Problem sentence example

problem
  • The problem wasn't Dulce or his father.

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  • To discover and define those laws is the problem of history.

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  • The problem is that the poor don't have enough money to afford the food.

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  • I had hoped that you would resolve your problem, but it seems to have no end.

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  • Neither of them lawyers had a problem with me either.

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  • Maybe his problem was a girlfriend.

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  • To me, that's problem number one.

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  • She had created this problem and now it was hers to face alone.

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  • She does have a problem with my keeping secrets from Julie.

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  • What's the problem with this jury business?

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  • This was Howie's problem, not ours.

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  • He knows the problem.

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  • Of course, a stream running through, or an island in the pond, would make the problem much more complicated.

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  • The father had some health problem, if I remember.

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  • When we consider the costs of all the wrong decisions ever made—a calculation I don't even know how to approach—we will think of it as a diminishing problem receding into the past.

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  • A bright idea, however, shot into my mind, and the problem was solved.

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  • The woman has a serious problem.

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  • No, that wasn't the only problem.

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  • I want to be able to focus on solving this problem, not worrying about what might be said or done to you.

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  • Problem is, it's a big state.

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  • What is this problem you speak of?

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  • I want to know what the problem is.

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  • Fred asked the question like a learned professor, speculating on a universal problem of time, space and the creation of the universe.

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  • The biggest problem was some hypothermia.

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  • Four years later Varley patented his artificial cable, which was the first near approach to a successful solution of the duplex problem on the principle now adopted.

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  • It'd never been a problem when it was just him.

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  • If Gerald was his problem, he gave no indication when they were together.

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  • Alex was momentarily taken by surprise, but appeared to have no problem maintaining his erect status in the saddle.

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  • I guess that could get to be a problem with a spouse.

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  • The problem is that he is making poor choices.

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  • He would tell her about his problem in his own timeframe – and maybe that would be when he felt she was less of a burden.

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  • The issue of a phone had virtually disappeared, but in its place was a fashion problem.

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  • The problem was that she hadn't been able to reach him, but she didn't want to start out nagging at him.

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  • We have a problem and I thought you would like to help solve it.

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  • You would do best to take care of your own problem now.

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  • The purpose of his paper was to show that there is no problem if the axis is moved to the left.

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  • The ancient geometry, as we know it, is a wonderful monument of ingenuity - a series of tours de force, in which each problem to all appearance stands alone, and, if solved, is solved by methods and principles peculiar to itself.

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  • Each problem was something unique; the elements of transition from one to another were wanting; and the next step which mathematics had to make was to find some method of reducing, for instance, all curves to a common notation.

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  • When that was found, the solution of one problem would immediately entail the solution of all others which belonged to the same series as itself.

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  • The problem of the curves is solved by their reduction to a problem of straight lines; and the locus of any point is determined by its distance from two given straight lines - the axes of co-ordinates.

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  • In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de) Fermat (1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661).

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  • It dashes at once into the middle of the subjects with the examination of a problem which had baffled the ancients, and seems as if it were tossed at the heads of the French geometers as a challenge.

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  • The disturbing conditions of will, life and organic forces are eliminated from the problem; he starts with the clear and distinct idea of extension, figured and moved, and thence by mathematical laws he gives a hypothetical explanation of all things.

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  • Such explanation of physical phenomena is the main problem of Descartes, and it goes on encroaching upon territories once supposed proper to the mind.

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  • Caesar had projected remedial measures, but (as in so many cases) had never been able to carry them out, and it was not until the time of Claudius that the problem was approached.

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  • In connexion with the problem of universals, he held that the diversity of individuals depends on the quantitative division of matter (materia signata), and in this way he attracted the criticism of the Scotists, who pointed out that this very matter is individual and determinate, and, therefore, itself requires explanation.

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  • He understood their problem and it helped galvanize him to volunteer to help them.

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  • The derrick crane introduces a problem for which many solutions have been sought, that of preventing the load from being lifted or lowered when the jib is pivoted up or down to alter the radius.

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  • The only new problem introduced is the simultaneous transmission of two messages in the same direction; this is sometimes ruplex called " diplex transmission."

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  • The only other suggested solution of the problem of isolation in connexion with wireless telegraph stations was given by Anders Bull (Electrician, 1901, 46, p. 573).

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  • A problem of great importance in connexion with electric wave telegraphy is that of limiting the radiation to certain directions.

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  • Another closely connected problem is that of locating or ascertaining the direction of the sending station.

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  • Marconi, however, gave in 1906 the first really practical solution of the problem by the use of bent transmitting and receiving antennae.

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  • Braun also gave an interesting solution of the problem of directive telegraphy.'

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  • The term " telephony " was first used by Philipp Reis of Friedrichsdorf, in a lecture delivered before the Physical Society of Frankfort in 1861.1 But, although this lecture and Reis's subsequent work received considerable notice, little progress was made until the subject was taken up between 1874 and 1876 by Alexander Graham Bell, a native of Edinburgh, then resident in Boston, Mass., U.S.A. Bell, like Reis, employed electricity for the reproduction of sounds; but he attacked the problem in a totally different manner.

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  • The problem, however, of constructing a deep-sea cable satisfactorily, with suitable inductance coils inserted at short distances apart, is a difficult one, and one which it cannot be said has been solved.

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  • It may help us if we rapidly review at this point the leading types of philosophy in their application to the theistic problem.

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  • It is a problem for empiricism; given a world where nothing but phenomenal sequences exist, to account for moral ideals.

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  • The problem has altered its form.

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  • Free will had not yet been formulated as a problem.

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  • Free will is shaping itself towards discussion in Aristotle's Ethics, but is hardly yet a formulated problem.

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  • From this theological entanglement the problem of free will did not escape for long centuries.

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  • The problem of the origin of the world was the first to engage man's speculative activity.

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  • Nor was this line of inquiry pursued simply as a step in the more practical problem of man's final destiny.

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  • As long as the problem was conceived in this simple manner there was, of course, no room for the idea of a necessary self-conditioned evolution.

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  • In Spinoza's pantheistic theory of the world, which regards thought and extension as but two sides of one substance, the problem of becoming is submerged in that of being.

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  • Yet by his very mode of solving the problem he is led on to consider the nature of the world-process.

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  • Like Schelling, Hegel conceives the problem of existence as one of becoming.

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  • As Ludwig Noire observes, Schopenhauer has no feeling for the problem of the origin of organic beings.

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  • In the Origin of Species, and in his other numerous and important contributions to the solution of the problem of biological evolution, Darwin confined himself to the discussion of the causes which have brought about the present condition of living matter, assuming such matter to have once come into existence.

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  • Mrs Stowe passed eighteen years in Cincinnati under conditions which constantly thrust the problem of human slavery upon her attention.

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  • Naturally he felt that the prevalence of Christianity was incompatible with his ideal of Roman prosperity, and therefore that the policy of the Flavian emperors was the only logical solution of an important problem.

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  • The question of the distribution of this stored energy to the separate protoplasts of the plant can be seen to be the same problem as the distribution of the food.

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  • The problem is a very difficult one and cannot be regarded as definitely settled, but it is difficult to understand why all this additional complexity in the division of the nucleus should be necessary if the final result is only a quantitative separation of the chromatin.

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  • The fitting of the oekumene to the sphere was the second theoretical problem.

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  • His argument as to the narrowness of the sea between West Africa and East Asia, from the occurrence of elephants at both extremities, is difficult to understand, although it shows that he looked on the distribution of animals as a problem of geography.

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  • The distribution of living organisms is a complex problem, a function of many factors, several of which are yet but little known.

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  • Tiedemann, 2 the Heidelberg anatomist, who has been generally ignored, although he surpassed many a recent zoogeographer by the wide view he took of the problem; in fact he was the first to connect distribution with environmental or bionomic factors; e.g.

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  • In 1826 the idea occurred to him of attacking this problem by means of pendulum experiments at the top and bottom of a deep mine.

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  • Riccati's name is best known in connexion with his problem called Riccati's equation, published in the Ada Eruditorum, September 1724.

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  • Antisthenes adopted this principle in its most literal sense, and proceeded to explain "knowledge" in the narrowest terms of practical action and decision, excluding from the conception everything except the problem of individual will realizing itself in the sphere of ordinary existence.

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  • In logic Antisthenes was troubled by the problem of the One and the Many.

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  • These two religions anticipated the discussion of the problem of faith and reason in the Christian church.

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  • In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him.

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  • In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and in 1754 he solved the problem of the precession of the equinoxes, determined its quantity and explained the phenomenon of the nutation of the earth's axis.

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  • Whatever be the true explanation of this problem, it is certain (1) that Peisistratus was regarded as a leading soldier, and (2) that his position was strengthened by the prestige of his family.

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  • So far he is in general agreement with Anaximander, but he differs from him in the solution of the problem, disliking, as a poet and a mystic, the primary matter which satisfied the patient researcher, and demanding a more vivid and picturesque element.

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  • For there is all the difference in the world between using a body of general theory as an indication of the factors to be considered in the study of a special problem, and undertaking special studies with a view to testing the general theory.

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  • Then, on Dec. 28, Monro received the expected sanction for evacuating that area also, and Birdwood promptly grappled with this fresh problem.

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  • The Belopoiica (on engines of war) is extant in Greek, and both this and the Mechanics contain Hero's solution of the problem of the two mean proportionals.

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  • A certain number of the most promising of these, from the purely optical point of view, had unfortunately to be abandoned for practical use owing to their chemical instability, and the problem of Fraunhofer, viz.

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  • Colin Maclaurin (1698-1746) and John Bernoulli (1667-1748), who were of this opinion, resolved the problem by more direct methods, the one in his Fluxions, published in 1742, and the other in his Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis pure mechanicis, which forms the fourth volume of his works.

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  • This problem he had attacked in 1774, and in subsequent years he made various attempts to discover the acid which, under the influence of his oxygen theory, he expected would be formed.

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  • How the small rival districts with their petty kings were united Hebrew into a kingdom under a single head is a disputed question; the stages from the half-Hittite, half-Egyptian land to the independent Hebrew state with its national god are an unsolved problem.

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  • To reinterpret all these features as mere symbols, the lumber of ancient days, is to avoid the problem of their introduction into the Temple, and to assume an advance of popular thought which is not confirmed by the retention and fresh developments of the old ideas both in the pseudepigraphical literature and in the literature of Rabbinical Judaism.'

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  • But a really economical solution of the problem was first definitely found in 1872 by Ernest Solvay, as the result of investigations begun about ten years previously.

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  • Thus the problem of the "thing-initself" is dismissed from the inquiry, and philosophy is limited to the sphere of pure thought.

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  • We need devices, indeed, to determine priority or superior claim to be " better known absolutely or in the order of nature," but on the whole the problem is fairly faced.4 Of science Aristotle takes for his examples sometimes celestial physics, more often geometry or arithmetic, sometimes a concrete science, e.g.

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  • In any case, however, the problem as to first principles remains fundamental.

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  • The epistemological problem as such was out of the purview.

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  • When Descartes, having faithfully and successfully followed the mathematico-physical inquiry of his more strictly scientific predecessors, found himself compelled to raise the question how it was possible for him to know what in truth he seemed to know so certainly, the problem entered on a new phase.

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  • This resolution or analysis into simple, because clear and distinct, elements may be brought to a standstill again and again by obscurity and indistinctness, but patient and repeated revision of all that is included in the problem should bring the analytic process to fruition.

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  • Locke, when Cartesianism had raised the problem of the contents of consciousness, and the spirit of Baconian positivism could not accept of anything that bore the ill-omened name of innate ideas, elaborated a theory of knowledge which is psychological in the sense that its problem is how the simple data with which the individual is in contact in sensation are worked up into a system.

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  • With Leibnitz, on the other hand, the logical problem holds the foremost place in philosophical inquiry.

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  • In recognizing, further, that the relation of an actual individual fact to its sufficient ground was not reducible to identity, he set a problem diversely treated by Kant and Herbart.

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  • If logic were treated as merely formal, the stress of the problem of knowledge fell upon the determination of the Log and processes of thepsychological mechanism.

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  • But much more it belongs to his transformation of the epistemological problem, and to the suggestiveness of his philosophy as a whole for an advance in the direction of a speculative construction which should be able to cancel all Kant's surds, and in particular vindicate a " ground of the unity of the supersensible which lies back of nature with that which the concept of freedom implies in the sphere of practice," I which is what Kant finally asserts.

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  • Schleiermacher's formula obviously ascribes a function in knowledge to thought as such, and describes in a suggestive manner a duality of the intellectual and organic functions, resting on a parallelism of thought and being whose collapse into identity it is beyond human capacity to grasp. It is rather, however, a statement of a way in which the relations of the terms of the problem may be conceived than a system of necessity.

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  • Moreover, few of the writers who, whatsoever it was that they baptized with the name of logic, were at least earnestly engaged in an endeavour to solve the problem of knowledge within a circle of ideas which was on the whole Kantian, were under the dominance of a single inspiration.

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  • Of the formal-symbolic logic all that falls to be said here is, that from the point of view of logic as a whole, it is to be regarded as a legitimate praxis as long as it shows itself aware of the sense in which alone form is susceptible of abstraction, and is aware that in itself it offers no solution of the logical problem.

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  • A situation involving a need of adaptation to environment arises and the problem it sets must be solved that the will may control environment and be justified by success.

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  • In the next year (16 B.C.), however, Augustus was suddenly called away from Rome to deal with a problem which engrossed much of his attention for the next twenty-five years.

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  • The exact determination of the appearances in any given case is a mere problem of convergents to a continued fraction.

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  • The question of the economic development of the state, and of trade to the Orient, the views of the mercenary labour-contractor and of the philanthropist, the factor of " upper-race " repugnance, the " economic-leech" argument, the " rat-rice-filth-and-opium " argument, have all entered into the problem.

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  • In their development the problem, as it were, worked out least tainted by foreign interference, showing at the same time a rich variety in detail; and it may also be said that their constitutional and economic history has been more thoroughly investigated than any other.

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  • The problem is, how this state of things arose.

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  • Jesus is the " Son of God "; and the great problem of theology becomes explicit.

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  • To them, therefore, Christianity presented itself not primarily as the religion of a redemption through the indwelling power of a risen saviour, as with Paul, nor even as the solution of the problem how the sins of men could be forgiven, but as the reconciliation of the antinomy of the intellect, indicated above.

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  • I also see the pace of problem solving—and change in general—accelerating at an astonishing rate.

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  • If I suggest her leaving a problem in arithmetic until the next day, she answers, "I think it will make my mind stronger to do it now."

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  • Disregarding the officers' orders, the soldiers stood leaning against their stretchers and gazing intently, as if trying to comprehend the difficult problem of what was taking place before them.

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  • This problem seemed to the ancients insoluble.

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  • The declared aim of the author 1 was to offer a complete solution of the great mechanical problem presented by the solar system, and to bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables.

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  • C. Maclaurin, Legendre and d'Alembert had furnished partial solutions of the problem, confining their 1 Annales de chimie et de physique (1816), torn.

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  • Finally, in a celebrated memoir, Theorie des attractions des spheroides et de la figure des planetes, published in 1785 among the Paris Memoirs for the year 1782, although written after the treatise of 1784, Laplace treated exhaustively the general problem of the attraction of any spheroid upon a particle situated outside or upon its surface.

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  • The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but Laplace first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum.

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  • The one is a problem of interpolation, the other a step towards the solution of an equation in finite differences.

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  • The problem of finding the sum of r terms is aided by graphic representation, which shows that the terms may be taken in pairs, working from the outside to the middle; the two cases of an odd number of terms and an even number of terms may be treated separately at first, and then combined by the ordinary method, viz.

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  • The progress of analytical geometry led to a geometrical interpretation both of negative and also of imaginary quantities; and when a " meaning " or, more properly, an interpretation, had thus been found for the symbols in question, a reconsideration of the old algebraic problem became inevitable, and the true solution, now so obvious, was eventually obtained.

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  • The particular problem - a heap (hau) and its seventh makes 19 - is solved as we should now solve a simple equation; but Ahmes varies his methods in other similar problems. This discovery carries the invention of algebra back to about 1700 B.C., if not earlier.

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  • But whereas Diophantus aimed at obtaining a single solution, the Hindus strove for a general method by which any indeterminate problem could be resolved.

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  • Although Pell had nothing to do with the solution, posterity has termed the equation Pell's Equation, or Problem, when more rightly it should be the Hindu Problem, in recognition of the mathematical attainments of the Brahmans.

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  • Archimedes' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.

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  • Korosec in the name of the Czech and Yugoslav Clubs unreservedly rejected it and claimed that the future of both nations was an international problem which only the future Peace Conference could solve.

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  • America pointedly defined the Adriatic problem as a test case, but amid the pressure of other affairs it was allowed to drift.

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  • During the final stages of the German treaty the Adriatic problem was once more shelved, until on June 29 and July 6 armed conflicts took place in the streets of Fiume between Italian and French soldiers, resulting in several deaths.

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  • On the one hand, the true method of arriving at a knowledge of the genealogical tree was recognized as lying chiefly in attacking the problem of the genealogical relationships of the smallest twigs of the tree, and proceeding from them to the larger branches.

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  • We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a function of r, the distance from the origin.

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  • In order to apply these ideas to the investigation of the secondary wave of light, we require the solution of a problem, first treated by Stokes, viz.

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  • On the electromagnetic theory, the problem of diffraction becomes definite when the properties of the obstacle are laid down.

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  • Throughout his life he paid great attention to the "rare earths" and the problem of separating and distinguishing them; in 1878 he extracted ytterbia from what was supposed to be pure erbia, and two years later found gadolinia and samaria in the samarskite earths.

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  • The conditions of the problem were such that unless Great Britain were to accept a humiliating rebuff, any correspondence, however skilfully conducted, was bound to bring into greater prominence the standing causes of offence between the two sides.

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  • For the problem of Arabic antiquities in Rhodesia see Rhodesia and Zimbabwe.

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  • This problem was taken up by Chrysippus, who admitted that he could not solve it.

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  • Taking up the idea of a divine education of the human race, which Lessing and Herder had made so familiar to the modern mind, and firmly believing that to each of the leading nations of antiquity a special task had been providentially assigned, Ewald felt no difficulty about Israel's place in universal history, or about the problem which that race had been called upon to solve.

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  • The principal political problem before the government of Peru was the ownership of the territories of Tacna and Arica.

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  • Archbishop Peckham, or Pisanus, in his Perspectiva Communis (1279), and Vitello, in his Optics (1270), also attempted the solution of Aristotle's problem, but unsuccessfully.

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  • Leonardo also discussed the old Aristotelian problem of the rotundity of the sun's image after passing through an angular aperture, but not so successfully as Maurolycus.

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  • He was the first correctly to solve Aristotle's problem, stated above, and to apply it practically to solar observations in a darkened room (Cosmographia, 1 535).

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  • Sir Isaac Newton, in his Opticks (1704), explains the principle of the camera obscura with single convex lens and its analogy with vision in illustration of his seventh axiom, which aptly embodies the correct solution of Aristotle's old problem.

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  • The simple distillation of sea-water, and the production thereby of a certain proportion of chemically fresh water, is a very simple problem; but it is found that water which is merely evaporated and recondensed has a very disagreeable flat taste, and it is only after long exposure to pure atmospheric air, with continued agitation, or repeated pouring from one vessel to another, that it becomes sufficiently aerated to lose its unpleasant taste and smell and become drinkable.

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  • The Comtist maintains that even if these five volumes together fail in laying down correctly and finally the lines of the new science, still they are the first solution of a great problem hitherto unattempted.

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  • Looking at the problem in this way, even a moralist who does not expect theology to be the instrument of social revival, might still ask whether the sympathetic instincts will not necessarily be already developed to their highest point, before people will be persuaded to accept the religion, which is at the bottom hardly more than sympathy under a more imposing name.

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  • The Perceval story is an admirable folk-tale, the Grail problem is the most fascinating problem of medieval literature; the two combined form a romance of quite unique charm and interest.

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  • But besides the vocation he had freely selected and assiduously laboured to fulfil, two more external influences helped to shape Martineau's mind and define his problem and his work; the awakening of English thought to the problems which underlie both philosophy and religion, and the new and higher opportunities offered for their discussion in the periodical press.

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  • Later, especially when scientific speculation had made the theistic problem urgent, he was a frequent contributor to the literary monthlies.

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  • What was implicit in nature had become explicit in man; the problem of the individual was one with the problem of universal experience.

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  • This was the problem which Martineau attempted to deal with in The Seat of Authority in Religion.

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  • This discrepancy caused anxiety at one time, but large fields suitable for colonization have been opened in Sakhalin, Korea, Manchuria and Formosa, so that the problem of subsistence has ceased to be troublesome.

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  • Finding the problem of life insolvable, they abandon the attempt to solve it and take refuge in the grave.

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  • Not until the Tokugawa family obtained military control of the whole empire (I6o3), and, fixing its capital at Yedo, required the feudal chiefs to reside there every second year, did the problem of roads and post-stations force itself once more on official attention.

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  • Swedenborg knew that the machine would not fly, but suggested it as a start and was confident that the problem would be solved.

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  • From this time he applied himself to the problem of discovering the nature of soul and spirit by means of anatomical studies.

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  • The problem was not solved, but the inadequate solutions were excluded, and the data to be considered in any adequate solution were affirmed.

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  • This problem interested the East for the most part; in the West there was waged a theological warfare around the nature of man and the work of Christ.

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  • On the problem of divine election Lutheranism and Calvinism remained divided.

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  • The enlargement of the horizon of knowledge by the advance of science, the recognition of the only relative validity of human opinions and beliefs as determined by and adapted to each stage of human development, which is due to the growing historical sense, the alteration of view regarding the nature of inspiration, and the purpose of the Holy Scriptures, the revolt against all ecclesiastical authority, and the acceptance of reason and conscience as alone authoritative, the growth of the spirit of Christian charity, the clamorous demand of the social problem for immediate attention, all combine in making the Christian churches less anxious about the danger, and less zealous in the discovery and condemnation of heresy.

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  • The latter received mythical representation in that most interesting god (but originally rather culture-hero) Maui, who, in NewZealand practically supplants Tangaloa, and becomes the god of the air and of the heaven, the creator and the causer of the flood.2 Speculation opened the usual deep problem; whence came the gods?

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  • Gray, a British officer who attempted to solve the Niger problem, visited Bondu in 1818 it had been removed to Bulibani, a small town, with about 3000 population, surrounded by a strong clay wall.

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  • The entropy tends to a maximum, and the state is one of stable equilibrium when the value of the entropy is the maximum value consistent with the conditions of the problem.

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  • There is good ground for believing that as Grail quester and winner, Gawain preceded alike Perceval and Galahad, and that the solution of the mysterious Grail problem is to be sought rather in the tales connected with the older hero than in those devoted to the glorification of the younger knights.

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  • Two newly-discovered creeds help us greatly to narrow down the limits of the problem.

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  • Western theologians approached the problem from another point of view.

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  • Its history has been the subject of much controversy for years past, but no longer presents an insoluble problem.

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  • The differences of opinion which arose on this problem naturally led to the inquiry as to whether any universally valid statement was possible.

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  • From this principle, it follows (I) that the distinction between right and wrong is part of the constitution of human nature; (2) that morality stands apart from theology, and the moral qualities of actions are determined apart from the arbitrary will of God; (3) that the ultimate test of an action is its tendency to promote the general harmony or welfare; (4) that appetite and reason concur in the determination of action; and (5) that the moralist is not concerned to solve the problem of freewill and determinism.

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  • There was a further complication in that each one of these characters had at least two different phonetic values; and there were other intricacies of usage which, had they been foreknown by inquirers in the middle of the 19th century, might well have made the problem of decipherment seem an utterly hopeless one.

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  • This made the problem of deciphering Persian inscriptions a relatively easy one.

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  • In point of fact this problem had been partially solved in the early days of the zgth century, thanks to the sagacious guesses of the German philologist Grotefend.

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  • As an additional claim to remembrance, he was the first to solve Leibnitz's problem of the isochronous curve (Acta Eruditorum, 1690).

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  • He proposed the problem of the catenary or curve formed by a chain suspended by its two extremities, accepted Leibnitz's construction of the curve and solved more complicated problems relating to it.

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  • In 1696 he proposed the famous problem of isoperimetrical figures, and offered a reward for its solution.

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  • This problem engaged the attention of British as well as continental mathematicians; and its proposal gave rise to a painful quarrel with his brother Jean.

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  • Jean offered a solution of the problem; his brother pronounced it to be wrong.

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  • The family quarrel about the problem of isoperimetrical figures above mentioned began about this time.

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  • The problem of vibrating cords, which had been some time before resolved by Brook Taylor (1685-1731) and d'Alembert, became the subject of a long discussion conducted in a generous spirit between Bernoulli and his friend Euler.

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  • In one of his early investigations he gave an ingenious though indirect demonstration of the problem of the parallelogram of forces.

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  • The problem of the cause of these striking and novel phenomena at first produced considerable perplexity.

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  • The problem of the stresses in rarefied gaseous media arising from inequalities of temperature, which is thereby opened out, involves some of the most delicate considerations in molecular physics.

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  • On this ground Maxwell inferred that the forces acting in the radiometer are connected with gliding of the gas along the unequally heated boundaries; and as the laws of this slipping, as well as the constitution of the adjacent layer, are uncertain, the problem becomes very intricate.

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  • The problem which was to be settled by a century of strife was now posed.

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  • This correlative numerical problem and the two purely geometrical problems are inseparably connected historically.

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  • The problem he set himself was the exact converse of that of Archimedes.

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  • For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

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  • De Spatii Sectione discussed the similar problem which requires the rectangle contained by the two intercepts to be equal to a given rectangle.

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  • This problem, which is sometimes known as the Apollonian Problem, was proposed by Vieta in the 16th century to Adrianus Romanus, who gave a solution by means of a hyperbola.

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  • The First Problem Which The Construction Of The Calendar Presents Is To Connect The Week With The Year, Or To Find The Day Of The Week Corresponding To A Given Day Of Any Year Of The Era.

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  • Hence, when the number of any proposed year in each of the cycles is known, its number in the Julian period can be determined by the resolution of a very simple problem of the indeterminate analysis.

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  • It is unnecessary, however, in the present case to exhibit the general solution of the problem, because when the number in the period corre sponding to any one year in the era has been ascertained, it is.

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  • But this advantage is only procured by the sacrifice of some accuracy; for notwithstanding the cumbersome apparatus employed, the conditions of the problem are not always exactly satisfied, nor is it possible that they can be always satisfied by any similar method of proceeding.

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  • At the same time, the possibility of a confusion between Ninib and Nergal must be admitted, and perhaps we are to see the solution of the problem in the recognition of two diverse schools of theological speculation, the one assigning to Ninib the role of the spring-tide solar deity, the other identifying him with the sun of the summer solstice.

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  • The Indian problem was important.

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  • Knowledge being limited to the ideas produced could never extend to the unperceived matter, or substance, or cause which produced them, and it became a problem for speculative science to determine the grounds for the very belief in its existence.

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  • Now Berkeley put this whole problem in a new light by pointing out a preliminary question.

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  • But this is by no means the whole or even the principal part of Berkeley's philosophy; it is essentially a theory of causality, and this is brought out gradually under the pressure of difficulties in the first solution of the early problem.

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  • He once for all lifted the problem of metaphysics to a higher level, and, in conjunction with his successor, Hume, determined the form into which later metaphysical questions have been thrown.

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  • The problem is complicated by the fact that, from the Egyptian evidence, not only was there at this time no remarkable emigration of oppressed Hebrews, but Bedouin tribes were then receiving permission to enter Egypt and to feed their flocks upon Egyptian soil.

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  • Thus, whatever evidence may be supplied by archaeological research, the problem of the Exodus must always be studied in the light of the biblical narratives.

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  • A month after the inauguration the murder of Lincoln left him president, with the great problem to solve of reconstruction of the Union.

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  • In the solution of this problem the common sense of Wellington and of Castlereagh, with whom the duke worked throughout in complete harmony, played a determining part; it was mainly owing to their influence that France escaped the dismemberment for which the German powers clamoured, and which was advocated for a while by Lord Liverpool and the majority of the British cabinet.

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  • The Balkan Wars, and Poincare's attitude towards the problem raised by them, greatly increased his prestige; he declared on Dec. 4 to the Foreign Affairs Committee of the Chamber that he was determined to secure respect for the economic and political interests of France, not only in the Balkan Peninsula, but in the Ottoman Empire generally, and especially in Syria.

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  • Hewitt has also attacked the problem by brominating the oxyazobenzenes, and has shown that when the hydrobromic acid produced in the reaction is allowed to remain in the system, a brombenzene-azo-phenol is formed, whilst if it be removed (by the addition of sodium acetate) bromination takes place in the phenolic nucleus; consequently the presence of the mineral acid gives the azo compound a pseudo-quinonoid character, which it does not possess if the mineral acid be removed from the sphere of the reaction.

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  • Poland is another case of the difficulty of managing a population which speaks a language not that of the governing majority, and Russia, in trying to solve one problem by absorbing Finland into the national system, is burdening herself with another which may work out in centuries of unrest, if not in domestic violence.

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  • Davis, he secured the passage of the Wade-Davis Bill (for the reconstruction of the Southern States), the fundamental principle of which was that reconstruction was a legislative, not an executive, problem.

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  • In fact, famine is, to all intents and purposes, endemic in India, and is a problem to reckon with every year in some portion of that vast area.

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  • The problem is very much the same as that met by the British Poor Law system.

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  • Adopting the definition we should have no difficulty in proving that in a vacuum tube gases may be luminous at very low temperatures, but we are doubtful whether such a conclusion is very helpful towards the elucidation of our problem.

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  • The problem, which, in the opinion of the present writer, is the one of interest and has more or less definitely been in the minds of those who have discussed the subject, is whether the type of wave sent out by a molecule only depends on the internal energy of that molecule, or on other considerations such as the mode of excitement.

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  • Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.

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  • In one solution of the former problem is the first recorded use of the property of a conic (a hyperbola) with reference to the focus and directrix.

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  • With the mention of the Porisms of Euclid we have an account of the relation of porism to theorem and problem.

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  • As the Turbellaria (Planarians) are the most primitive division of the Platyelmia, the problem of the affinities of this phylum resolves itself into that of the relationships of the Turbellaria.

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  • And the question as to the true theory of these relations is known as the Synoptic Problem.

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  • This oral theory was for a long time the favourite one in England; it was never widely held in Germany, and in recent years the majority of English students of the Synoptic Problem have come to feel that it does not satisfactorily explain the phenomena.

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  • An interesting sociological problem is raised by the presence of the large Asiatic element in the population.

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  • Another fact which is possibly contributing to the solution of the problem is that the Japanese are leaving the islands in large numbers as compared with the Koreans.

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  • The problem of magnesium reduction is in many respects similar to that of aluminium extraction, bait the lightness of the metal as compared, bulk for bulk, with its fused salts, and the readiness with which it burns when exposed to air at high temperatures, render the problem somewhat more difficult.

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  • Thus in presence of the problem which is the crux of materialism, the origin of consciousness, he first propounds a gratuitous hypothesis that everything has mind, and then gives up the origin of conscious mind after all.

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  • It is Wundt's own statement of his solution of the epistemological problem " that on the one hand the whole outer world exists for us only in our ideas, and that on the other hand a consciousness without objects of idea is an empty abstraction which possesses no actuality " (System, 212 -213).

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  • Caesarea, indeed, as a city of mixed population and lying just outside Judaea proper - a place, moreover, where Timothy might have become known during Paul's two years' detention there - would satisfy many conditions of the problem.

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  • Now this in Timothy's case, as far as we can trace his steps, was Ephesus; and it is natural to ask whether it will not suit all the conditions of the problem.

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  • And, again, if this transaction settled the investiture question, it did not solve the problem of the reconciliation of the universal power of the popes with the claims of the emperors to the government of Europe; and the conflict subsisted - slumbering, it is true, but ever ready to awake under other forms. Nevertheless, the two great Christian agitations directed by the papacy at the end of the nth century and the beginning of the 12th - the reformation and the crusade - were of capital importance for the foundation of the immense religious monarchy that had its centre in Rome; and it is from this period that the papal monarchy actually dates.

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  • This contingency explains the vacillating and illogical character of the papal diplomacy with regard to the Byzantine problem, and, inter slid, the opposition of Eugenius III.

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  • To him, also, in his capacity of theologian, the whole of Europe submitted every obscure, delicate or controverted question, whether legal problem or case of conscience.

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  • To them the Eastern problem presented a less complex aspect.

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  • This document, which confused the political problem with the theological, was bound to envenom the quarrel between emperor and pope beyond all remedy.

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  • To this difficult problem he brought remarkable skill and aptness, energy and ability.

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  • His solution of the first problem entitles Julius II.

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  • The Holy See directed all its energies towards the solution of the problem; in the event of its proving to be insoluble, it would take care that it should remain a festering sore in the body of the monarchy.

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  • Die Trennung der beiden Mdchte and das Problem ihrer Wiedervereinigung bis zum Untergange des byzantinischen Reichs (Berlin, 1903), which contains an account of the question of the East in its relations with the papal policy, from the rise of the schism down to the end of the middle ages.

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  • At last, in 1845, Faraday attacked the old problem, but this time with complete success.

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  • In the later years of his life he applied himself to the problem of obtaining alumina in the crystalline form, and succeeded in making rubies identical with the natural gem not merely in chemical composition but also in physical properties.

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  • Apparently the real problem is one of population adequate to effect the improvements demanded.

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  • Since then the problem has been disentangled; and now minor points only remain to be cleared up. Jaeschke devoted special attention to the dialectical sounds, and showed in several papers and by the comparative table prefixed to his dictionary that in the western and eastern dialects these sounds correspond more or less closely to the written forms.

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  • On the 3rd of October, therefore, the British government authorized the occupation of the Chumbi valley, and an advance to Gyantse in Tibet and military preparations, with the difficult attendant problem of transport, were undertaken.

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  • Willard Gibbs, who considered the whole problem of physical and chemical equilibrium in papers published in 1877, though the application of his principles only began to make extensive progress about twenty years after the publication of his purely theoretical investigations.

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  • It is possible to state the conditions of solubility in terms of the theory of available energy, but the result comes to little more than a re-statement of the problem in other terms. Nevertheless, such a re-statement is in itself sometimes an advance in knowledge.

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  • In considering the corresponding relation for a solution instead of a pure liquid, possible differences in concentration make the column method difficult of application, and it is better to attach the problem by means of an imaginary cycle of isothermal operation.

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  • The results are true whatever theory be in vogue, but the results throw no light on the problem of which theory to choose.

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  • The practical difficulty of the constitutional problem gave the "court parson" - as Gneisenau had contemptuously called him - excuse enough for a change of front which, incidentally, would please his exalted patrons.

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  • We are gradually approaching a solution of this obscure problem.

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  • Concrete by itself, though strong in compression, can offer but little resistance to tensile and shearing stresses, and as these stresses always occur in beams the problem arises how best to arrange the steel so as to assist the concrete in bearing them.

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  • And, when the whole facts are borne in mind, there can be no reasonable doubt that the Mendelian principles offer an intelligible solution of the problem.

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  • The entire problem is not without its difficulties still, after all the research lavished upon it, but the probabilities seem to converge upon the conclusion that Paul was never released from his imprisonment, and consequently that he never revisited the East.

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  • It assumes the moral distinction of the righteous and the ungodly, and seeks a solution for the problem of the lack of harmony of present character and condition.

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  • It appears, then, that, confronted with the "problem of ascertaining the relative diameter of the particles of which, he was convinced, all gases were made up, he had recourse to the results of chemical analysis.

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  • Baron de Henouville, unsuccessfully attempted "to reduce the base of alum" to a metal, and shortly afterwards various other investigators essayed the problem in vain.

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  • The outstanding problem of African missions at least north of the Equator (south there is the Ethiopian question) is not the degradation of the black races, nor the demoralizing influences of heathen Christians, nor even the slave dealer, though all these obstacles are present and powerful.

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  • Besides these matters which concerned Hinduism there was the problem of converting sixty million Mahommedans.

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  • The problem presented by the simple existence of the facts just summed up remains in either case absolutely the same.

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  • A special application of his theory of continuous groups was to the general problem of non-Euclidean geometry.

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  • Perhaps the strangest problem in the whole of Switzerland is that presented by the so-called Klip pen.

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  • As for the explanation of the community between the alpine and arctic floras, all authorities are agreed that the key to the problem is furnished by the occurrence of the glacial period.

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  • A problem to which he returned repeatedly was that of separating nickel and cobalt from their ores and freeing them from arsenic; and in the course of his long laboratory practice he worked out numerous processes for the preparation of pure chemicals and methods of exact analysis.

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  • These and kindred difficulties make each new shape or size a new problem, and in particular they require that for each and every individual casting a new sand or clay mould shall be made with care by a skilled workman.

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  • The solution of this problem is of vital importance in connexion with the early history of man's development in the Babylonian region.

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  • The regulation of the rivers, more especially of the Tiber, is probably the most efficient method for coping with the problem.

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  • In order to make perfectly clear the full significance of the principle which Hume applied to the solution of the chief philosophical questions, it is necessary to render somewhat more precise and complete the statement of the psychological view Theory which lies at the foundation of the empirical theory, and to distinguish from it the problem of the theory of knowledge upon which it was brought to bear.

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  • Without entering into details, which it is the less necessary to do because the subject has been recently discussed with great fulness in works readily accessible, it may be said that for Locke as for Hume the problem of psychology was the exact description of the contents of the individual mind, and the determination of the conditions of the origin and development of conscious experience in the individual mind.

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  • And the answer to the problem which was furnished by Locke is in effect that with which Hume started.

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  • Either we have a right to the assumption contained in the conception of the individual mind as standing in relation to things, in which case the grounds of the assumption must be sought elsewhere than in the results of this reciprocal relation, or we have no right to the assumption, in which case reference to the reciprocal relation can hardly be accepted as yielding any solution of the psychological problem.

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  • With Locke, Hume professes to regard this problem as virtually covered or answered by the fundamental psychological theorem; but the superior clearness of his reply enables us to mark with perfect precision the nature of the difficulty inherent in the attempt to regard the two as identical.

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  • Now if this mode of treatment be accepted as the only possible method, and its results assumed to be conclusive as regards the problem of knowledge, the fundamental peculiarity of cognition is overlooked.

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  • With regard, then, to the first problem, the formal element in knowledge, Hume has to consider several questions, distinct in nature and hardly discriminated by him with sufficient precision.

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  • Beyond all question Hume, in endeavouring to answer this problem, is brought face to face with one of the difficulties inherent in his conception of conscious experience.

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  • It will probably be sufficient to indicate the problem as conceived by Hume, and the relation of the method he adopts for solving it to the fundamental doctrine of his theory of knowledge.

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  • For in the problem of real cognition he is brought face to face with the characteristic feature of knowledge, distinction of self from matters known, and reference of transitory states to permanent objects or relations.

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  • The final problem of Hume's theory of knowledge, the discussion of the real significance of the two factors of cognition, self and external things, is handled in the Treatise with great fulness and dialectical subtlety.

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  • As in the case of the previous problem, it is unnecessary to follow the steps of his analysis, which are, for the most part, attempts to self substitute qualities of feeling for the relations of thought The .

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  • The closing sentences of this passage may be regarded as pointing to the very essence of the Kantian attempt at solution of the problem of knowledge.

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  • It is a problem how to reconcile his ignorance, his weakness, his superstition, his crude notions, his erroneous observations, his ridiculous influences and theories, with his grasp of method, his lofty views of the true scope of medicine, his lucid statements, his incisive and epigrammatic criticisms of men and motives.

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  • The next question constitutes perhaps the most important problem in Greek political development.

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  • In this last achievement Professor Finke finds the solution of a problem which Langlois had declared to be insoluble.

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  • His fortunes were presenting a most interesting problem when, on the 31st of December 1882, at his house in Ville d'Avray, near Sevres, he died by a shot from a revolver which accidentally went off.

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  • Sibylla was the heiress of the kingdom; the problem of her marriage was important.

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  • He failed to understand the great spiritual movement which was convulsing the Church; and instead of bending his mind to the problem of the Reformation, he from the first subordinated the cause of Catholicism and of the world to his interests as an Italian prince and a Medici.

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  • A different type of problem is presented in those cases in which the temperature at each point varies with the time, as is the case near the surface of the soil with variations in the external conditions between day and night or summer and winter.

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  • In the Bible the philosophical-religious problem is nowhere discussed, but Christian ethics as set forth in the New Testament assumes throughout the freedom of the human will.

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  • The first difficult problem he had to face was the Seven Years' War.

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  • In the chapter (xx.) of that work where Hobbes dealt with the famous problem whose solution he thought he had found, there were left expressions against Vindex (Ward) at a time when the solutions still seemed to him good; but the solutions themselves, as printed, were allowed to be all in different ways halting, as he naively confessed he had discovered only when he had been driven by the insults of malevolent men to examine them more closely with the help of his friends.

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  • Pascal solved the hitherto refractory problem of the general quadrature of the cycloid, and proposed and solved a variety of others relating to the centre of gravity of the curve and its segments, and to the volume and centre of gravity of solids of revolution generated in various ways by means of it.

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  • The problem was to get the water from the Gunnison over the mountain range into the Uncompahgre valley; and a tunnel, 6 m.

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  • Thus, in the first decade of the 20th century a great advance had been made in the way in which the whole problem was being viewed in America, though the very immensity of the problem of bringing the Federal power to bear on operations on so vast a scale, involving the limitation of private land speculation in important areas, still presented political difficulties of considerable magnitude.

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  • If this view be, rejected and it is necessary to fall back on the choice between 64 and 67, the problem is perhaps insoluble, but 64 has somewhat more intrinsic probability, and 67 can be explained as due to an artificial system of chronology which postulated for Peter an episcopate of Rome of twenty-five years - a number which comes so often in the early episcopal lists that it seems to mean little more than "a long time," just as "forty years" does in the Old Testament.

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  • In his researches on the bleaching compounds of chlorine he was the first to advance the view that bleaching-powder is a double compound of calcium chloride and hypochlorite; and he devoted much time to the problem of economically obtaining soda and potash from seawater, though here his efforts were nullified by the discovery of the much richer sources of supply afforded by the Stassfurt deposits.

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  • The indispensable preliminary to a really historic view of these writings is some solution of the problem of their mutual relations.

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  • Towards the solution of this problem two contributions of prime importance have recently been made.

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  • The supposed connexion with the Israelites has made the problem of the Hyksos attractive, but light is coming upon it very slowly.

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  • Later, he interested himself in the problem of mechanical flight.

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  • The effect upon the railway problem is of course very great, inasmuch as, while the supply of trucks required per day in 1906 was from moo to 1200, about 80% of these had to be sent down empty to the harbour.

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  • The political problem presented was a very difficult one.

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  • The revolution in Turkey had entirely changed the face of the Eastern Question; the problem of Macedonian reform was swallowed up in that of the reform of the Ottoman empire generally, there was even a danger that a rejuvenated Turkey might in time lay claim to the provinces occupied by Austria-Hungary under the treaty of Berlin; in any case, the position of these provinces, governed autocratically from Vienna, between a constitutional Turkey and a constitutional Austria-Hungary, would have been highly anomalous.

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  • They attempted to solve the problem by granting to the Federalists all their demands.

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  • A very important problem is presented by bk.

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  • He took up the project with characteristic ardour, and set out at once for Europe to investigate the problem.

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  • How far the country generally may be regarded as Hellenized is a problem which involves the vexed question what right the Macedonian people itself has to be classed among the Hellenes, and Macedonian to be considered a dialect of Greek.'

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  • The taxation of the great cities formed a separate and very difficult problem.

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  • The existing assessment, made before the British occupation, had long been condemned by all competent authorities, but the inherent intricacies and difficulties of the problem had hitherto postponed a solution.

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  • But the secret of the black granite school, and its excellence, is the main problem unsolved in the history of the art.

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  • Before that time, in spite of successive efforts to establish a chronology, the problem is very obscure.

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  • The British government had begun by excluding it from the Th S dan problem, and by declaring that for events in these queest,00n.

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  • Hence a final conclusion can hardly be expected, but with certain modifications in detail the following solution of the problem may be accepted as representing the point of view of recent criticism.

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  • Immediately after his accession, in 528, he appointed a commission to deal with the imperial constitutions (jus novum), this being the easier part of the problem.

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  • This accordingly becomes the central problem of pragmatism.

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  • It is by means of the cytological evidence, however, that this problem will finally be solved.

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  • The imaginative force of the presentation, coming from a man of DUrer's powers, is intense; but what consciously occupied him most may well have been the problem how to draw accurately the proportions and action of a horse in motion.

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  • You should never disregard professional advice or delay in seeking advice because of something in the Contents and you should not use the Contents for diagnosing a health or other problem or prescribing a medication.

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  • It is not possible here to unravel the problem, but documents at St Andrews, now printed, demonstrate the error of the historians who regard Graham as a holy man, persecuted because he was half a premature Protestant.

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  • Bateson is pre-eminent, would appear to simplify the problem of variation, especially on its mechanical and physiological sides.

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  • For an attempt to treat the whole problem of differential fertility and assortative mating numerically, see Pearson, The Grammar of Science, 2nd edition, London, 1900.

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  • And in India the problem still remains to trace, in the literature, the gradual growth of the system - the gradual formation of new sections among the people, the gradual extension of the institution to the families of people engaged in certain trades, belonging to the same group, or sect, or tribe, tracing their ancestry, whether rightly or wrongly, to the same source.

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  • The first transportation problem was to connect Lake Michigan and the Mississippi river; this was accomplished by building the Illinois & Michigan canal to La Salle, at the head of the navigation on the Illinois river, a work which was begun in 1836 and completed in 1848 under the auspices of the state.

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  • The slavery question, however, was the problem of lasting political importance.

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  • On what is perhaps the vital problem of modern education, the question of ancient versus modern languages, he pronounced that the latter "are indispensable accomplishments, but they do not form a high mental training" - an opinion entitled to peculiar respect as coming from a president of the Modern Language Association.

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  • In his De Quadratura Circuli he professed to have solved the problem; and in his Conjectura de novissimis diebus he prophesied that the world would come to an end in 1734.

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  • The nature of axiomatic certainty is part of the fundamental problem of logic and metaphysics.

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  • In 1920 he and his executive were faced by the difficult problem of the refusal of Irish railwaymen to handle munitions of war; and the only solution he and they could suggest was that the Government should cease to send such munitions and that the Labour party should make an appeal to the Irish people - a solution which ministers, of course, could not accept.

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  • When they were baffled, the Sadducees, to whose party the chief priests belonged, sought in vain to pose Him with a problem as to the resurrection of the dead; and after that a more honest scribe confessed the truth of His teaching as to the supremacy of love to God and man over all the sacrificial worship of the Temple, and was told in reply that he was not far from the kingdom of God.

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  • The enormous dramatic development in the symphonic music of Beethoven made the problem of the Mass with orchestral accompaniment almost insoluble.

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  • The only other artistic solution of the problem is to follow Berlioz, Verdi and Dvorak in the complete renunciation of all ecclesiastical style.

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  • Truly perceiving that the ultimate metaphysical problem is, here as ever, the relation of the One and the Many, McTaggart starts with a definition of the ideal in which our thought upon it can come to rest.

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  • The agenda of the diet contained many things seriously affecting all Germany, but the one problem which every one was thinking about was how Luther would be dealt with.

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  • Complex truths of reason or essence raise the problem of definition, which consists in their analysis into simpler truths and ultimately into simple - i.e.

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