of authority; Ormazd struggling with a giant of evil - the Mithraic gigantomachy.

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  • The head of the divine hierarchy of Mithras was Infinite Time - Cronus, Saturn; Heaven and Earth were his offspring, and begat Ocean, who formed with them a trinity corresponding to Jupiter, Juno, and Neptune.

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  • God is not fully comprehensible by us, says Albert, because the finite is not able to grasp the infinite, yet he is not altogether beyond our knowledge; our intellects are touched by a ray of his light, and through this contact we are brought into communion with him.

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  • In the former the ideas of personality and infinite power have vanished, all power being conceived as inherent in God.

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  • His development of the equation x m +- px = q in an infinite series was extended by Leonhard Euler, and particularly by Joseph Louis Lagrange.

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  • A period of infinite confusion and extreme misery now ensued, of which only the salient points can here be noted.

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  • obtained by taking the qth root of I + p (1) x+ p (2) x 2 + ..., is an infinite series, i.e.

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  • A continued product of this kind can, by taking logarithms, be replaced by an infinite series.

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  • Bromwich, Introduction to the Theory of Infinite Series (1908); H.

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  • In the particular case of a rectangular aperture the course of things can be readily followed, especially if we conceive f to be infinite.

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  • If r, or z, be infinite, Jo(z), J 1 (z) vanish, and the whole illumination is expressed by 71-R 2, in accordance with the general principle.

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  • According to Aristotle, "the first of Eleatic unitarians was not careful to say whether the unity which he postulated was finite or infinite, but, contemplating the whole firmament, declared that the One is God."

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  • By chemical warnings the defensive processes seem to be awakened, or summoned; and when we think of the infinite variety of such possible phases, and of the multitude of corresponding defensive agents, we may form some dim notion of the complexity of the animal blood and tissues, and within them of the organic molecules.

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  • Of such we may cite tuberculosis of the larynx, formerly as incurable as distressing; and "adenoids" - a disease revealed by intrascopic methods - which used grievously to thwart and stifle the growth both of mind and body in children, are now promptly removed, to the infinite advantage of the rising generation.

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  • He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely proportional to their breadth, or to the horizontal sections of the reservoir.

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  • sin e 0 - i) U 2 /2g, having a maximum a U 2 /2g, (21) which must be less than the head at infinite distance to avoid cavitation at the surface of the sphere.

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  • Helmholtz, of the efflux of a jet between two edges A and A 1 in an infinite wall, is obtained by the symmetrical duplication of the above, with n = 1, b = o, a' = - oo, as in fig.

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  • Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.

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  • (I) Over the jet surface 4'=m, q=Q, u=-e rr,lm= -berslc, ch SZ=cos n0= e>rsle+I, shS2 =i sin ins =tan ds 2n (3) e2 =tan nO, - c dB sin 2,10' For a jet impinging normally on an infinite plane, as in fig.

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  • The motion of a jet impinging on an infinite barrier is obtained by putting j = a, j' = a'; duplicated on the other side of the barrier, the motion reversed will represent the direct collision of two jets of unequal breadth and equal velocity.

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  • Kirchhoff's solution is obtained of a barrier placed obliquely in an infinite stream.

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  • +4) =0, (19) and this is the infinite boundary ellipsoid if we make the upper limi =co.

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  • As workers in metals and as potters they displayed infinite variety of design, while as cultivators and engineers they excelled their European conquerors.

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  • The attention devoted to the matter soon elucidated the phenomena of meteors, and proved them to be small planetary bodies, practically infinite in numbers and illimitable in the extent and variety of their orbits.

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  • A great shock of rough, dusky, dark hair; bright, laughing, hazel eyes; massive aquiline face, most massive yet most delicate; of sallow brown complexion, almost Indian-looking, clothes cynically loose, free-and-easy, smokes infinite tobacco.

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  • Maurice, whose character, marked by " religious realism," sought in the past " the witness to eternal truths, the manifestation by time-samples of infinite realities and unchanging relations";4 and Charles Kingsley, " a great teacher," though one " certain to go astray the moment he becomes didactic."

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  • The same law prevailing in all natures creation, in the plumage of birds, the painting of butterifies wings, the marking of shells, and in all the infinite variety and beauty of the floral kingdom, the lesson is constantly renewed to the observant eye.

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  • This is illustrated by the difficulties inherent in the conception of Cause, Space, Time, Matter, Motion, the Infinite, and the Absolute, and by the" relativity of knowledge,"which precludes knowledge of the Unknowable, since" all thinking is relationing."Yet the Unknowable may exist, and we may even have an" indefinite knowledge "of it, positive, though vague and extralogical.

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  • Again, an infinite world cannot be wholly engaged either in evolution or in dissolution, so that it is really unmeaning to discuss the universality of the cosmic process until it is settled that we have a universe at all, capable of being considered as a whole.

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  • In 1734 he also published Prodromus philosophiae ratiocinantis de infinito et causa finali creationis, which treats of the relation of the finite to the infinite, and of the soul to the body, seeking to establish a nexus in each case as a means of overcoming the difficulty of their relation.

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  • Neither by geometrical, nor physical, nor metaphysical principles had he succeeded in reaching and grasping the infinite and the spiritual, or in elucidating their relation to man and man's organism, though he had caught glimpses of facts and methods which he thought only required confirmation and development.

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  • His esse is infinite love; His manifestation, form or body is infinite wisdom.

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  • In God there are three infinite and uncreated "degrees" of being, and in man and all things corresponding three degrees, finite and created.

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  • With all the Puritan eagerness to push a clear, uncompromising, Scripture-based distinction of right and wrong into the affairs of every-day life, he has a thoroughly English horror of casuistry, and his clumsy canons consequently make wild work with the infinite intricacies of human nature.

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  • With infinite tact and admirable self-denial he gave free scope to ministers whose superiority in their various departments he frankly recognized, rarely interfering personally unless absolutely called upon to do so.

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  • having a charge Q repels a unit charge placed at a distance x from its centre with a force Q/x 2 dynes, and therefore the work W in ergs expended in bringing the unit up to that point from an infinite distance is given by the integral W = Q x 2 dx = Hence the potential at the surface of the sphere, and therefore the potential of the sphere, is Q/R, where R is the radius of the sphere in centimetres.

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  • The capacity of a conductor is defined to be the charge required to raise its potential to unity, all other charged conductors being at an infinite distance.

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  • Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential v is v dq.

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  • 5) a point-charge of positive electricity +q _q/ +q and an infinite conducting plate PO, shown in section, connected to earth and therefore at zero potential.

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  • So the potential distribution in the space due to the electric point-charge +q as A together with -q at B is the same as that due to +q at A and the negative induced charge erected on the infinite plane (earthed) metal sheet placed half-way between A and B.

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  • by the substitution of " infinite " and " reasoning " for such archaisms as " incomprehensible " and " reasonable."

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  • He is the efficient and final cause of all, the beginning, middle, and end, eternal and infinite.

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  • Of these monads the number is infinite.

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  • From the hypothesis of an external world a series of contradictions are deduced, such as that the world is both finite and infinite, is movable and immovable, &c.; and finally, Aristotle and various other philosophers are quoted, to show that the external matter they dealt with, as mere potentiality, is just nothing at all.

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  • In it the union between the finite self-consciousness and the infinite ego or God is handled in an almost mystical manner.

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  • The infinite God is the all; the world of independent objects is the result of reflection or self-consciousness, by which the infinite unity is broken up. God is thus over and above the distinction of subject and object; our knowledge is but a reflex or picture of the infinite essence.

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  • As early as 1797 Fichte had begun to see that the ultimate basis of his system was the absolute ego, in which is no difference of subject and object; in 1800 the Bestimmung des Menschen defined this absolute ego as the infinite moral will of the universe, God, in whom are all the individual egos, from whom they have sprung.

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  • The individual ego is only possible as opposed to a non-ego, to a world of the senses; thus God, the infinite will, manifests himself in the individual, and the individual has over against him the non-ego or thing.

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  • This is the doctrine of the infinite divisibility of bodies, and it is in direct contradiction with the theory of atoms.

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  • The attempt to apply numerical methods to the comparison of geometrical quantities led to the doctrine of incommensurables, and to that of the infinite divisibility of space.

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  • From this point of view the atomic doctrine might be regarded as a relic of the old numerical way of conceiving magnitude, and the opposite doctrine of the infinite divisibility of matter might appear for a time the most scientific. The atomists, on the other hand, asserted very strongly the distinction between matter and space.

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  • Let us suppose that an infinite number of exactly similar systems start simultaneously from all possible values of pi, q1,

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  • become very great, the ratio P/p becomes infinite.

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  • The first book with his imprint is The Psalms of David Imitated in For the prevention of counterfeiting continental paper money Franklin long afterwards suggested the use on the different denominations of different leaves, having noted the infinite variety of leaf venation.

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  • These poems are in a sense valuable as repertoires of antiquities; but their style is on the whole bad, and infinite patience is required to clear up their numerous and obscure allusions.

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  • jectivism by calling in the aid of a universal or infinite mind or by an appeal to a total or absolute experience to which our own is relative.

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  • The universal or infinite is one that realizes itself in finite particular minds and wills, not as accidents or imperfections of it, but as its essential form.

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  • No conception of the infinite can therefore be true which does not leave room for movement, process, free creation.

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  • It involves, it will be said, the reality of time, the dependence of the Infinite in the finite, and therewith a departure from the whole line of Hegelian thought.

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  • It is to be remedied not by giving up the idea of the Infinite but by ceasing to think of the Infinite as of a being endowed with a static perfection which the finite will merely reproduces, and definitely recognizing the forward effort of the finite as an essential element in Its self-expression.

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  • are not infinite; this condition is not satisfied in the cases here considered.

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  • It is also clearly impossible to express u as an algebraical function of x and y if some value of du/dx or duldy is to be infinite.

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  • The difficulties of organizing the new Dominion, the questions arising from diverse claims and the various conditions of the country, called for infinite tact and resource on the part of the premier.

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  • the already full, operative existence of eternal beauty, truth and goodness, of infinite Personality and Spirit independently of our action, and not, as in ethics, the simple possibility and obligation for ourselves to produce such-like things.

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  • We may therefore put y=a sin -T (x - e) +b sin (x - f)+c sin 6 (x - g) +&c. (21) where the terms may be infinite in number, but always have wavelengths submultiples of the original or fundamental wave-length A.

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  • The answer to dogmatic atheism, that it implies infinite knowledge, has been well stated in John Foster's Essays, and restated by Chalmers in his Natural Theology, and its force is recognized in Holyoake's careful qualification of the sense in which secularism accepts atheism, " always explaining the term atheist to mean `not seeing God' visually or inferentially, never suffering it to be taken for anti-theism, that is, hating God, denying God - as hating implies personal knowledge as the ground of dislike, and denying implies infinite knowledge as the ground of disproof."

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  • - f min ., from which the working stress is deduced, is not the ordinary range of stress which is repeated a practically infinite number of times, but is a range of stress to which the bridge is subjected only at comparatively long intervals.

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  • run in tons, is wa = (wl+w2)1r/(K-lr) according to a formula already given, then w 3 becomes infinite if k-lr =o, or if 1 = K/r, F I --xJ- ----- ---- -?

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  • 72 with arcs of the length 1,, l2, l3, &c., and with the radii r1, r 2, &c. (note, for a length 2l 1 at each end the radius will be infinite, and the curve must end with a straight line tangent to the last arc), then let v be the measured deflection of this curve from the straight line, and V the actual deflection of the bridge; we have V = av/b, approximately.

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  • Louis fought a battle beneath the walls of Zara (July ist, 1346), which has been immortalized by Tintoretto, but was defeated and compelled to abandon the city to the republic. The struggle was renewed eleven years later when Louis, having formed, with infinite trouble, a league of all the enemies of Venice, including the emperor, the Habsburgs, Genoa and other Italian towns, attacked his maritime rival with such vigour that she sued for peace, and by the treaty of Zara (February 18th, 1358) ceded most of the Dalmatian towns and renounced the title of duke of Dalmatia and Croatia, hitherto borne by the doge.

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  • Here the land surface has been carved into forms in infinite variety.

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  • This gave infinite pain to the queen, and at length she wrote to Lord Aberdeen on the subject.

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  • With him he stayed for about eighteen months, and has as usual infinite complaints to make of his employer and some strange stories to tell.

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  • Anselm and the scholastics regarded the atonement as an offering to God of such infinite value as to outweigh men's sins, a view sometimes styled the " Commerical Theory."

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  • AEON, a term often used in Greek (aion) to denote an indefinite or infinite duration of time; and hence, by metonymy, a being that exists for ever.

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  • The tasks, almost infinite in number, confronting the new State were of great gravity.

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  • Still the Knights had been driven beyond the Vistula, and Poland had secured a seaboard; and it was due entirely to the infinite patience and tenacity of the king that even as much as this was won at last.

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  • The country, in the words of an expert sent to report on the subject by the French government, " can produce an infinite variety of wines suitable to every constitution and to every caprice of taste."

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  • 3 It was believed that the Written Word had an infinite fulness; according to the Midr. Bemidbar Rabbah every word of the Law had seventy different aspects, and Philo of Alexandria held that there are no superfluous words in Scripture.

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  • After the battle of Bull Run Jackson spent some time in the further training of his brigade which, to his infinite regret, he was compelled to leave behind him when, in October, he was assigned as a major-general to command in the Shenandoah Valley.

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  • The primeval Being is, as opposed to the many, the One; as opposed to the finite, the Infinite, the unlimited.

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    0
  • Thus even when the argument is real log x has an infinite number of values; for putting 71 =o and taking positive, in which case a = o, we obtain for log the infinite system of values log +2n7ri.

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    0
  • The introduction of infinite series into mathematics effected a great change in the modes of calculation and the treatment of the subject.

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  • The ingenuity of nature, however, in adapting animals is not infinite, because the same devices are repeatedly employed by her to accomplish the same adaptive ends whether in fishes, reptiles, birds or mammals; thus she has repeated herself at least twenty-four times in the evolution of long-snouted rapacious swimming types of animals.

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  • This survey of the phenomena of extinction in one great class of animals certainly establishes the existence of an almost infinite variety of causes, some of which are internal, some external in origin, operating on animals of different kinds.

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  • The novice is classified according as his destination is the priesthood or lay brotherhood, while a third class of "indifferents" receives such as are reserved for further inquiry before a decision of this kind a strict retreat, practically in solitary confinement, during which he receives from a director, yet relying on Thine infinite kindness and mercy and impelled by the desire of serving Thee, before the Most Holy Virgin Mary and all Thy heavenly host, I, N., vow to Thy divine Majesty Poverty, Chastity and Perpetual Obedience to the Society of Jesus, and promise that I will enter the same Society to live in it perpetually, understanding all things according to the Constitutions of the Society.

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  • Nature must not be conceived as merely abstract limit to the infinite striving of spirit, as a mere series of necessary thoughts for mind.

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  • If we make =,u=v o, p is infinite, and we obtain lap, bq, cr} 2 =o as the equation to the circular points.

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  • A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis - considered as a circle of infinite radius.

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  • quam Archimedes, we may direct our attention either to the infinite series of geometrical operations or to the corresponding infinite series of arithmetical operations.

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  • gives us at once an expression for the diameter in terms of the circumference by means of an infinite series.'

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  • 4/7r, is equal to the infinite product 3.3.5.5.7.7.9...

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  • Besides all this, however, and far beyond it in importance, was his use of infinite series.

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  • With infinite exertion he succeeded in obtaining from government a promise of 20,000, and after four years spent in preparation, sailed in September 1728, accompanied by some friends and by his wife, daughter of Judge Forster, whom he had married in the preceding month.

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  • Apart from the illuminated MSS., the mural paintings, the mosaics, and the goldsmith's work of Mount Athos are of infinite interest to the student of Byzantine art.

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  • The moral law is merely a collection of rules of conduct based on an infinite number of special cases in which the convenience of society or its rulers has subordinated the inclination of individuals.

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  • A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.

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  • There is a region within the band where µ = o, and this would give an infinite shift in the opposite direction.

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  • - When a simple periodic force acts on a system capable of oscillatory motion the ultimate forced vibration has a period equal to that of the impressed force, but the ultimate state is only reached theoretically after an infinite time, and if meanwhile the vibrating system suffers any perturbations its free periods will at once assert themselves.

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  • itself, not in Aristotle's sense of any individual existing differently from anything else, but in the novel meaning of something existing alone, he concluded, logically enough from this mere misunderstanding, that there can be only one substance, and that, as no finite body or soul can exist alone, everything finite is merely a mode of one of the attributes of the one infinite substance which alone can exist by itself.

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  • By changing the meaning of "noumenon " from the thing apprehended (voouµevov) to the thought (vOnya), and in the hypothesis of a common consciousness, he started the view that a thing is not yours or my thought, but a common thought of all mankind, and led to the wider view of Schelling and Hegel that the world is an absolute thought of infinite mind.

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  • Schelling and Hegel thought it was infinite reason; Schopenhauer, unconscious will; Hartmann, unconscious intelligence and will; Lotze, the activity or life of the divine spirit; Fechner, followed by Paulsen, a world of spiritual actualities comprised in the one spiritual actuality, God, in whom we live and move and have our being.

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  • If things different but similar have the same attributes, and are thereby the same, then in the first place the Kantian categories, though thoughts of mental origin and therefore confined to mind, are nevertheless applicable to things, because things, though different from, are the same as, thoughts, and have the categories of thoughts; in the second place, the Fichtian Ego of mankind is not the Absolute Reason of God, and yet is the same Absolute Reason; in the third place, the Schellingian Nature is the "other " of Spirit, and yet, being a mere reflex of the Idea of Nature, is identical with Spirit; and as this Spirit is everywhere the same in God and men, Nature is also identical with our Spirit, or rather with the Infinite Spirit, or Absolute Reason, which alone exists.

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  • Schelling perceived that Hegel, in reducing everything to infinite mind, absorbed man's free but finite personality in God, and, in declaring that everything real is rational, failed to explain evil and sin: indeed, the English reader of T.

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  • Hence he rejected the infinite intelligence supposed by Fichte, Schelling and Hegel against whom he urged that blind will produces intelligence, and only becomes conscious in us by using intelligence as a means to ends.

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  • teleologism," to express its conclusion that the known Lotze world beyond phenomena is neither absolute thought nor unconscious will, nor the unconscious at all, but the activity of God; causing in us the system of phenomenal appearances, which we call Nature, or bodies moving in time and space; but being in itself the system of the universal reciprocal actions of God's infinite spirit, animated by the design of the supreme good.

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  • Calderwood, in his Philosophy of the Infinite (1854), made the pertinent objection that, though thought, conception and knowledge are finite, the object of thought may be infinite.

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  • We never know anything except as determined by its attributes; but that would not prevent us from inferring something determined as unconditioned, whether infinite or absolute.

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  • Like Kant, he supposes that experience is concerned with sensations, distinguishes matter and form in sense, identifies time and space, eternal time and infinite space, with the formal element, and substitutes 'synthesis of sensations of touch and sight for association and inference, as the origin of our knowing such a solid material object as a bell.

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  • High as man is placed above the creatures around him, there is a higher and far more exalted position within his view; and the ways are infinite in which he occupies his thoughts about the fears, or hopes, or expectations of a future life.

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  • - Cotton goods are of an infinite variety, and the titles that experience or fancy have evoked are even more numerous than the kinds.

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  • Between 1840 and 1850 he edited Swedenborg's treatises on The Doctrine of Charity, The Animal Kingdom, Outlines of a Philosophic Argument on the Infinite, and Hieroglyphic Key to Natural and Spiritual Mysteries.

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  • The corresponding relation for a pure liquid can be regained by considering that at infinite dilution the liquid becomes pure solvent, and the change of volume becomes equal to the volume V.of solvent added.

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  • Thus the pious Hindu, confronted by the impossibility of obtaining perfect knowledge by the senses or by reason, finds his sole perfection in the contemplation of the infinite (Brahma).

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  • Unlike the Hindu, Xenophanes inclined to pantheism as a protest against the anthropomorphic polytheism of the time, which seemed to him improperly to exalt one of the many modes of finite existence into the place of the Infinite.

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  • To explain the universe Spinoza proceeds to argue that God, though undetermined ab extra, is capable of infinite self-determination.

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  • Thus God, the causa sui, manifests himself in an infinite multiplicity of particular modes.

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  • Plotinus, on the other hand, cannot admit any realization or manifestation of the Infinite: God is necessarily above the world - he has no attributes, and is unthinkable.

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  • He devoted infinite pains and thought to the reform of government both in England and Normandy.

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  • Even at the lowest ebb of his fortunes Christian had never lost hope of retrieving them, and between 1629 and 1643 the European situation presented infinite possibilities to politicians with a taste for adventure.

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  • The curve is symmetrical about the line x = y, and consists of two infinite branches asymptotic to the line x+y+a = o and a loop in the first quadrant.

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  • (a) The nature of space and time as elements in conscious experience is considered by Hume in relation to a special problem, that of their supposed infinite divisibility.

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  • Evidently upon his and view of conscious experience, of the world of imagination, ti such infinite divisibility must be a fiction.

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  • For Philo lays stress upon the weakness of the analogical argument, points out that the demand for an ultimate cause is no more satisfied by thought than by nature itself, shows that the argument from design cannot warrant the inference of a perfect or infinite or even of a single deity, and finally, carrying out his principles to the full extent, maintains that, as we have no experience of the origin of the world, no argument from experience can carry us to its origin, and that the apparent marks of design in the structure of animals are only results from the conditions of their actual existence.

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  • He moved his capital northward to Akhetaton (El Amarna) and strove to suppress the worship of Ammon, doing infinite damage to the monuments of Thebes by defacing his name and figure.

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  • Theoretically this requires an infinite plate; or a perfect heat insulator, so that the lateral flow can be prevented or rendered negligible.

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  • As in the case of steady-flow methods, by far the simplest example to consider is that of the linear flow of heat in an infinite solid, which is most nearly realized in nature in the propagation of temperature waves in the surface of the soil.

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  • More attention seems to have been given to the matter in the United States of America and in Germany and Russia than in England, but the infinite variety of samples known to the commercial expert, and the impossibility of standardizing those in such a manner as to make readily recognizable what the chemist has treated, renders most of the recorded analyses of uncertain value.

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  • Space is infinite, and there is an illimitable multitude of indestructible, indivisible and absolutely compact atoms in perpetual motion in this illimitable space.

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  • This universe of ours is only one section out of the innumerable worlds in infinite space; other worlds may present systems very different from that of our own.

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  • They went back to the later period of Plato's thought, the period when Plato endeavoured to combine his doctrine of Ideas with the Pythagorean number-theory, and identified the Good with the One, the source of the duality of the Infinite and the Measured (rd .bretpov and 71-pas) with the resultant scale of realities from the One down to the objects of the material world.

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  • He had strong sense, quick discernment, wit, humour, immense knowledge of literature and of life, and an infinite store of curious anecdotes.

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  • The infinite is of special importance on account of its being preserved very fully in Coptic. It is generally of masculine form, but feminine in III.

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  • The infinite superiority of the Greek alphabet with its full notation of vowels was readily seen, but piety and custom as yet barred the way to its full adoption.

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  • The Bucolic war caused infinite damage to the agriculture of the country and marks the beginning of its rapid decline under a burdensome taxation.

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  • His main result is that God is infinite, and as such, incomprehensible; that his attributes of goodness, knowledge and power are credited to him only by inference from their effects; that this inference is logically valid and sufficient for human thought.

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  • Where so much was necessarily uncertain and fluctuating, there was room for an almost infinite variety of development.

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  • The aim of germination is the fixing of the embryo in the soil, effected usually by means of the root, which is the first part of the embryo to appear, in preparation for the elongation of the epicotyledonary portion of the shoot, and there is infinite variety in the details of the process.

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  • In them, working with infinite preliminary pains, as a vast number of extant drawings and studies testify, he produced what have been accounted his four capital works in painting, besides several others of minor importance.

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  • Mayflies and dragon-flies danced in the sunlight; lizards darted across the paths; and legions of spiders pervaded the grass, many very beautiful - frosted - silver backs, or curious, like the saltigrades, who took a few steps and then gave a leap. There were crickets in infinite numbers; and flies innumerable, from slim daddy-long-legs to ponderous, black, hairy fellows known to science as Dejeaniae; hymenopterous insects in profusion, including our old friend the bishop of Ambato (possibly Dielis), in company with another formidable stinger, with chrome antennae, called by the natives ` the Devil '; and occasional Phasmas (caballo de palo) crawling painfully about, like animated twigs."

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  • In Jesus Hegel finds the expression for something higher than mere morality: he finds a noble spirit which rises above the contrasts of virtue and vice into the concrete life, seeing the infinite always embracing our finitude, and proclaiming the divine which is in man and cannot be overcome by error and evil, unless the man close his eyes and ears to the godlike presence within him.

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  • A people's religion completes and consecrates their whole activity: in it the people rises above its finite life in limited spheres to an infinite life where it feels itself all at one.

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  • Even philosophy with Hegel at this epoch was subordinate to religion; for philosophy must never abandon the finite in the search for the infinite.

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  • Soon, however, Hegel adopted a view according to which philosophy is a higher mode of apprehending the infinite than even religion.

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  • This is, however, an application of categories from a field where the conditions are finite to a sphere in which the circumstances are infinite."

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  • But this form disappears with the decease of Greek national life, and on its collapse follows the romantic, the third form of art; where the harmony of form and content again grows defective, because the object of Christian art - the infinite spirit - is a theme too high for art.

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  • The completeness and self-consistency which our ideal requires can be realized only in a form of being in which subject and object, will and desire, no longer stand as exclusive opposites, from which it seemed at once to follow that the finite self could not be a reality nor the infinite reality a self.

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  • The durability and the extraordinary ductility and pliancy of gold, its power of being subdivided, drawn out or flattened into wire or leaf of almost infinite fineness, have led to its being used for works where great minuteness and delicacy of execution were required; while its beauty and rarity have, for the most part, limited its use to objects of adornment and luxury, as distinct from those of utility.

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  • But though agriculture thus forms the staple industry of the country, its practice is pursued in different provinces with infinite variety of detail.

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  • It can be shown that, if the density of distribution of the stars through infinite space is nowhere less than a certain limit (which may be as small as we please), the total amount of light received from them (assuming that there is no absorption of light in space) would be infinitely great, so that the background of the sky would shine with a dazzling brilliancy.

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  • The propositions maintained in the argument are - "(1) That something has existed from eternity; (2) that there has existed from eternity some one immutable and independent being; (3) that that immutable and independent being, which has existed from eternity, without any external cause of its existence, must be self-existent, that is, necessarily existing; (4) what the substance or essence of that being is, which is self-existent or necessarily existing, we have no idea, neither is it at all possible for us to comprehend it; (5) that though the substance or essence of the self-existent being is itself absolutely incomprehensible to us, yet many of the essential attributes of his nature are strictly demonstrable as well as his existence, and, in the first place, that he must be of necessity eternal; (6) that the self-existent being must of necessity be infinite and omnipresent; (7) must be but one; (8) must be an intelligent being; (9) must be not a necessary agent, but a being endued with liberty and choice; (to) must of necessity have infinite power; (I I) must be infinitely wise, and (12) must of necessity be a being of infinite goodness, justice, and truth, and all other moral perfections, such as become the supreme governor and judge of the world."

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  • Clarke has been generally supposed to have derived the opinion that time and space are attributes of an infinite immaterial and spiritual being from the Scholium Generale, first published in the second edition of Newton's Principia (1714).

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  • The infinite essence of God, which may indeed be described as nihilum (nothing) is that from which all is created, from which all proceeds or emanates.

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  • We mean neither a definite number of individuals, nor yet an infinite number, but an incalculable number, whether experienced or inferred to exist.

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  • Here the minor being the infinite term " not-recognized " in the conclusion, must be the same term also in the minor premise.

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  • If we reject the infinite regress and the circle in proof (circulus in probando) which resolves itself ultimately into proving A by B and B by A, 7 we are confronted by the need for principles of two kinds, those which condition all search scientific for truth, and those which are the peculiar or proper principles.

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  • The former is in an indeterminate or infinite subject-matter impossible.

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  • It rested these in turn upon a general induction enumerative in character of enormous and practically infinite range and always uncontradicted.

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  • § 190), with consequent lapse into the inductive syllogism, and, finally, since inductive syllogism is involved in the infinite process, into analogy.

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  • p. 631) showed how to calculate the effective number of molecules n" = (1 +ek/ko)n,from the molecular conductivity k of the solution and its value ko at infinite dilution, for an electrolyte giving rise to e +I ions.

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  • The most noticeable point is the position assigned by Chalybaus to the "World Ether," which is defined as the infinite in time and space,.

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  • Their speculation as to the nature of God had led them gradually to separate him by an infinite distance from all creation, and to feel keenly the opposition of the finite and the infinite, the perfect and the imperfect, the eternal and the temporal.

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  • By it we perceive how God, the infinite, the absolute, the eternal, is yet not separated from the finite, the temporal, the relative, but, through the incarnation, enters into humanity.

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  • It is not God as abstract, infinite and eternal, as the far-away creator of the universe, or even as the ruler of the world, which Paul worships, but it is God revealed in Jesus Christ, the Father of Jesus Christ, the grace and mercy in Jesus Christ which deliver from evil.

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  • For some the first thought of God, the infinite and ultimate reality lying beyond and behind all phenomena, predominates.

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  • He first, so far as we know, sought to go behind the infinite multiplicity of phenomena in the hope of finding an infinite unity from which all difference has been evolved.

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  • This substance he called "the Infinite" (TO a rEipov).

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  • Unlike Thales, he was struck by the infinite variety in things; he felt that all differences are finite, that they have emerged from primal unity (first called epxn by him) into which they must ultimately return, that the Infinite One has been, is, and always will be, the same, indeterminate but immutable.

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  • The individual, like the phenomena of sense, comes out of the infinite and again is merged; hence on the one hand he is never a separate entity at all, while on the other hand he exists in the infinite and must continue to exist.

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  • Originally they existed in infinitesimal fragments, infinite in number and devoid of arrangement.

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  • The sides of the force-polygon may in the first instance be arranged in any order; the force-diagram can then be completed in a doubly infinite number of ways, owing to the arbitrary position of 0; and for each force-diagram a simply infinite number of funiculars can be drawn.

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  • Each extraneous force W acting on a bar may be replaced (in an infinite number of ways) by two components P, Q in lines through the centres of the pins at the extremities.

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  • The composition of finite rotations about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane.

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  • It follows that when a body has two degrees Of freedom it can twist about any one of a singly infinite system of screws whose axes lie on a certain cylindroid.

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  • Conversely it is seen that any wrench can be replaced in an infinite number of ways by two forces, and that the line of action of one of these may be chosen quite arbitrarily.

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  • The triply infinite system of null-lines form what is called in linegeometry a complex.

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  • If, however, the links are in involution, these forces become infinite or indeterminate.

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  • When a frame has a critical form it may be in a state of stress independently of the action of extraneous forces; moreover, the stresses due to extraneous forces are F indeterminate, and may be infinite.

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  • If A, B have the same sign, this is equivalent to au = cosh mO, (23) if the origin of 0 be suitably adjusted; hence r has a maximum value a, and the particle ultimately approaches the pole asymptotically by an infinite number of convolutions.

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  • The most important applications of the theory of vibrations are to the case of continuous systems such as strings, bars, membranes, plates, columns of air, where the number of degrees of freedom is infinite.

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  • At the same time, in judging the apparently inhuman way in which the Sudras were treated in the caste rules, one has always to bear in mind the fact that the belief in metempsychosis was already universal at the time, and seemed to afford the only rational explanation of the apparent injustice involved in the unequal distribution of the good things in this world; and that, if the Sudra was strictly excluded from the religious rites and beliefs of the superior classes, this exclusion in no way involved the question of his ultimate emancipation and his union with the Infinite Spirit, which were as certain in his case as in that of any other sentient being.

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  • His last "famous discovery, or rather revival of Dr Giles Fletcher's," which he mentions in his autobiography with infinite complacency, was the identification of the Tatars with the lost tribes of Israel.

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  • From the stores of valuable materials contained in those ten volumes, it will be enough here to cite (1) the Ricordi politici, already noticed, consisting of about 400 aphorisms on political and social topics; (2) the observations on Machiavelli's Discorsi, which bring into remarkable relief the views of Italy's two great theorists on statecraft in the 16th century, and show that Guicciardini regarded Machiavelli somewhat as an amiable visionary or political enthusiast; (3) the Storia Fiorentina, an early work of the author, distinguished by its animation of style, brilliancy of portraiture, and liberality of judgment; and (4) the Dialogo del reggimento di Firenze, also in all probability an early work, in which the various forms of government suited to an Italian commonwealth are discussed with infinite subtlety, contrasted, and illustrated from the vicissitudes of Florence up to the year 1 494.

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  • The postulate of an Evil Being arises from the difficulty, at all times acutely felt by a certain type of mind, of reconciling the existence of evil with the divine attributes of perfect goodness, full knowledge and infinite power.

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  • Shall he not be able thereby to produce worthy effects, and to endow the life of man with infinite commodities ?

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  • Secondly, we must have instances in which the nature is absent; only as such cases might be infinite, attention should be limited to such of them as are most akin to the instances of presence.'

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  • Hegel, before the anthropological stage, found it in magic. Max Muller, building on philosophy and mythology, affirmed that " Religion consists in the perception of the infinite under such manifestations as are able to influence the moral character of man " (Natural Religion, 18 99, p. 188).

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  • If some, and not the least essential, of these aspects are quasi-negative, it must be remembered that negations - witness the Unseen, the Unknown, the Infinite of a more advanced theology - are well adapted to supply that mystery on which the religious consciousness feeds with the slight basis of conceptual support it needs.

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  • It accounts, too, for his polemic on the one hand against a Substantial Soul, a Buddhistic Absolute, an Infinite Spiritual Substance; on the other hand against the no less mysterious material or dynamic substratum by which naturalistic Monism explains the world.

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  • He would, however, regard atheism as preferable to a belief in an infinite Deity.

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  • Assam is a fertile series of valleys, with the great channel of the Brahmaputra (literally, the Son of Brahma) flowing down its middle, and an infinite number of tributaries and watercourses pouring into it from the mountains on either side.

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  • Such pairs of colour may be regarded as infinite in number; but there are three pairs which stand out prominently, and admit of easy expression for the ratio in which each contributes to the total action.

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  • The term "Nature" is put more into the foreground in the Treatise, a point which might be urged as evidence of Bruno's influence - the dialogues, moreover, being specially concerned to establish the unity, infinity and selfcontainedness of Nature 2; but the two opposed Cartesian attributes, thought and extension, and the absolutely infinite substance whose attributes they are - substance constituted by infinite attributes - appear here as in the Ethics.

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  • The histories of philosophy may quite correctly describe his theory as the logical development of Descartes's doctrines of the one Infinite and the two finite substances, but Spinoza himself was never a Cartesian.

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  • He was the friend of regular correspondent - a third of the letters preserved to us are to or from him; and it appears from his first letter that their talk on this occasion was "on God, on infinite extension and thought, on the difference and the agreement of these attributes, on the nature of the union of the human soul with the body, as well as concerning the principles of the Cartesian and Baconian philosophies."

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  • The foundation of the system is the doctrine of one infinite substance, of which all finite existences are modes or limitations (modes of thought or modes of extension).

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  • It was impossible, indeed, to resist openly so highly gifted and so popular a sovereign; it was only by the despicable expedient of assassination that the last great monarch of Sweden was finally removed, to the infinite detriment of his country.

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  • In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations.

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  • This number is only finite if the object and aperture are assumed to be " infinitely small of a certain order"; and with each order of infinite smallness, i.e.

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  • By one, and likewise by several, and even by an infinite number of thin lenses in contact, no more than two axis points can be reproduced without aberration of the third order.

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  • is infinite it is said to be a non - terminating or infinite continued fraction.

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  • - The infinite continued fraction I I II I I I I 77 I I a2+a3+

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  • Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.

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  • We have seen that the simple infinite continued fraction converges.

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  • The infinite general continued fraction of the first class cannot diverge for its value lies between that of its first two convergents.

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  • ” If in the infinite continued fraction of the second class an?bn+i for all values of n, it converges to a finite limit not greater than unity.” 3.

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  • The Incommensurability of Infinite Continued Fractions.

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  • - There is no general test for the incommensurability of the general infinite continued fraction.

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  • The infinite continued fraction a2 +a3+ an ..

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  • The infinite continued fraction b z l!

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  • We may require to represent the infinite convergent power series ao+alx+ a2x 2 + ...

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  • by an infinite continued fractionof the form 00 01 X r2X 03x I- I - I - I -...

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  • Here, again, the theology was further developed, and an attempt made to annul the old dualism by envisaging both Ormuzd and Ahriman as emanations of an original principle of infinite time (Zervan), a doctrine which long enjoyed official validity under the Sassanids till, in the reign of Chosroes I., the sect of Zervanites was pronounced heretical.i But, above all, the ritual and the doctrine of purity were elaborated and expanded, and there was evolved a complete and detailed system of casuistry, dealing with all things allowed and forbidden, the forms of pollution and the expiation for each, &c., which, in its arid and spiritles1 monotony vividly recalls the similar prescriptions in the Pentateuch.

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  • CHAOS, in the Hesiodic theogony, the infinite empty space, which existed before all things (Theog.

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  • Metaphorically it is used for the immeasurable darkness, eternity, and the infinite generally.

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  • a sufficient, proof of the divine existence, since the idea of the Infinite must be derived from the Infinite.

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  • "The father of Russian diplomacy," as he has justly been called, was remarkable throughout his career for infinite tact and insight, and a wonderfully correct appreciation of men and events.

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  • Five months after it appeared, "on the 21st of January 1609, at four in the morning, he fell asleep in Heinsius's arms. The aspiring spirit ascended before the Infinite.

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  • If we next introduce a new function of f and write f .f 4(f) d f =Il (f), (23) then m m' II(f) will represent - (I) The work done by the attractive force on the particle m, while it is brought from an infinite distance from m' to the distance f from m'; or (2) The attraction of a particle m on a narrow straight rod resolved in the direction of the length of the rod, one extremity of the rod being at a distance f from m, and the other at an infinite distance, the mass of unit of length of the rod being m'.

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  • If we next write f II (f) d f =, P(z), (24) then 27rmagz) will represent - (I) The work done by the attractive force while a particle m is brought from an infinite distance to a distance z from an infinitely thin stratum of the substance whose mass per unit of area is Z o; (2) The attraction of a particle m placed Q 2 at a distance z from the plane surface of an infinite solid whose density is a.

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  • Multiplying this by m and by 7(f), we obtain for the work done by the attraction of this element when m is brought from an infinite distance to P1, maur1 fI I (f)dfdw.

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  • We may also write ur 1 = I +zu 1+ &c., since z is very small compared with u, and expressing u in terms of w by (25), (we find l 21- mv i fi(z) i I +z(c R w + ' R 2 w) do) = 27rmoti(z) I -f-ZZ (Ki + R2/ This then expresses the work done by the attractive forces when a particle m is brought from an infinite distance to the point P at a distance z from a stratum whose surface-density is a, and whose principal radii of curvature are R 1 and R2.

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  • This expression, when integrated, gives (I) the work done on a particle m while it is brought from an infinite distance to the point P, or (2) the attraction on a long slender column normal to the surface and terminating at P, the mass of unit of length of the column being m.

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  • Now 2 7rmpi,t(c) represents the attraction between a particle m and the plane surface of an infinite mass of the liquid, when the distance of the particle outside the surface is c. Now, the force between the particle and the liquid is certainly, on the whole, attractive; but if between any two small values of c it should be repulsive, then for films whose thickness lies between these values the tension will increase as the thickness diminishes, but for all other cases the tension will diminish as the thickness diminishes.

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  • If a i, a 2 represent the densities of the two infinite solids, their mutual attraction at distance z is per unit of area 21ra l a fZ '(z)dz, (30) or 27ra l 02 0(z), if we write f 4,(z)dz=0(z) (31) The work required to produce the separation in question is thus 2 7ru l a o 0 (z)dz; (32) and for the tension of a liquid of density a we have T = a f o 0 (z)dz.

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  • z, (39) K o = 4 7 (- 4, To = 3715 (40) The range of the attractive force is mathematically infinite, but practically of the order (31, and we see that T is of higher order in this small quantity than K.

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  • We get II (z) _ - n +1, «z)=++, zn+1 zn+3 27rzn+4 (41) K0 = n+4 n+3 fl+I 0 The intrinsic pressure will thus b infinite whatever n may be.

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  • If n +4 be positive, the attraction of infinitely distant parts contributes to the result; while if n+4 be negative, the parts in immediate contiguity act with infinite power.

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  • p. 113, 1887), of n+4 =o, Ko is also infinite.

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  • When the number of steps is infinite, the capillary pressure disappears altogether."

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  • These component deformations are in general infinite in number, of very wave-length and of arbitrary phase; but in the first stages of the motion, with which alone we are at present concerned, each produces its effect independently of every other, and may be considered by itself.

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  • Being is the Full i pes, plenum); not-Being is the Void (nEvov, vacuum), the infinite space in which moved the infinite number of atoms into which the single:Being of the Eleatics was broken up. These atoms are eternal and invisible; absolutely small, so small that their size cannot be diminished (hence the name IITOµos, "indivisible"); absolutely full and incompressible, they are without pores and entirely fill the space they occupy; homogeneous, differing only in figure (as A from N), arrangement (as AN from NA), position (as N is Z on its side), magnitude (and consequently in weight, although some authorities dispute this).

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  • An infinite number of atoms was carried downwards through infinite space.

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  • Atoms and void being infinite in number and extent, and motion having always existed, there must always have been an infinite number of worlds, all consisting of similar atoms, in various stages of growth and decay.

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  • The other colours result from various mixtures of these four, and are infinite in number.

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  • From the 12th to the 15th century inclusive, sealing was the ordinary process of authenticating legal documents; and during that period an infinite variety of seals was in existence.

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  • A similar idea is prominent in many philosophico-religious systems wherein the idea of God or the Infinite is, as it were, the union of the ego and the non-ego, of subject and object.

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  • The self of man is regarded as having limitations, whereas the Godhead is infinite and all-inclusive.

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  • In many mystical Oriental religions the perfection of the human self is absorption in the infinite, as a ripple dies away on the surface of water.

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  • He was at issue, however, with the atomistic materialism of Democritus in regard to its twin assumptions of absolute atoms and infinite space.

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  • The method by which the cycloid is generated shows that it consists of an infinite number of cusps placed along the fixed line and separated by a constant distance equal to the circumference of the rolling circle.

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  • Plucker finally (Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice.

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  • Huxley acknowledged an immeasurable and practically infinite divergence, ending in the present enormous psychological gulf between ape and man.

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  • philosophy from his theology, except as the former is contained in the early notes on the Mind, where he says that matter exists only in idea; that space is God; that minds only are real; that in metaphysical strictness there is no being but God; that entity is the greatest and only good; and that God as infinite entity, wherein the agreement of being with being is absolute, is the supreme excellency, the supreme good.

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  • One of these was a cartoon or monochrome painting of Adam and Eve in tempera, and in this, besides the beauty of the figures, the infinite truth and elaboration of the foliage and animals in the background are celebrated in terms which bring to mind the treatment of the subject by Albrecht Darer in his famous engraving done thirty years later.

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  • Thus mathematics assumes space as an existent infinite, without investigating in what sense the existence or the infinity of this Unding, as Kant called it, can be asserted.

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  • In the article Refraction it is shown that a ray of light traversing a homogeneous medium is deviated from its rectilinear path when it enters a medium of different refractive index; it is therefore readily seen that the path of a ray through continuously varying media is necessarily curvilinear, being compounded of an infinite number of infinitesimally small rectilinear deviations.

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  • And thus in Philo's conception the Logos is much more than "the principle of reason, informing the infinite variety of things, and so creating the World-Order"; it is also the divine dynamic, the energy and self-revelation of God.

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  • The Stoics indeed sought, more or less consciously, by their doctrine of the Logos as the Infinite Reason to escape from the belief in a divine Creator, but Philo, Jew to the core, starts from the Jewish belief in a supreme, self-existing God, to whom the reason of the world must be subordinated though related.

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  • He therefore insisted that England should be required not merely to pay damages for the havoc wrought by the " Alabama " and other cruisers fitted out for Confederate service in her ports, but that, for " that other damage, immense and infinite, caused by the prolongation of the war," the withdrawal of the British flag from this hemisphere could " not be abandoned as a condition or preliminary of such a settlement as is now proposed."

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  • Hence arise infinite and inextricable difficulties which obstruct the study of canon law; an immense field for controversy and litigation; a thousand perplexities of conscience; and finally contempt for the laws."' We know how the Vatican council had to separate without approaching the question of canonical reform; but this general desire for a recasting of the ecclesiastical code was taken up again on the initiative of Rome.

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  • At such time I found the method of Infinite Series; and in summer 1665, being forced from Cambridge by the plague, I computed the area of the Hyperbola at Boothby, in Lincolnshire, to two and fifty figures by the same method."

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  • The modern literature is infinite; perhaps the most exhaustive works are W.

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  • As reason has apprehended these two simultaneous phenomena, attention and sensation, and led us The immediately to conceive the two sorts of distinct they are related, so, from the notion of this limitation, we find it impossible under the same guide not to conceive a supreme cause, absolute and infinite, itself the first and last cause of all.

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  • Charge of from each other and from the infinite cause.

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  • It is preoccupied by the infinite.

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  • The finite and the infinite become two real correlatives in the relation of cause and product.

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  • This is the third and highest stage of development, the relation of the finite and the infinite.

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  • The East typifies the infinite, Greece the finite or reflective epoch, the modern era the stage of relation or correlation of infinite and finite.

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  • Y g Y g infinite or causes, correlative and reciprocally finite, to which absolute.

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  • Cousin Relations was opposed to Kant in asserting that the uncondi- to Kant, tioned in the form of infinite or absolute cause is but Schelling a mere unrealizable tentative or effort on the part of and Hegel.

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  • The absolute or infinite - the unconditioned ground and source of all reality - is yet apprehended by us as an immediate datum or reality; and it is apprehended in consciousness - under its condition, that, to wit, of distinguishing subject and object, knower and known.

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  • The correlation of the ideas of infinite and finite does not necessarily imply their correality, as Cousin supposes; on the contrary, it is a presumption that finite is simply positive and infinite negative of the same - that the finite and infinite are simply contradictory relatives.

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  • A study of the few sentences under this head might have obviated the trifling criticism of Hamilton's objection which has been set afloat recently, that the denial of a knowledge of the absolute or infinite implies a foregone knowledge of it.

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  • Once applied to the facts at all, it would drive us beyond the first antecedent or term of antecedents of volition to a still further cause or ground - in fact, land us in an infinite regress of causes.

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  • This is a mere paralogism; we can never infer either absolute or infinite from relative or finite.

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  • And whether the laws of our reason are the laws of all intelligence and being - whether and how we are to relate our fundamental, intellectual and moral conceptions to what is beyond our experience, or to an infinite being - are problems which Cousin cannot be regarded as having solved.

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  • In many examples of apparent plasticity it can be shown that this effect has been produced by an infinite number of minute slippings within the rock substance.

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  • Between this opening and this close the pageant of history and of legend, marshalled and vivified by the will and the hand of the poet, ranges through an infinite variety of action and passion, of light and darkness, of terror and pity, of lyric rapture and of tragic triumph.

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  • A curve is a line, or continuous singly infinite system of points.

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  • Obviously the number of such geometrical or kinematical definitions is infinite.

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  • The branch, whether re-entrant or infinite, may have a cusp or cusps, or it may cut itself or another branch, thus having or giving rise to crunodes or double points with distinct real tangents; an acnode, or double point with imaginary tangents, is a branch by itself, - it may be considered as an indefinitely small re-entrant branch.

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  • Names may also be used for the different forms of infinite branches, but we have first to consider the distinction of hyperbolic and parabolic. The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other.

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  • As mentioned with regard to a branch generally, an infinite branch of any kind may have cusps, or, by cutting itself or another branch, may have or give rise to a crunode, &c.

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  • It may be remarked generally that there are at most three infinite branches, and that there may besides be a re-entrant branch or oval.

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  • There are two non-singular kinds, the one with, the other without, an oval, but each of them has an infinite (as Newton describes it) campaniform branch; this cuts the axis at right angles, being at first concave, but ultimately convex, towards the axis, the two legs continually tending to become at right angles to the axis.

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  • The oval may unite itself with the infinite branch, or it may dwindle into a point, and we have the crunodal and the acnodal forms respectively; or if simultaneously the oval dwindles into a point and unites itself to the infinite branch, we have the cuspidal form.

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  • The ideal Akil is grave, calm and dignified, with an infinite capacity of keeping a secret, and a devotion that knows no limits to the interests of his creed.

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  • INFINITE (from Lat.

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  • Mundane distances become trivial when compared with the distance from the earth of the sun and still more of other heavenly bodies: hence we infer infinite space.

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  • The same problem, variously expressed, has engaged the attention of philosophers throughout the ages_ In Christian theology God is conceived as infinite in power, knowledge and goodness, uncreated and immortal: in some Oriental systems the end of man is absorption into the infinite, his perfection the breaking down of his human limitations.

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  • Sir William Hamilton's " philosophy of the unconditioned," and, Herbert Spencer's doctrine of the infinite " unknowable "); if it is argued that knowledge of a thing arises only from the recognition of its differences from other things (i.e.

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  • from its limitations), it follows that knowledge of the infinite is impossible, for the infinite is by hypothesis unrelated.

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  • With this conception of the infinite as absolutely unconditioned should be compared what may be described roughly as lesser infinities which can be philosophically conceived and mathematically demonstrated.

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  • Thus a point, which is by definition infinitely small, is as compared with a line a unit: the line is infinite, made up of an infinite number of points, any pair of which have an infinite number of points between them.

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  • The line itself, again, in relation to the plane is a unit, while the plane is infinite, i.e.

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  • made up of an infinite number of lines; hence the plane is described as doubly infinite in relation to the point, and a solid as trebly infinite.

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  • This is Spinoza's theory of the infinitely infinite," the limiting notion of infinity being of a numerical, quantitative series, each term of which is a qualitative determination itself quantitatively little, e.g.

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  • A similar relation exists in thought between the various grades of species and genera; the highest genus is the " infinitely infinite," each subordinated genus being infinite in relation to the particulars which it denotes, and finite when regarded as a unit in a higher genus.

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  • In mathematics, the term " infinite " denotes the result of increasing a variable without limit; similarly, the term " infinitesimal," meaning indefinitely small, denotes the result of diminishing the value of a variable without limit, with the reservation that it never becomes actually zero.

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  • .; the discussion of these so-called infinite sequences is given in the articles Series and Function.

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  • If human understanding cannot fully solve the infinite problem of the universe, man may at least see that at no stage of his finite experience is he necessarily the sport of chance, and that he can practically secure his own wellbeing.

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  • Locke says that our " ideas " all come, either from the five senses or from reflective consciousness; and he proposes to show that even those concerned with the Infinite depend at last on one or other of these two sources: our " complex ideas " are all made up of " simple ideas," either from without or from within.

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  • The modifications of which these are susceptible he reports to be " inexhaustible and truly infinite, extension alone affording a boundless field to the mathematicians."

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  • When we reflect on immensity and eternity, we find them negations of all that is imaginable; and that whether we try infinite addition or infinite subdivision.

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  • After all our additions we are as far from the infinite idea as we were at the beginning.

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  • This is cautiously qualified thus in a letter to Anthony Collins, written by Locke a few months before he died: " Though I call the thinking faculty in me ` mind,' yet I cannot, because of that name, equal it in anything to that infinite and incomprehensible Being, which, for want of right and distinct conceptions, is called ` Mind ' also."

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  • Porion and Deherain have shown 1 the "infinite superiority" in yield over the ordinary wheats of a particular square-headed variety grown on rich soil in the north of France.

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  • Six years later he conducted a large fleet of warships to England, which did infinite damage, but failed to capture London.

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  • The ultimate sanctions of the moral code were the infinite rewards and punishments awaiting the immortal soul hereafter; but the church early felt the necessity of withdrawing the privileges of membership from apostates and allowing them to be gradually regained only by a solemn ceremonial expressive of repentance, protracted through several years.

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  • " The idea," he says, " of a Supreme Being, infinite in power, goodness, and wisdom, whose workmanship we are, and upon whom we depend, and the idea of ourselves, as understanding rati as are clear in us, would, I suppose, i pursued, afford such foundations of our d as might place morality among the sciences capable of demonstration; wherein, I doubt not, but from self-evident propositions, by necessary consequences as incontestable as those in mathematics, the measure of right and wrong might be made out."

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  • It is known that, while infinite diversity is found among the bodies of the universe, there are also common characteristics throughout its whole extent.

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  • Imagining, as we may well do, that the radius of this sphere is infinite - then every direction, whatever the origin, may be represented by a point on its surface.

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  • Another corollary is that in the case of a body moving in a parabolic orbit the velocity at any moment is that which would be acquired by the body in falling from an infinite distance to the place it occupies at the moment.

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  • In this case the variation will be simply periodic, The value of any element of the planet's motion will generally be represented by the sum of an infinite series of such periodic quantities, having different periods.

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  • If 1 be the mean longitude of the planet whose motion we are considering, and 1' that of the attracting planet affecting it, the periodic inequalities of the elements as well as of the co-ordinates of the attracted planet, may be represented by an infinite series of terms like the following: a sin (l' - l)+b sin (2l' - l)+c sin (l'- 2l)+&c.

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  • The longitudes, latitudes and radii vectores of a planet, being algebraically expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions.

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  • The curve is symmetrical about the axis of x, and consists of two infinite branches asymptotic to the line BT and forming a cusp at the origin.

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  • The expressions for the longitude, latitude `and parallax appear as an infinite trigonometric series, in which the coefficients of the sines and cosines are themselves infinite series proceeding according to the powers of the above small numbers.

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  • The dominant thought is the infinite and transcendent sovereignty of God, to know whom is the supreme end of human endeavour.

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  • It is above all the substance of religious feeling, which is the immediate consciousness of the unity of the world, of the absolute oneness behind the infinite multiplicity of contrasts; indeed, it is the religious conviction of the unity which is the best guarantee of the truth of the suppositions of philosophy.

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  • The divine omnipotence is quantitatively represented by the sum of the forces of nature, and qualitatively distinguished from them only as the unity of infinite causality from the multiplicity of its finite phenomena.

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  • Schleiermacher's psychology takes as its basis the phenomenal dualism of the ego and the non-ego, and regards the life of man as the interaction of these elements with their interpenetration as its infinite destination.

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  • In his earlier days he called it a feeling or intuition of the universe, consciousness of the unity of reason and nature, of the infinite and the eternal within the finite and the temporal.

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  • The specific feature of Christianity is its mediatorial element, its profound feeling of the striving of the finite individual to reach the unity of the infinite whole, and its conception of the way in which Deity deals with this effort by mediatorial agencies, which are both divine and human.

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  • He states the various proofs for the existence of an immaterial, infinite, supreme Being, asserts that this Being is the author of the visible universe, and strongly defends the doctrine of the foreknowledge and particular providence of God.

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  • But the justice of God demands satisfaction; and as an insult to infinite honour is in itself infinite, the satisfaction must be infinite, i.e.

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  • The merit of it is therefore infinite; God's justice is thus appeased, and His mercy may extend to man.

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  • (2) In like manner the Many must be numerically both finite and infinite - numerically finite, because there are as many things as there are, neither more nor less; numerically infinite, because, that any two things may be separate, the intervention of a third thing is necessary, and so on ad infinitum.

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  • Hence, that a body may pass from one point to another, it must traverse an infinite number of divisions.

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  • But an infinite distance (which Zeno fails to distinguish from a finite distance infinitely divided) cannot be traversed in a finite time.

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  • Thus Zeno again confounds a finite distance infinitely divided with an infinite distance.

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  • Achilles, on the supposition that his speed is ten times that of the tortoise, must traverse an infinite number of spaces - 1000 ft., loo ft., to ft., &c. - and the tortoise must traverse an infinite number of spaces - loo ft., to ft., I ft., &c. - before they reach the point, distant from their starting-points III I y ft.

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  • The former should be regarded as asserting that the whole is, not temporally, but logically, subsequent to the part, and that therefore there is an infinite regress in the notion of a whole which is infinitely divisible - a view which at any rate demands a serious refutation.

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  • Dr Hahn tries to prove (by philology's " artful aid ") that the name really means " red dawn," and is a Hottentot way of speaking of the infinite.

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  • If we grant, however, for the sake of argument, that the early Hottentots worshipped the infinite under the figure of the dawn, and that, by forgetting their own meaning, they came to believe that the words which really meant " red dawn" meant " wounded knee " we must still admit that the devout have assigned to their deity all the attributes of an ancestral sorcerer.

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  • This may be taken either in a refined sense, as if Aditi were the " infinite " region from which the solar deities rise,' or we may hold with the Taittirya-Brahmana' that Aditi was a female who, being desirous of offspring, cooked a brahmandana offering for the Sadhyas.

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  • More valid instances of the anticipation of modern discoveries may be found in his prevision that a small annual parallax would eventually be found for some of the fixed stars, and that extra-Saturnian planets would at some future time be ascertained to exist, and in his conviction that light travels with a measurable, although, in relation to terrestrial distances, infinite velocity.

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  • (On this hypothesis, it may be explained by regarding the air as an electrolyte of infinite specific resistance.) It is also profoundly modified by the state of the exposed surfaces, a coating of oxide on the copper greatly increasing the effect, as it would in a voltaic cell.

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  • Religious thinkers are faced by the problem of the Creator and the created, and the necessity for formulating a close relationship between God and man, the Infinite and Perfect with the finite and imperfect.

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  • Campbell) so far as to postulate a divine element in human beings, so definitely bridging over the gap between finite and infinite which was to some extent admitted by the bulk of early Christian teachers.

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  • In support of such a view are adduced not only the metaphysical difficulty of postulating any relationship between the infinite and the purely finite, but also the ethical 1 P. G., tom.

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  • how a merely human being could appreciate the nature of or display divine goodness - and the epistemological problem of explaining how finite mind can cognize the infinite.

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  • The later sect of the Zervanites held that both were visible manifestations of the primeval principle Zruvan akarana (Infinite Time).

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  • In the next reign, however, both father and son caused infinite trouble to loyal servants of Egypt like Rib-Addi, governor of Gubla (Gebal).

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  • To his infinite chagrin, during this brief absence his father died.

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  • According to the amount of union of the lobes and the unequal development of different parts of their surface an infinite variety of forms is produced.

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  • He was a soldier of infinite personal courage and daring, of striking military energy, initiative and resource; a high, pure and single character, dwelling much in the region of the unseen.

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  • You have infinite immortals at your disposal.

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  • The group left the Jeep and spent more than an hour on foot with Cynthia taking infinite care with each of her photos.

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  • Cynthia, in her infinite wisdom, arranged a generous monetary scale of chores-for-bucks that seemed to take care of the problem.

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  • Communication is a gestalt, made up of gesture, tone and the infinite vagaries of the living face.

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  • Career: Willem's main academic achievement was to solve Einstein's field equations for an infinite rotating cylinder.

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  • Against this conception Critchley has articulated an ethical discourse based on infinite alterity as a demand that calls us to engage with the world.

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  • The ' exclusive ' option then raises the attack power to 99.9 and gives infinite ammo.

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  • infinite ammo free mode: Complete all stages with a 100% rating.

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  • They demonstrate how to design a one-dimensional cellular automaton that supports infinite families of signals of different speeds.

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  • axiom of infinity - that there is an infinite set?

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  • bluish glow, a sort of blue mist - at an infinite distance below.

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  • He also considered a list of infinite cardinals: where each is the smallest cardinal which is strictly greater than.

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  • ceil rate is not infinite and may in fact be quite low.

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  • We have a number of pieces, like those in drafts, set out on an infinite chessboard.

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  • To a considerable extent, finite and infinite combinatorics are parts of the same subject.

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  • And all this without bargain or condition, and unconstrained by any motive save His own infinite compassion.

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  • Man's sin was brought into the presence of infinite holiness, a divine compassion and a perfect redemption.

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  • comprehend the infinite.

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  • Why are you so conceited that you think your life is worth anything at all to an infinite God?

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  • These are infinite decimals in which the digits are uniformly distributed.

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  • It gives a continuous curve which is of infinite length and nowhere differentiable.

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  • An alternative method is the application of the frontal method at infinite dilution.

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  • Otherwise an infinite sequence of events must have already elapsed.

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  • Second-order equations: wave, diffusion, Laplace equations; traveling waves, d'Alembert solution, 1-D infinite and semi- infinite regions.

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  • fathomless depths seem to hold infinite nameless creatures of the night.

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  • Furthermore, it is not possible for the infinite and finite and finite to mix, making an infinite finite.

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  • The interpretation we produced was itself either finite or denumerably infinite.

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  • For them, the realities of a very finite planet simply do not equate with their conventional wisdoms of infinite growth.

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  • Indeed, we only have a sense of the infinite, or what is not finite, or what is not finite, from various created finite viewpoints.

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  • As speculative computations may be infinite, while mandatory ones remain finite, while mandatory ones remain finite, divergence should be defined with the greatest care.

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  • His fulness is an infinite fulness; and he is infinitely sweet, as well as infinitely full.

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  • Its place in ethics has to be taken by the idea of infinite goodness.

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  • But He's not just the God of infinite holiness and justice; He's a God of amazing love.

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  • Why does defining a set make the actual infinite a reality?

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  • For Aristotle all the elements in an actual finite exist simultaneously, whereas a potential infinite is realized over time by addition or division.

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  • infinite regress of nested beliefs.

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  • infinite wisdom they have recently changed the format in which these are sent.

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  • infinite loop.

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  • infinite mercy To thy holy presence.

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  • infinite recursions, we must distinguish between the two different types of mappings.

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  • infinite patience, the minutes end here.

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  • Note that all these sets have a countably infinite number of members.

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  • Consider the language obtained from 1 K = by adding a denumerably infinite stock of new individual constants c 0, c 1, .

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  • However, if these sets are considered as single rep-tiles, then I cannot demonstrate that the full set of rep-tiles is uncountably infinite.

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  • There is a seemingly infinite textural variety in these pieces.

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  • Anchors occur throughout all of our sensory channels in a potentially infinite number of ways.

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  • In the Lear CD there are an almost infinite number of pathways through the material.

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  • The question is if G-d's knowledge is infinite, how can something infinite be placed in something finite, the written torah.

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  • DVD run time is 30 minutes however, with looping it becomes infinite.

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  • infinite in extent.

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  • infinite in number, then these two " probabilities " are identical.

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  • The finite nature of the human mind cannot grasp and comprehend the infinite.

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  • It is beyond finite minds to understand the infinite.

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  • This paper offers a glimpse of how Euler used infinitesimals and infinite series to compute differentials for the elementary functions.

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  • But then this was a fellow of " excellent fancy " as well as " infinite jest.

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  • l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.

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  • lass="ex">l p = h. If the momentum of the electrons is zero, then the wavelength they have is infinite.

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  • Noreve the international leader of top-of-the-line leather cases for Hi-Tech devices offers you infinite possibilities for the customization of your products.

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  • This is provided for network software to avoid infinite delivery loops.

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  • Dwelling in a womb of blood and brimstone, my days became malleable, my nights infinite.

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  • The research will focus on the analysis of infinite dimensional Hamiltonian systems in continuum mechanics.

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  • mechanizethis to investigate some new geometric relations as well as ways of rigorously mechanizing geometric proofs that involve infinitesimal and infinite arguments.

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  • And be brought by thine infinite mercy To thy holy presence.

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  • In general some of the bands may collapse into points, which represent eigenvalues of infinite multiplicity of the operator under consideration.

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  • You are a finite concept that represents the negation of your own infinite essence.

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  • Suddenly the machine emitted a noise that was like every sound ever made in the world put together, infinite frequencies.

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  • numberless forms of infinite variety, visible and invisible.

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  • observable universe is neither static, nor infinite.

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  • Current astronomical observations can't really tell us whether the world really did have an infinite past or just a finite one.

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  • Since there is an infinite ordinal, every finite ordinal is a set and the first infinite ordinal ω is a set.

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  • Since there is an infinite ordinal, every finite ordinal is a set and the first infinite ordinal ω is a set.

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  • Similar systems, infinite chains of linearly coupled nonlinear oscillators, are also discussed.

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