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fundamental

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fundamental

fundamental Sentence Examples

  • In the end, our fundamental challenge is to become better individuals, and technology offers little help on that front; it is up to each one of us to solve that for ourselves.

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  • The fundamental substance or stroma is colorless and homogeneous.

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  • In correspondence with the fundamental constitution of the zooid, each of the three segments has its own body-cavity separated from the others.

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  • There are those who would elevate the right to food as being a fundamental human right.

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  • The characteristic by which we recognize the fundamental element in a series is its intuitive or self-evident character; it is given by "the evident conception of a healthy and attentive mind so clear and distinct that no doubt is left."

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  • 3 In his view of touch and taste, as the two fundamental and essential senses, he may remind one of Herbert Spencer's doctrine.

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  • In all green plants which have a special protective epidermis, the cortex of the shoot has to perform the primitive fundamental function of carbon assimilation.

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  • The former moves in a world of "values," and judges things as they are related to our "fundamental self-feeling."

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  • Their fundamental conception is that of Democritus; they seek to account for the formation of the cosmos, with its order and regularity, by setting out with the idea of an original (vertical) motion of the atoms, which somehow or other results in movements towards and from one another.

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  • The first error is to assert that history unfolds in a basically linear fashion, that there is a fundamental continuity between the past, present, and future.

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  • There can be no doubt that there is no fundamental difference between the living substance of animals and plants, for many forms exist which cannot be referred with certainty to either kingdom.

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  • You can be a subsistence farmer and perhaps produce some excess, but given the prior observation about the fundamental volatility of farming, you will always be at risk of not producing enough.

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  • "Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.

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  • It must be remembered that speech contributed in no way to her fundamental education, though without the ability to speak she could hardly have gone to higher schools and to college.

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  • 17 The principle of ministerial parity which is fundamental in Presbyterianism is founded not merely on apostolic example but on the words of Christ Himself:" Ye know that the princes of the Gentiles exercise dominion over them, and they that are great exercise authority upon them.

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  • Taking the centimetre, gramme and second as our fundamental units, the most convenient unit of force is that which, acting on a gramme for a second, produces in it a velocity of a centimetre per second; this is called a Dyne.

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  • In the psychology of Descartes there are two fundamental 2 Ib.

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  • The fundamental principle of the magneto system has been described in connexion with the " Standard board."

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  • In general they are characterized by a firm adherence to the fundamental articles of Catholic orthodoxy, tempered by a tolerant attitude towards those not of "the household of the faith."

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  • Considering the wide differences between the two groups in the size and external characters, and in the mode of life, including the mode of feeding, it is indeed surprising that in every important organ the two groups should show a fundamental morphological identity.

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  • trace a three-fold division of tissue systems, a division of which there are indications among the lower plants, and which is the expression of the fundamental conditions of the evolution of a bulky differ- Tissue entiated plant-body.

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  • But in addition to bringing forward a fundamental and philosophical view of morbid processes, which probably contributed more than any other single cause to vindicate for pathology the place which he claimed for it among the biological sciences, Virchow made many important contributions to histology and morbid anatomy and to the study of particular diseases.

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  • In the matter of criminal jurisdiction we paused for a moment at the edict of Milan; but we may at once trace this second or civil branch of episcopal judicature or quasi-judicature down as far as the reign of Charlemagne, when it underwent a fundamental change, and became, if either litigant once chose, no longer a matter of consent but of right.

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  • With the old Czechs he refused to recognise the constitution of 1867; he helped to draft the declaration of 1868 and the fundamental articles of 1871, and took a leading part in the negotiations during the ministry of Potocki and Hohenwart.

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  • The fundamental conception that underlay all Berthelot's chemical work was that all chemical phenomena depend on the action of physical forces which can be determined and measured.

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  • The infallibility of the Church, thus limited, is a necessary outcome of the fundamental conception of the Catholic Church and its mission.

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  • Experience forbids our excluding organic activity from natural causes, also our excluding intelligence from purposeful (zwecktdtigen) causes; hence experience forbids our defining the fundamental force or first cause out of which living creatures arose.'

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  • From this fundamental difference between the view held by history and that held by jurisprudence, it follows that jurisprudence can tell minutely how in its opinion power should be constituted and what power-- existing immutably outside time--is, but to history's questions about the meaning of the mutations of power in time it can answer nothing.

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  • This leads up to the fundamental distinction, introduced by Lord Kelvin, between "available energy," which we can turn to mechanical effect, and "diffuse energy," which is useless for that purpose.

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  • The peace of Tilsit (July 7, 1807) enabled Napoleon to press on his projects for securing the command of the Mediterranean, thenceforth a fundamental axiom of his policy.

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  • Ezekiel's own moral code is that of the prophets, which insists on the practice of the fundamental civic virtues.

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  • The differences between the nutritive processes of the animal and the plant are not therefore fundamental, as they were formerly held to be.

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  • Those who favour state connexion and those who oppose it agree in claiming spiritual independence as a fundamental principle of Presbyterianism.

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  • His fundamental idea - the interruption of the current - was a fatal mistake, which was not at the time properly understood.

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  • Caird (Glasgow: Fundamental Ideas of Christianity, comp. his earlier Introduc. to the Phil.

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  • The so-called Celtic type, exemplified by individuals of rather less than average height, brown-haired and brachycephalic, is the fundamental element in the nation and peoples the region between the Seine and the Garonne; in southern France a different type, dolichocephalic, short and with black hair and eyes, predominates.

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  • In his Entwickelungsgeschichte der Thiere (p. 264) he distinctly tells us that the law of growing individuality is " the fundamental thought which goes through all forms and degrees of animal development and all single relations.

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  • The observation that large groups of species of widely different habits present the same fundamental plan of structure; and that parts of the same animal or plant, the functions of which are very different, likewise exhibit modifications of a common plan.

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  • The fundamental law was altered in 1848 and the Dutch monarchy, from being autocratic, became henceforth constitutional.

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  • Since Huxley and Sully wrote their masterly essays in the 9th edition of this encyclopaedia, the doctrine of evolution has outgrown the trammels of controversy and has been accepted as a fundamental principle.

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  • The fundamental principle of ecclesiastical jurisdiction with its sanction " of excommunication will be found in Christ's words in Matt.

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  • Its fundamental principle is that, by a combination of glass scales with a micrometer screw, " the chief part of the distance to be measured is read off on the scale; the fractional part of the scalespace is not estimated but measured by the screw."

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  • Though all descended from one stock, there are twelve distinct tribes of the Andamanese, each with its own clearly-defined locality, its own distinct variety of the one fundamental language and to a certain extent its own separate habits.

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  • Nature of the Food of Planls.The recognition of the fundamental identity of the living substance in animals and plants has directed attention to the manner in which plants are nourished, and especially to the exact nature of their food.

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  • Already anxieties appear as to the theological verdict upon two of his fundamental views - the infinitude of the universe, and the earth's rotation round the sun.

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  • Other elements of the problem there are none, except mere numbers and angles, which do not depend upon the fundamental measurements of space, time and mass.

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  • The word is derived from the general resemblance of the texture of plant substance to that of a textile fabric, and dates from a period when the fundamental constitution of plant substance from individual cells was not yet discovered.

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  • The events form one of the fundamental problems of biblical history.

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  • Hence both science and religion must come to recognize as the" most certain of all facts that the Power which the Universe manifests to us is utterly inscrutable."Thus to be buried side by side in the Unknowable constitutes their final reconciliation, as it is the refutation of irreligion which consists of" a lurking doubt whether the Incomprehensible is really incomprehensible."Such are the foundations of Spencer's metaphysic of the Unknowable, to which he resorts in all the fundamental difficulties which he subsequently encounters.

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  • The fundamental position of the work is that all legislative as well as all paternal power is derived from God, and that the authority of every law resolves itself into His.

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  • Aristotle's suggestion that Thales was led to his fundamental dogma by observation of the part which moisture plays in the production and the maintenance of life, and Simplicius's, that the impressibility and the binding power of water were perhaps also in his thoughts, are by admission purely conjectural..

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  • The aim of his whole policy was to secure for this measure, which was proclaimed as a fundamental law in 1724, the approval of Europe; and by promises and threats he did at last obtain the guarantee of the states of the Empire and the leading European powers.

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  • It was empowered to arrange the fundamental laws of the confederation; to fix the organic institutions relating to its external, internal and military arrangements; to regulate the trade relations between the various federated states.

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  • Finally it~was laid down by Article 7 that a unanimous vote was necessary for changing fundamental laws, organic institutions, individual rights, or in matters of religion, a formula wide enough to embrace every question of importance with which the diet might be called upon to deal.

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  • So far from enlarging the powers of the diet, it reaffirmed the doctrine of non-intervention; and, above all, it renewed the clause forbidding any fundamental modification of the constitution without a unanimous vote.

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  • Unfortunately, however, it was necessary to enter upon the discussion of the fundamental laws, a subject presenting many opportunities for the display of rhetoric and intellectual subtlety.

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  • fundamental rights, was only saved fron the fury of the mob by Prussian troops.

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  • The fundamental American vestibule patent, issued to H.

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  • Few fundamental alterations have been made in the constitution of the city, but in the reign of Charles II.

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  • Thus may be obtained, either separately or in various combinations, the four notes whose vibrations are in the ratios of the above numbers, and which therefore form the fundamental chord (Cegc 1).

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  • i., 1862), who, though he never entirely accepted the new position, contributed by his searching analysis of the unreality of P's narrative to the formation (for example, in the mind of Kuenen) or ratification of the judgment on that work which is fundamental to the general theory.

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  • In this article we shall confine ourselves to the fatty compounds, from which the fundamental notions were first obtained; reference may be made to the article Chemistry: Organic, for the general structural relations of organic compounds, both fatty and aromatic.

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  • They emphasized the fundamental distinction between the Soul and the Body.

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  • Thus, the creation of a new series of forts extending from Thionville (Diedenhofen) to Metz and thence south-eastward was coupled with the construction of twelve strategic railway stations between Cologne and the Belgian frontier, and laterthe so-called fundamental plan of operations against France having apparently undergone modification in consequence of changes in the foreign relations of the German governmentan immense strategic railway station was undertaken at Saarburg, on the right rear of Thionville and well away from the French frontier, and many important new works both of fortification and of railway construction were begun in Upper Alsace, between Colmar and Basel.

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  • To this end John Locke drafted for them in 1669 the famous Fundamental Constitutions providing for the division of the province into eight counties and each county into seigniories, baronies, precincts and colonies, and the division of the land among hereditary nobles who were to grant three-fifths of it to their freemen and govern through an elaborate system of feudal courts.

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  • The fundamental points of difference between North Carolina and South Carolina were exemplified in the slavery conflict.

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  • The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article Crystallography; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy.

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  • On the fundamental question, however, of the psychophysical connexion and the derivation of mind from matter, his utterances are neither clear nor consistent.

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  • It has been generally assumed that the ecclesiastical authority was always competent to determine what are the fundamental articles of the Christian faith, and to detect any departures from them; but it is necessary to admit the possibility that the error was in the church, and the truth was with the heresy.

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  • It was maintained at the bar that the denial of the most fundamental doctrines of Christianity would not be a lawful cause for such rejection, but the judgment only queries whether a denial of the personality of the devil or eternal punishment is consistent with membership of the church.

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  • The hydrogen theory and the doctrine of polybasicity as enunciated by Liebig is the fundamental characteristic of the modern theory.

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  • The natural result of all these causes was that a feeling of antipathy rose against Athens in the minds of those to whom autonomy was the breath of life, and the fundamental tendency of the Greeks to disruption was soon to prove more powerful than the forces at the disposal of Athens.

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  • If the length of the thread be k"pt invariable, a certain tension will give but one ventral segment; the fundamental note of the thread is then of the same pitch as the note of the body to which it is attached.

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  • Fundamental Relations.

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  • Hence if all the energy supplied to the train is utilized at one axle there is the fundamental relation RV (I) Continuing the above arithmetical illustration, if the wheels to the axle of which the torque is applied are 4 ft.

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  • The fundamental condition governing the design of all tractive machinery is that the wheels belonging to the axles to which torque is applied shall roll along the rails without slipping, and exert a tractive force on the train.

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  • The fundamental relation between the applied torque and the tractive force F will be understood from fig.

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  • The coefficient of friction is a variable quantity depending upon the state of the rails, but is usually taken to be This is the fundamental equation between the forces acting, however the torque may be applied.

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  • Multiplying through by w we obtain Tw = 2FwD = 2µWwD = RV (4) This is a fundamental energy equation for any form of locomotive in which there is only one driving-axle.

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  • The fundamental difference between the two methods is that while the mechanical energy developed by a steam engine is in the first case applied directly to the driving-axle of the locomotive, in the second case it is transformed into electrical energy, transmitted over relatively long distances, and retransformed into mechanical energy on the driving-axles of the train.

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  • Equation (3), § I expresses the fundamental condition which must be satisfied when a locomotive is starting a train.

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  • Palestine, in spite of the numerous vicissitudes to which it has been subjected, has not lost its fundamental characteristics.

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  • Tradition concentrated upon Ezra and his age many events and changes of fundamental importance.

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  • Convinced as he was of the necessity for union and reform, he contributed more than any one to the adoption of the principle that, since the schism had survived the council of Pisa, it was necessary again to take up the work for a fundamental union, without considering the rights of John XXIII.

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  • Where the same root exists in Arabic, Syriac and Hebrew, its fundamental consonants are usually the same in all three languages.

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  • This externality of religious truth to the mind is fundamental in scholasticism, while the opposite view is equally fundamental in mysticism.

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  • Embracing the whole philosophic movement under the name of "the Cartesian system," Reid detects its fundamental error in the unproved assumption shared by these thinkers "that all the objects of my knowledge are ideas in my own mind."

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  • Reid, however, attacks the fundamental assumption.

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  • No man mastered more thoroughly the fundamental principles of government and the currents of feeling which influence the destiny of nations.

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  • On questions of fundamental doctrine they held to the belief XI.

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  • Peace, he thought, might be made "if men would not call all opinions by the name of religion, and superstructures by the name of fundamental articles."

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  • recoiled from this as being too great a leap in the dark, and such a fundamental difference of opinion between king and minister was bound to lead to a breach sooner or later.

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  • We have seen, for example, that he was led to investigate the subject of logic because he found in attempting to advance his humanitarian schemes in politics an absence of that fundamental agreement which he recognized as the basis of scientific advance.

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  • When we come to exclusively modern questions, there is no reason or necessity for a fundamental change of method.

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  • Much suggestive work on this subject of a general character is incorporated in economic books of the present day, but there is room for a whole series of careful monographs on a question of such fundamental importance.

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  • Others, which were considered of fundamental importance, owe their position in modern economics and the form in which they are stated to the " tradition of the elders."

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  • This reasoning of Fechner's has given rise to a great mass of controversy, but the fundamental mistake in it is simple.

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  • The fact that all the Euthyneura are hermaphrodite is not a fundamental difference; several Streptoneura are so, likewise Valvata, Oncidiopsis, Marsenina, Odostomia, Bathysciadium, Entoconcha).

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  • He thus set up a formal theory of allegorical exegesis, which is not quite extinct in the churches even yet, but in his own system was of fundamental importance.

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  • What makes Origen's answer so instructive is that it shows how close an affinity existed between Celsus and himself in their fundamental philosophical and theological presuppositions.

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  • Indeed this is the fundamental idea of Origen - "the original and indestructible unity of God and all spiritual essences."

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  • Where his fundamental conception admits of it, he tries to solve historical problems by historical methods.

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  • While, again, legitimately insisting upon personality as a fundamental constituent in any true theory of reality, the relation between human individualities and the divine Person is left vague and obscure; nor is it easy to see how the existence of several individualities - human or divine - in one cosmos is theoretically possible.

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  • Everywhere there was a show of knowledge concealing fundamental ignorance.

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  • are: - (1) The extensive work on the fundamental notions of physics, called Communia Naturalium, which is found in the Mazarin library at Paris, in the British Museum, and in the Bodleian and University College libraries at Oxford; (2) on the fundamental notions of mathematics, De Cornmunibus Mathematicae, part of which is in the Sloane collection, part in the Bodleian; (3) Baconis Physica, contained among the additional MSS.

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  • His fundamental physical maxims are matter and force; the latter he calls virtus, species, imago agentis, and by numberless other names.

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  • This view of nature Bacon considered fundamental, and it lies, indeed, at the root of his whole philosophy.

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  • It was governed under a "plantation covenant" until the 4th of June 1639, when, at a general meeting, the "free planters" adopted the fundamental principles of a new government.

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  • Now frequency of movement, average daily price variation, and range of price movements are matters of fundamental importance to the public. Hence for practical purposes we require several kinds of measurement of price movements, and it is impossible to weigh exactly the one against the other in respect of importance.

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  • There are other sayings in the book that appear to be at variance with its fundamental thought.

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  • We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

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  • One of these is the position of the line MN through the sun at F in which the plane of the orbit cuts some fundamental plane of reference, commonly the ecliptic. This is called the line of nodes, and its position is specified by the angle which it makes with some fixed line FX in the fundamental plane.

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  • At one of the nodes, say N, the body passes from the south to the north side of the fundamental plane; this is called the ascending node.

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  • The other element is the inclination of the plane of the orbit to the fundamental plane, called the inclination simply.

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  • The senses with their changing and inconsistent reports cannot cognize this unity; it is by thought alone that we can pass beyond the false appearances of sense and arrive at the knowledge of being, at the fundamental truth that "the All is One."

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  • Thus he based Judaism on love, not on knowledge; love was the bond between God and man, and man's fundamental duty was love as expressed in obedience to God's will.

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  • The separation of the Ratitae from the other birds, and their seemingly fundamental differences, notably the absence of the keel and of the power of flight, induced certain authors to go so far as to derive the Ratitae from the Dinosaurian reptiles, whilst Archaeopteryx (q.v.) and the Carinatae were supposed to have sprung from some Pterosaurian or similar reptilian stock.

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  • The fundamental chemical classification of matter, on the other hand, recognizes two groups of substances, namely, elements, which are substances not admitting of analysis into other substances, and compounds, which do admit of analysis into simpler substances and also of synthesis from simpler substances.

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  • The existence of a fundamental principle, unalterable and indestructible, prevailing alike through physical and chemical changes, was generally accepted.

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  • At the hands of Stahl and his school, the phlogistic theory, by exhibiting a fundamental similarity between all processes of combustion and by its remarkable flexibility, came to be a general theory of chemical action.

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  • He established as fundamental that combustion and calcination were attended by an increase of weight, and concluded, as did Jean Rey and John Mayow in the 17th century, that the increase was due to the combination of the metal with the air.

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  • The fundamental theme of the epistle is The Unity of Mankind in Christ, and hence the Unity and Divinity of the Church of Christ.

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  • Before speaking of the more fundamental grounds urged for the rejection of Ephesians, we may look at various points of detail which are of less significance.

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  • (d) The most fundamental elements in the system of thought do not differ from those of the earlier epistles.

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  • With regard to the fundamental doctrines of Christianity,.

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  • In 1677 the fundamental laws of West New Jersey were published, and recognized in a most absolute form the principles of democratic equality and perfect freedom of conscience.

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  • To the latter Brown really belonged, but he had preserved certain doctrines of the older school which were out of harmony with his fundamental view.

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  • The poets - especially the authors of the New Comedy - strongly inculcate humanity, and insist on the fundamental equality of the slave.

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  • We have seen that slavery was a fundamental element of the old Roman constitution.

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  • A circular was soon after sent to the governors and marshals of the nobility all over Russia proper, informing them of this desire of the Lithuanian nobles, and setting out the fundamental principles which should be observed " if the nobles of the provinces should express a similar desire."

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  • Among its fundamental rules we find a provision for dividing the society into bands of five or ten persons who spoke freely and plainly to each other as to the real state of their hearts.

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  • Thus the Zarvanites represented Ormazd and Ahriman as twin sons proceeding from the fundamental principle of all - Zrvana Akarana, or limitless time.

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  • Though the intellectual world of the sages is different from that of the prophetic and legal Hebraism, they do not break with the fundamental Jewish theistic and ethical creeds.

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  • The United States left the task of altering the laws to the people, as far as there was no conflict between them and the Constitution of the United States and fundamental American legal customs. Copies of the Spanish codes were very rare, and some of them could not be had in the colonies.

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  • The government of intervention at first directed its main effort simply to holding the country together, without undertaking much that could divide public opinion or seem of unpalatably foreign impulse; and later to the establishment of a few fundamental laws which, when intervention ceased, should give greater simplicity, strength and stability to a new native government.

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  • All fundamental repairs thus fell to the charge of the state, which could not afford to effect them, and the vakuf revenues decreased so rapidly that already in the reign of Selim I.

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  • It is possible that some of these rocks are also of Huronian age, but it is doubtful whether the rocks so designated by the geologists of the " Alert " and " Discovery " expedition are really the rocks so known in Canada, or are a continuous portion of the fundamental or oldest gneiss of the north-west of Scotland and the western isles.

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  • A cry now arose in Holland for a revision of the fundamental law and for more liberal institutions; ministerial responsibility was introduced, and the royal control over finance diminished.

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  • Tschermak, in 1878, regarded them as isomorphous mixtures of the following fundamental molecules: H 2 KA1 3 (SiO 4) 3, corresponding with muscovite; Mg 6 Si 3 0 12, a hypothetical polymer of olivine; and H4S15012, a hypothetical silicic acid.

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  • +A(524) (13) +...; then D5D1D1 (213) (214) (15) =A; every other term disappearing by the fundamental property of D8.

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  • 132, 03,�.� we start with the fundamental relation (1+alx+aly)(1+a2x +t2Y) (1+a3x +03y)...

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  • In this notation the fundamental relation is written (l + a i x +01Y) (I + a 2x+l32Y) (1 + a3x+133y)...

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  • For write (pq) =s� and take logarithms of both sides of the fundamental relation; we obtain slox +soot' = + (3ly) S20x 2 +2siixy+s02y 2 = E(aix+(3 ly) 2, &C., and siox+SOly - (S 20 x2 + 2s ii x y+ s ooy 2) +...

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  • This notion is fundamental in the present theory because we will find that one of the most valuable artifices for finding invariants of a single quantic is first to find simultaneous invariants of several different quantics, and subsequently to make all the quantics identical.

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  • These fundamental or ground forms are connected by the relation - 2 1 (f,4) 1) 2 = -2f4,(f, 4,)2+ 02(f,f')2.

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  • - (aa) and then expresses the coefficients, on the right, in terms of the fundamental invariants.

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  • The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.

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  • For the unipartite ternary quantic of order n he finds that the fundamental system contains a (n+4) (n -1) individuals.

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  • Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

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  • Every symmetric function denoted by partitions, not involving the figure unity (say a non-unitary symmetric function), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.

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  • symbolically, to be the fundamental form of seminvariant of degree 0 and weight w; he observes that every form of this degree and weight is a linear lic expressions.

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  • sin w The fundamental fact that he discovered was the invariance of 2 COS w xy+y 2, viz.

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  • then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i = Xa i +,ia2, A2= - �ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (XA) = X i A2 - X2 Ai = (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (xa) possess the invariant property.

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  • For the linear forms aoxi+aix2=ax = b x there are four fundamental forms ax=a:,x i --+a i x 2 of degree-order (1, 1), x7-1--4_ � (0, 2), a i x, 1), a b =a2+ai � (2, 0), (iii.) and (iv.) being the linear covariant and the quadrinvariant respectively.

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  • This is the fundamental system; we may, if we choose, replace (ab) 2 by ab =a, 2, +2a1+a2 since the identity a a b b - a, = (ab) 2 shows the syzygetic relation (74+a 2) 2 - (ao +2a +�2) = 2(aoa2 - ai).

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  • On the 2 1st of January 1903 Cardinal Richard publicly condemned the book, as not furnished with an imprimatur, and as calculated gravely to trouble the faith of the faithful in the fundamental Catholic dogmas.

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  • On the r4th of February Mgr Amette, the new archbishop of Paris, prohibited his diocesans to read or defend the two books, which "attack and deny several fundamental dogmas of Christianity," under pain of excommunication.

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  • The fundamental articles of Parker's religious faith were the three "instinctive intuitions" of God, of a moral law, and of immortality.

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  • From this the distance of the sun can be at once determined by a fundamental equation of planetary motion.

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  • Putting a for the mean distance of the earth from the sun, and n for its mean motion in one second, we use the fundamental equation a3 n2 = Mo-1-M', Mo being the sun's mass, and M' the combined masses of the earth and moon, which are, however, too small to affect the result.

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  • Such experiments as these demonstrate the fundamental law that like poles repel each other; unlike poles attract.

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  • Until the mysteries of molecular constitution have been more fully explored, perhaps D may be most properly regarded as the fundamental phenomenon from which the others follow.

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  • He considers that Hall's is the fundamental phenomenon, and that the Nernst effect is essentially identical with it, the primary electromotive force in the case of the latter being that of the Thomson effect in the unequally heated metal, while in the Hall experiment it is derived from an external source.

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  • The fundamental method of research which Riemann employed has just been alluded to; the results will be best indicated in his own words: "The methods in use hitherto for treating functions of a complex variable always started from an expression for the function as its definition, whereby its value was given for every value of the argument; by our investigation it has been shown that, in consequence of the general character of a function of a complex variable, in a definition of this sort one part of the determining conditions is a consequence of the rest, and the extent of the determining conditions has been reduced to what is necessary to effect the determination.

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  • 2 From the fundamental principle of virtual velocities, which thus acquired a new significance, Lagrange deduced, with the aid of the calculus of variations, the whole system of mechanical truths, by processes so elegant, lucid and harmonious as to constitute, in Sir William Hamilton's words, "a kind of scientific poem."

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  • By his mode of regarding a liquid as a material system characterized by the unshackled mobility of its minutest parts, the separation between the mechanics of matter in different forms of aggregation finally disappeared, and the fundamental equation of forces was for the first time extended to hydrostatics and hydrodynamics.'

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  • between the adherents of spiritual prophecy and a party whose national worship of Yahweh involved for them no fundamental separation from the surrounding nations.

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  • These fundamental truths are the causes or "reasons" (apxai) of all derivative facts.

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  • This Light is not corporeal and yet is the fundamental reality of things.

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  • The institutions adopted were to be as far as possible in accordance with the wishes of the people, but it was a fundamental condition " that there should not be in the eye of the law any distinction or disqualification whatever, founded on mere difference of colour, origin, language or creed."

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  • Prantl has professed to find the headstream of Nominalism also in Scotus Erigena; but beyond the fact that he discusses at considerable length the categories of thought and their mutual relations, occasionally using the term voces to express his meaning, Prantl appears to adduce no reasons for an assertion which directly contradicts Erigena's most fundamental doctrines.

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  • Against the system of non-difference Abelard has a number of logical and traditional arguments to bring, but it is sufficiently condemned by his fundamental doctrine that only the individual exists in its own right.

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  • The Ars magna of the former professed by means of a species of logical machine to give a rigid demonstration of all the fundamental Christian doctrines, and was intended by its author as an unfailing instrument for the conversion of the Saracens and heathen.

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  • That this condition of things could not be allowed to continue was, indeed, recognized by all parties; the fundamental difference of opinion was as to the method by which it was to be ended.

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  • These attempts at the unification of algebra, and its separation from other branches of mathematics, have usually been accompanied by an attempt to base it, as a deductive science, on certain fundamental laws or general rules; and this has tended to increase its difficulty.

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  • While, therefore, the logical development of algebraic reasoning must depend on certain fundamental relations, it is important that in the early study of the subject these relations should be introduced gradually, and not until there is some empirical acquaintance with the phenomena with which they are concerned.

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  • (c) The fundamental properties of subtraction and of division are that A - B +B = A and m X m of A = A, since in each case the second operation restores the original quantity with which we started.

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  • Investigation of the writings of Indian mathematicians has exhibited a fundamental distinction between the Greek and Indian mind, the former being pre-eminently geometrical and speculative, the latter arithmetical and mainly practical.

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  • Fundamental theorems in the theory of equations are to be found in the same work.

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  • This study was inaugurated by George Peacock, who was one of the earliest mathematicians to recognize the symbolic character of the fundamental principles of algebra.

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  • A series of incidents proved the difference of outlook to be not merely personal but fundamental.

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  • He is also responsible for the formulation of an important principle, called by Haeckel " the biogenetic fundamental law," viz.

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  • Another important development of Darwin's conclusions deserves special notice here, as it is the most distinct advance in the department of bionomics since Darwin's own writings, and at the same time touches questions of fundamental interest.

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  • The contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the resolving power of optical instruments.

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  • In spite of the many improvements introduced by Rowland and of the care with which his observations were made, recent workers have come to the conclusion that .errors of unexpected amount have crept into his measurements of wave-lengths, and there is even a disposition to discard the grating altogether for fundamental work in favour of the so-called " interference methods," as developed by A.

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  • And it remains to be seen, how far the death of any form of living matter, at a given temperature, depends on the destruction of its fundamental substance at that heat, and how far death is brought about by the coagulation of merely accessory compounds.

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  • Religious dress (whether of priests or worshippers) was regulated by certain fundamental ideas concerning access to the deity and its consequences.

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  • According to our present knowledge of physiological and pathological processes, we must regard the cell as the ultimate biological unit - a unit of structure and a unit of function; this was first put forward by Schleiden in 1838, and by Schwann in 1839, but we owe to Virchow the full recognition of the fundamental importance of the living cell in all the processes of life, whether in health or disease.

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  • (4) They believe that the fundamental doctrines of their religion are also the basis of every true religion.

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  • From this definition we have the following important fundamental property which belongs to all hodographs, viz.

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  • The most fundamental division is into internal and external medicine, or into medicine proper and surgery.

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  • The standard of excellence in the ancient writers was indeed far above the level of the 16th century; but the fatal habit of taking at second hand what should have been acquired by direct observation retarded progress more than the possession of better models assisted it, so that the fundamental faults of medieval science remained uncorrected.

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  • But the development of mathematical and physical science soon introduced a fundamental change in the habits of thought with respect to medical doctrine.

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  • But in the absence of a general demonstration of that principle, his results did not command the confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending solely on the fundamental laws of mechanics.

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  • At the same time, it delights the pure theorist by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations, insomuch that hydrostatics may be considered as the Euclidean pure geometry of mechanical science.

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  • This fundamental principle of hydrostatics follows at once from the principle of the normality of fluid pressure implied in the definition of a fluid in § 4.

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  • If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.

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  • (a) The Anglo-Saxon legal system cannot be understood unless one realizes the fundamental opposition between folk-right and privilege.

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  • He starts from the fundamental thought of Jewish apocalyptic that the end of the world will be brought about by the direct intervention of God when evil has reached its climax.

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  • Its fundamental motive is the serious consideration, in a continuous and concrete manner, of that union of philosophy and history which had been glimpsed by earlier thinkers, but had hitherto been pursued in a manner more or less capricious.

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  • This knowledge, however, is by no means positivistic or empirical, but on the contrary it is dialectical and a priori synthetic, brought about by the spiritual categories; and from it there constantly arise new problems, an ever new position of the fundamental categories.

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  • By these and similar arguments he arrives at the fundamental principle of Scepticism, the radical and universal opposition of causes; panti logo logos antikeitai.

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  • The fundamental principle of the Frankish military system, that the man served at his own expense, was still unchanged.

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  • Underlying all the apparent confusion of fact and practice were certain fundamental principles and relationships, which were alike everywhere, and which really gave shape to everything that was feudal, no matter what its form might be.

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  • But from the fact that the bulk of the Tunisian population belongs to the Iberian section of the Berbers, and to this being no doubt the fundamental stock of most Italian peoples, the intermixture of the Italianized Berber with his African brother has not much affected the physique of the people, though it may have slightly tinged their mental characteristics.

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  • We must therefore regard the law in question as the broadest and most fundamental one which nature makes known to us.

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  • A more fundamental question is whether the name Yahweh originated among the Israelites or was adopted by them from some other people and speech.'

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  • But neither Elijah nor Elisha raised a voice against the cult; then, as later, in the time of Amos, it was nominally Yahweh-worship, and Hosea is the first to regard it as the fundamental cause of Israel's misery.

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  • The name in various modifications - Micaiahu, Micaiehu, Micaiah - is common in the Old Testament, expressing as it does a fundamental point of Hebrew faith: Who is like Yahweh ?

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  • Gordon Jones, Fundamental Principles of Positive Philos.

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  • He felt the majesty of these truths to be the greater that they so represented to him not only the most fundamental of human beliefs, but also all that man could be reasonably expected to believe, though to believe with his whole reason.

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  • The same fundamental rule applied, too, whether the field of the decoration was silk, paper or metal.

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  • It is a fundamental theorem in attractions that a thin spherical shell of matter which attracts according to the potential law of the inverse square acts on all external points as of a if it were concentrated at its centre.

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  • This is the cycle employed by Carnot for the establishment of his fundamental principle of reversibility as the criterion of perfect efficiency in a heat engine.

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  • This most fundamental point was finally settled by a more delicate test, devised by Lord Kelvin, and carried out in conjunction with Joule (1854), which showed that the fundamental assumption W =H in isothermal expansion was very nearly true for permanent gases, and that F'(t) must therefore vary very nearly as J/T.

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  • Although the value of G in any case cannot be found without that of 0, and although the consideration of the properties of the thermodynamic potential cannot in any case lead to results which are not directly deducible from the two fundamental laws, it affords a convenient method of formal expression in abstract thermodynamics for the condition of equilibrium between different phases, or the criterion of the possibility of a transformation.

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  • Tertullian exhausted the resources of dialectic in the endeavour to define and vindicate the relation of the spiritualists to the "psychic" Christians; but no one will say he has succeeded in clearing the Montanistic position of its fundamental inconsistency.

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  • Its causes and results are fundamental for the study of ethnology (formation and mixture of races), of political and social history (formation of states and survival of institutions), and of political economy (mobility of labour and utilization of productive forces).

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  • As has been well said by a learned Baptist theologian, Dr Green: " It was by a true divine instinct that the early theologians made Christ Himself, in His divine-human personality, their centre of the creeds."' The fundamental questions of Christianity, exhibited in theApostles' Creed, should be marked In response to an invitation issued by the archbishop of Canterbury, acting on a resolution of the Lambeth Conference of 1908, a committee of eminent scholars met in April and May 1909 for the purpose of preparing a new translation.

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  • Under (ii.) they laid stress on the fundamental articles of the faith (Art.

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  • The personal contact between Luther and Zwingli led to no mental rapprochement between the two; but in the following year the Articles of Marburg did good service as one of the preliminaries to the Augsburg Confession, and remain a valuable document for the fundamental principles common to the Lutheran and Reformed Churches.

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  • The Assyrians with all their culture, never attained the stage of analysis which demonstrates that only a few fundamental sounds are involved in human speech, and hence that it is possible to express all the niceties of utterance with an alphabet of little more than a score of letters.

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  • In 1779 he was a member of the convention which framed the constitution of Massachusetts that was adopted in 1780, and is still, with some amendments, the organic law of the commonwealth and one of the oldest fundamental laws in existence.

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  • Availing himself of the favourable moment, he obtained the enactment of the fundamental law of the 17th of December 1819, by which the republics of Venezuela and New Granada were henceforth to be united in a single state, under his presidency, by the title of the Republic of Colombia.

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  • "Carnot's principle" is fundamental in the theory of thermodynamics.

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  • He founded the science of politics for the modern world, by concentrating thought upon its fundamental principles.

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  • We may regard it as a supplement or appendix to the Principe and the Discorsi, since Machiavelli held it for a fundamental axiom that states are powerless unless completely armed in permanence.

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  • Fundamental alterations were made upon them: their wooden tubes were replaced by tubes of metal; 1 Description de l'observatoire central de Pulkowa, p. 208.

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  • Bjerknes have been usefully applied in many cases, but they cannot take the place of direct observations of currents and of the fundamental processes and conditions underlying them.

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  • Through all this runs the train of thought resulting naturally from Bruno's fundamental principles, and familiar in modern philosophy as Spinozism, the denial of particular providence, the doctrine of the uselessness of prayer, the identification in a sense of liberty and necessity, and the peculiar definition of good and evil.

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  • The result is that although the forms of apparatus utilized for this purpose are all based on the one fundamental principle of bringing about the contact of the carbide with the water which is to enter into double decomposition with it, they have been multiplied in number to a very large extent by the methods employed in order to ensure control in working, and to get away from the dangers and inconveniences which are inseparable from a too rapid generation.

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  • On the National Insurance bill in 1911 he pointed out that a fundamental change of opinion had taken place, both parties now accepting the principle that social welfare was the care of the State.

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  • The remainder of the year he spent at Zurich, slowly perfecting his thoughts on the fundamental problems left for solution in the Kantian philosophy.

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  • The philosophy of Fichte, worked out in a series of writings, and falling chronologically into two distinct periods, that of Jena and that of Berlin, seemed in the course of its development to undergo a change so fundamental that many critics have sharply separated and opposed to one another an earlier and a later phase.

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  • But as a rule most of those who have adopted this view have done so without the full and patient examination which the matter demands; they have been misled by the difference in tone and style between the earlier and later writings, and have concluded that underlying this was a fundamental difference of philosophic conception.

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  • We shall here note only three points: - (a) the origin in Kant; (b) the fundamental principle and method of the Wissenschaftslehre; (c) the connexion with the later writings.

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  • To Kant the fundamental condition was given in the synthetical unity of consciousness.

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  • But if complete, this Wissenschaftslehre must be able to deduce the whole organism of cognition from certain fundamental axioms, themselves unproved and incapable of proof; only thus can we have a system of reason.

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  • Of these, evidently the first must be the fundamental; to some extent it conditions the other two, though these cannot be deduced from it or proved by it.

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  • We progress by making explicit the oppositions contained in the fundamental synthesis, by uniting these opposites, analysing the new synthesis, and so on, until we reach an ultimate pair.

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  • By means of lighted candles violently dashed to the ground and extinguished the faithful were graphically taught the meaning of the greater excommunication - though in a somewhat misleading way, for it is a fundamental principle of the canon law that disciplina est excommunicatio, non eradicatio.

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  • This distinction is probably the most fundamental one, and itself supports a conclusion which is, on other grounds, becoming more and more likely, namely, that these two divisions are not related phylogenetically; but have, on the contrary, a radically different origin.

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  • Fourthly, and lastly, there was the most fundamental difficulty of all, the extent to which the pope, as the universally acknowledged head of the Church, was justified in interfering in the internal affairs of particular states.

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  • (1316-1334)1334) to control the election of the emperor called forth the first fundamental and critical attack on the papal monarchy, by Marsiglio of Padua, who declared in his Defensor pacis (1324) that the assumed supremacy of the bishop of Rome was without basis, since it was very doubtful if Peter was ever in Rome, and in any case there was no evidence that he had transmitted any exceptional prerogatives to succeeding bishops.

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  • He found it impossible to reconcile Tetzel's views of indulgences with his own fundamental theory of salvation.

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  • His fundamental religious conception was his assurance of salvation.

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  • He was suddenly forced to take up the consideration of some of the most fundamental points in the orthodox theology by the appearance of Tetzel in 1517.

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  • Apart from fundamental rejection of the papal supremacy, there was little novel in Luther's appeal.

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  • The edict of Worms was entirely in harmony with the laws of Western Christendom, and there were few among the governing classes in Germany at that time who really understood or approved Luther's fundamental ideas; nevertheless - if we except the elector of Brandenburg, George of Saxony, the dukes of Bavaria, and Charles V.'s brother Ferdinand - the princes, including the ecclesiastical rulers and the towns, commonly neglected to publish the edict, much less to enforce it.

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  • A fundamental difference as to the doctrine of the eucharist, however, stood in the way of the real union.

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  • no strong evangelical movement, and that Henry's pretty consistent adherence to the fundamental doctrines of the medieval Church was agreeable to the great mass of his subjects.

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  • Communion under both kinds and the marriage of the clergy were sanctioned, thus gravely modifying two of the fundamental institutions of the medieval Church.

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  • It was not until 1789 that the French Church of the middle ages lost its vast possessions and was subjected to a fundamental reconstruction by the Civil Constitution of the Clergy (1791).

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  • Luther and his sympathizers were blind to the reasonableness of the fundamental teachings of these " brethren."

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  • Chief among these encumbering presuppositions was that of a fundamental distinction between perception and conception and consequent upon it between the synthetic and the analytic use of thought.

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  • Equally fundamental is the element of synthesis.

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  • Of fundamental importance was the trade with the French West Indies, licit and illicit, particularly after the Peace of Utrecht (1713).

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  • yc,o f30vX1 7), named after the hill, is to be compared in origin and fundamental character with the council of chiefs or elders which we find among the earliest Germans, Celts, Romans, and other primitive peoples.

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  • His services to his church have been summed up thus: - (I) he has a keen sense of the proportion of the faith and maintains a clear distinction between what is fundamental, needing ecclesiastical commands, and subsidiary, needing only ecclesiastical guidance and suggestion; (2) as distinguished from the earlier protesting standpoint, e.g.

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  • Thus it has been used broadly of all theological doctrines, and also in a narrower sense of fundamental beliefs only, confession of which is insisted upon as a term of church communion.

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  • Along with this goes the fundamental Catholic view of " dogmatic faith " - the expression is as old as Cyril of Jerusalem (died 386), if not older - according to which it consists in obedient assent to the voice of authority.

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  • Quenstedt (c. 1685) and others - in a controversial interest, to blacken the Calvinists still more - distinguished which articles were " fundamental."

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  • Heinrich 3 is willing to speak of "fundamental dogmas," those which must be known for salvation; those for which " implicit " faith does not suffice.

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  • It has been supposed by many that he lived to a great age, and argued that "the never-to-be-mistaken fundamental tone of his performance is the quiet talkativeness of a highly cultivated, tolerant, intelligent, old man" (Dahlmann).

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  • Luther was content with changes in one or two fundamental doctrines; Zwingli aimed at a reformation of government and discipline as well as of theology.

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  • And behind these questions is the fundamental problem of the text, which has been somewhat too slightly treated.

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  • The fundamental assumption is that each group of strips of the trapezette may be replaced by a figure for which differences of u, above those of a certain order, vanish (§ 54).

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  • The use of quadrature-formulae is important in actuarial work, where the fundamental tables are based on experience, and the formulae applying these tables involve the use of the tabulated values and their differences.

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  • That these purely mechanical arrangements have any psychic, occult or predictive meaning is a fantastic imagination, which seems to have a peculiar attraction for certain types of mind, and as there can be no fundamental hypothesis of correlation, its discussion does not lie within the province of reason.

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  • So says Dr Hort (p. 229), adding that " the very origin and fundamental nature of the Ecclesia as a community of disciples renders it impossible that the principle should rightly become obsolete."

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  • Gioja's fundamental idea is the value of statistics or the collection of facts.

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  • A fundamental code was adopted in 1845 and a provisional government was established, to endure until " the United States of America extend their jurisdiction over us."

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  • In some cases of echo, when the original sound is a compound musical note, the octave of the fundamental tone is reflected much more strongly than that tone itself.

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  • If, for the single toothed wheel, be substituted a set of four with a common axis, in which the teeth are in the ratios 4: 5: 6: 8, and if the card be rapidly passed along their edges, we shall hear distinctly produced the fundamental chord C, E, G, C 1 and shall thus satisfy ourselves that the intervals C, E; C, G and C, C 1 are, 2 and 2 respectively.

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  • ix.) used a string loaded at the middle point so that the higher tones were several octaves above the fundamental, and so not likely to be mistaken for it; he found that with 37 vibrations per second a very weak sensation of tone was heard, but with 34 there was scarcely anything audible left.

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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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  • If the series were complete we should have terms which separately would correspond to the fundamental, its octave, its twelfth, its double octave, and so on.

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  • Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.

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  • If, for instance, a note is struck and held down on a piano, a little practice enables us to hear both the octave and the twelfth with the fundamental, especially if we have previously directed our attention to these tones by sounding them.

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  • The first mode of vibration gives the " fundamental tone," and the succeeding modes are termed " overtones."

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  • A " stopped pipe " in an organ is a pipe of this type, and both the fundamental and the overtones may occur simultaneously when it is blown.

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  • Thus if a fork Ut 3 = 256 is used, the length of pipe for the fundamental at o° C. is about 33,000/4X256 =33 cms. If a fork Solo= 768 is used the pipe resounds to it according to the mode of the first overtone.

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  • The fundamental mode is that in which H and K represent the ends of the pipe.

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  • The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..

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  • If the frequency is 256 the corrected length for the fundamental is about (33,000/2 X256) (1 +.

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  • When the pipe is blown softly the fundamental is very predominant, and there is a node at the middle point.

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  • The other end of the sounder is stroked outwards with a damp cloth so as to make it sound its fundamental.

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  • The fundamental mode is that in which A and B represent the ends of the string.

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  • If D is removed and the string is bowed in the middle, the fundamental is brought out.

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  • Not only may the fundamental and its harmonics be obtained separately, but they are also to be heard simultaneously, particularly the earlier ones, which are usually more prominent than those higher in the series.

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  • 36, for the fundamental and the first harmonic. When a string is struck or bowed at a point, any harmonic with a node at that point is absent.

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  • But keeping r/X small we may as before form stationary waves, and it is evident that the series of fundamental and overtones will be just as with the air in pipes, and we shall have the same three types - fixed at one end, free at both ends, fixed at both ends - with fundamental frequencies respectively 41, p ' 21 V p, and I velocity in rod =velocity in air X distance between dust heaps.

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  • For a bar free at both ends the fundamental mode of vibration has two nodes, each 0.224 of the length from the end.

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  • The fundamental mode has that node only.

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  • The first overtone has frequency 6.25 that of the fundamental, and is not in the harmonic series.

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  • If the wire is stretched across a room and stroked in the middle with a damp cloth the fundamental is easily obtained, and the first harmonic can be brought out by stroking it at a quarter the length from one end.

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  • Young's modulus may be obtained for the material of a rod by clamping it in the middle and obtaining the frequency of the fundamental when Y = 412n2p.

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  • If a rod is clamped at one end and free at the other, the fundamental frequency is (i/1)¦l (n/p).

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  • When the flame is at a certain distance within the tube the air is set in vibration, and the sounding tube gives out its fundamental note continuously.

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  • But we have to remember that with strings, pipes and instruments generally the fundamental tone is accompanied by overtones, called also " upper partials," and beating within the dissonance range may occur between these overtones.

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  • Thus, suppose a fundamental 256 has present with it overtone harmonics 512, 768, 1024, 1280, &c., and that we sound with it the major seventh with fundamental 480, and having harmonics 960, 1440, &c. The two sets may be arranged thus c 256 512 768 1024 1280 h 480 960 1440, and we see that the fundamental of the second will beat 32 times per second with the first overtone of the first, giving dissonance.

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  • The fundamental and overtones of the second all coincide with overtones of the first.

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  • Take as a further example the fifth with harmonic overtones as under The fundamental and overtones of the second either coincide with or fall midway between overtones in the first, and there is no approach to a dissonant frequency of beats, and the concord is perfect.

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  • Koenig, Quelques experiences d'acoustique (1882) describes apparatus and experiments, intended to show, in opposition to Helmholtz, that beats coalesce into tones, and also that the quality of a note is affected by alteration of phase of one of its component overtones relative to the phase of the fundamental.

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  • As assemblyman, as police commissioner, as naval secretary and as president, he advocated this fundamental doctrine.

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  • His history of the War of 1812 between the United States and Great Britain, written when he was twentyfour years old, is still the standard history of that conflict, and his Winning of the West is probably the best work which has been written on American frontier life of the 19th century, a life that developed certain fundamental and distinctive American social and political traits.

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  • In mathematical geography the problem of representing the surface of a sphere on a plane is of fundamental importance; this subject is treated in the article MAP.

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  • A fundamental difference in girder bridges arises from the mode of support.

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  • Next follow chapters on the literary renaissance of the nation, its progress in art, mathematics, chemistry and natural science; the magnificent development of agriculture, modern industry, commerce and finance; and in particular its flourishing selfgovernment, " which will be exercised in the fullest freedom," and in which " the communal organization embodies in the highest degree the conception of self-government " (p. 234), and " the independent sphere of activity unlimited in its fundamental principle " (p. 235) in that " State control is exercised seldom and discreetly " (p. 236).

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  • Politically the organization of the state on the fundamental principle of national autonomy was to follow; he hoped to get round the nationalist obstacles in Bohemia by a rearrangement of districts with local delimitation according to nationality.

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  • 22 that this resolution was totally opposed to that of May 1917, which could still be reconciled with the fundamental conceptions of patriotism.

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  • The first and fundamental characteristic of Ultramontanism is its championship of a logical carrying out of the so-called " papalistic system," the concentration, that is, of all ecclesiastical power in the person of the Roman bishop. This.

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  • That science must be left free to determine the aims of her investigation, to select and apply her own methods, and to publish the results of her researches without restraint, is a postulate which Ultramontanism either cannot understand or treats with indifference, for it regards as strange and incredible the fundamental law governing all scientific research - that there is for it no higher aim than the discovery of the truth.

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  • Again, the attempt to subordinate all intellectual life to ecclesiastical control was a feature of the medieval Church, and the fundamental attitude of that Church towards heresy was fixed during the same period.

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  • Thus Ultramontanism is not to be conceived as a theological movement, but as the programme of a party whose principles are in fundamental opposition to modern culture, modern education, modern tolerance and the modern state - a party which seeks to carry out its campaign against the society of to-day, not by bridging the gulf betwixt creed and creed, but by widening it, by awakening religious fanaticism, and by closing the way to a peaceful co-operation of Catholics and non-Catholics in the highest tasks of culture and human civilization.

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  • The former, besides embodying catechetical instruction in Christian conduct (the "Two Ways"), which goes back in substance to the early apostolic age and is embodied also in "Barnabas," depicts in outline the fundamental usages of church life as practised in some conservative region (probably within Syria) about the last quarter of the 1st century and perhaps even later.

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  • The result of this act of 1873 was to effect a fundamental change in the judicature system.

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  • The last subdivision is fundamental.

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  • denoted a necklace of twenty-seven pearls; 1 and the fundamental equality of the parts was figured in an ancient legend, by the compulsion laid upon King Soma (the Moon) to share his time impartially between all his wives, the twenty-seven daughters of Prajapati.

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  • Their number, as a multiple of four, was prescribed by the quaternary partition of the heavens, fundamental in Chinese astronomy.

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  • They served, in fact, and still serve (though with astrological ends in view), the precise purpose of " fundamental stars " in European astronomy.

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  • In 1848 the Grondwet, or fundamental law of the Netherlands, recognized for the first time the responsibility of the Dutch nation for its colonial dependencies.

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  • Metaphysics, again, is concerned with the ultimate problems of matter and spirit; it endeavours to go behind the phenomena of sense and focus its attention on the fundamental truths which are the only logical bases of natural science.

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  • Mayer entirely ignored the grand fundamental principle laid down by Sadi Carnot - that nothing can be concluded as to the relation between heat and work from an experiment in which the working substance is left at the end of an operation in a different physical state from that in which it was at the commencement.

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  • We must be content to treat the aether as a plenum, which places it in a class by itself; and we can thus recognize that it may behave very differently from matter, though in some manner consistent with itself - a remark which is fundamental in the modern theory.

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  • The greatest obstacle to such a search for the fundamental medium is the illimitable complexity of matter, as contrasted with the theoretical simplicity and uniformity of the physical agencies which connect together its different parts.

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  • The laws of thermodynamics, including the fundamental principle that a physical property, called temperature, can be defined, which tends towards uniformity, are thus relations between the properties of types of material bodies that can exist permanently in presence of each other; why they so maintain themselves remains unknown, but the fact gives the point d'appui.

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  • The fundamental character of energy in material systems here comes into view; if there were any other independent scalar entity, besides mass and energy, that pervaded them with relations of equivalence, we should expect the existence of yet another set of qualities analogous to those connected with temperature.

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  • On such a view the aether might conceivably be a perfect fluid, its fundamental property of elastic reaction arising (as at one time suggested by Kelvin and G.

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  • The most fundamental experimental confirmation that the theory of the aether has received on the optical side in recent years has been the verification of Maxwell's proposition that radiation exerts mechanical force on a material system, on which it falls, which may be represented in all cases as the resultant of pressures operating along the rays, and of intensity equal at each point of free space to the density of radiant energy.

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  • He thus did away with the fundamental distinction between Jews and Gentiles.

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  • Other fundamental principles of Paul's failed of comprehension and acceptance, but the belief finally prevailed that the observance of Jewish law and custom was unnecessary, and that in the Christian Church there is no distinction between the circumcised and the uncircumcised.

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  • This double conception of salvation and of the means thereto was handed down to the Church of subsequent generations and became fundamental in its thought.

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  • Agreeing as they did in this fundamental theory, all differences were of minor concern.

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  • However much it agreed in admiration of the ancients, it differed absolutely in its preservation of the fundamental ideas of Christianity.

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  • Their object had been to purify the Church of medieval accretions, and to restore the primitive model in the light of the new learning; the idea of rival " churches," differing in their fundamental doctrines and in their principles of organization, existing side by side, was as abhorrent to them as to the most rigid partisan of Roman centralization.

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  • The anathema of the Roman Church had fallen upon all the fundamental doctrines for which the Reformers had contended and died; the right of free discussion within the limits of the creeds, which had given room for the speculations of the medieval philosophers, was henceforth curtailed and confined; and the definitions of the schoolmen were for ever exalted by the authority of Rome into dogmas of the Church.

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  • The fundamental type of the Arabic sanctuary can be traced through all the Semitic lands, and so appears to be older than the Semitic dispersion; even the technical terms are mainly the same, so that we may justly assume that the more developed ritual and priesthoods of the settled Semites sprang from a state of things not very remote from what we find among the heathen Arabs.

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  • So fundamental a change as lies between Hosea and the Priestly Code was only possible in the general dissolution of the old life of Israel produced by the Assyrians and by the prophets; and indeed the new order did not take shape as a system till the exile had made a great change in old institutions.

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  • Legendre's theorem is a fundamental one in geodesy, and his contributions to the subject are of the greatest importance.

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  • flattening of particles by compression, orientation of particles by flow and formation of laminar crystals, the fundamental explanation of slaty cleavage is found.

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  • In fundamental principles he follows almost entirely Locke and Pufendorf; but he works out with great skill the theory of moral obligation, referring it to the command or will of God.

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  • In 1636 Hartford was the meeting-place of the first general court of the Connecticut colony; the Fundamental Orders, the first written constitution, were adopted at Hartford in 1639; and after the union of the colonies of New Haven and Connecticut, accomplished by the charter of 1662, Hartford became the sole capital; but from 1701 until 1873 that honour was shared with New Haven.

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  • The fundamental idea of Soxhlet's method for sterilizing milk is to boil it for forty minutes in small bottles holding just enough for one meal, and closing the same with an impervious stopper, which is only removed just before use.

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  • The Mathesis universalis, a more elementary work, contains copious dissertations on fundamental points of algebra, arithmetic and geometry, and critical remarks.

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  • In impressive and persuasive oratory he sets before Israel, in a form adapted to the needs of the age in which he lived, the fundamental principles which Moses had taught.

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  • This is the fundamental thought which is insisted on and developed in Deuteronomy with great eloquence and power.

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  • The fundamental peculiarity of the movement lies in the fact that it is a criticism of what is supreme in Israel - its religion, and that it has rendered possible a true appreciation of this by showing that, like all living and life-giving systems of thought, belief and practice, the religion of Israel was subject to development.

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  • Inherent in this view of religious development and the new critical position were far-reaching changes in the literary, historical and religious criticism of the Old Testament: these have been gradually rendered clear as the fundamental positions on which they rest have been secured by the manifold work of two generations of scholars.

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  • Other important works in which English and American scholars have co-operated are the Encyclopaedia Biblica (1899-1903) and Hastings' Bible Dictionary (1898-1904) - the latter less radical, but yet on the whole based on acceptance of the fundamental positions of Vatke, Graf, Wellhausen.

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  • The reasons which converge upon the conclusion just expressed as to the origin and nature of the fundamental documents worked up in our present Synoptic Gospels are as follows: (i.) The literary analysis of the Synoptic Gospels brings out a number of sections common to Matthew and Luke which probably at one time existed as an independent document.

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  • And this belief was the fundamental principle that determined the marking off of the writings of the first, or apostolic, age from the rest.

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  • There are some fundamental divergencies in the representations of the traditions of both David and Saul (qq.v.), and there is indirect and 1 Cf.

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  • Sabine remarked when awarding him the Rumford medal of the Royal Society in 1872, contains a fundamental principle of spectrum analysis, and though for a number of years it was overlooked it entitles him to rank as one of the founders of spectroscopy.

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  • The fundamental idea that Yahweh guides His people by the word of revelation is older than the separation of special classes of theocratic organs; Moses, indeed, is not only prophet and priest, but judge and ruler.

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  • xix., 1871, p. 236, &c.) therefore relied upon more fundamental characters, notably the presence or absence of osteoderms, the formation of the skull, the teeth and the tongue.

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  • (a) Its fundamental law to circulate the Bible alone, without note or comment, was vehemently attacked by Bishop Marsh and other divines of the Church of England, who insisted that the Prayer Book ought to accompany the Bible.

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  • In 1826 the society finally resolved that its fundamental law be fully and distinctly recognized as excluding the circulation "of those Books, or parts of Books, which are usually termed Apocryphal."

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  • Authoritative standards and instruments for the measurement of electricity, based on the fundamental units of the metric system, have been placed in the Electrical Laboratory of the Board of Trade.

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  • So far this later research appears to confirm the opinion of Böckh (2) that fundamental units of measure were at one time derived from weights and capacities.

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  • For engineering and manufacturing purposes the more important linear gauges are, however, now used, adjusted to some fundamental unit of measure as the inch; although in certain trades, as for wires and flat metals, gauges continue to be used of arbitrary scales and of merely numerical sizes, having no reference to a legal unit of measure; and such are rarely accurate.

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  • As a moral philosopher Smith cannot be said to have won much acceptance for his fundamental doctrine.

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  • But it is evident, and Smith himself felt, that their agreements were much more fundamental than their differences; and, if we regard them as historical forces, they must be considered as working towards identical ends.

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  • The following fundamental properties of log x are readily deducible from the definition (i.) log xy= log x-Flog y.

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  • The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x.

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  • The calculation of the logarithms not only of numbers but also of the trigonometrical functions is therefore due to Briggs and Vlacq; and the results contained in their four fundamental works - A rithmetica logarithmica (Briggs), 1624; Arithmetica logarithmica (Vlacq), 1628; Trigonometria Britannica (Briggs), 1633; Trigonometria artificialis (Vlacq), 1633 - have not been superseded by any subsequent calculations.

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  • Those engaged upon the work were divided into three sections: the first consisted of five or six mathematicians, including Legendre, who were engaged in the purely analytical work, or the calculation of the fundamental numbers; the second section consisted of seven or eight calculators possessing some mathematical knowledge; and the third comprised seventy or eighty ordinary computers.

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  • This definitely directed evolution, or development in a few determinable directions, has since been termed " orthogenetic evolution," and is recognized by all workers in invertebrate palaeontology and phylogeny as fundamental because the facts of invertebrate palaeontology admit of no other interpretation.

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  • Williams observes (Geological Biology, p. 268) that the evolution of those fundamental characters which mark differences between separate classes, orders, sub-orders, and even families of organisms, took place in relatively short periods of time.

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  • Natural Hist., 1906, p. 317) notes that the fundamental advances in the growth of fish life have always been sudden, beginning with excessive vigour at the end of long periods of apparent stagnation; while each advance has been marked by the fixed and definite acquisition of some new anatomical character or " expression point," a term first used by Cope.

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  • And out of the combination of these two dualisms arose the teaching of Gnosticism, with its thoroughgoing pessimism and fundamental asceticism.

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  • With this fundamental doctrine of Gnosticism is connected, as Anz has shown in his book which we have so often quoted, a side of their religious practices to which we have already alluded.

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  • Of all the fundamental ideas of Gnosticism of which we have so far treated, it can with some certainty be assumed that they were in existence before the rise of Christianity and the influence of Christian ideas on the development of Gnosticism.

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  • The fundamental conception varies greatly.

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  • But the fundamental ideas of Gnosticism and of early Christianity had a kind of magnetic attraction for each other.

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  • Nadaillac, Prehistoric America (New York, 1895); Zelia Nuttall, The Fundamental Principles of the Old and New World Civilizations (Arch.

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  • The fundamental assumption is that the medium contains positively and negatively charged ions or electrons which are acted on by the periodic electric forces which occur in wave propagation on Maxwell's theory.

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  • The fundamental features of knowledge, whether as activity or as sum of apprehended fact, and of conduct had been deduced as elements necessary in the attainment of self-consciousness.

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  • Its manifoldness is not then to be taken as excluding its fundamental unity; the divisions which our ordinary perception and thought introduce into it have not absolute validity, but are to be interpreted as the outcome of the single formative energy or complex of forces which is the inner aspect, the soul of nature.

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  • The dynamical series of stages in nature, the forms in which the ideal structure of nature is realized, are matter, as the equilibrium of the fundamental expansive and contractive forces; light, with its subordinate processes - magnetism, electricity, and chemical action; organism, with its component phases of reproduction, irritability and sensibility.'

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  • His tendency towards mystical speculation formed a not less fundamental quality of his mind than its strong grasp of positive scientific truth.

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  • It was an enlarged sketch, prepared in four months, in which more stress was laid on fundamental theories than on the facts, which are more rigidly linked together than their historical sequence warrants.

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  • But many of the directions are much too serious and fundamental to have been given in this form; one can hardly imagine that Paul considered Timothy (or Titus) still in need of elementary advice and warning upon such matters, and especially on personal purity.

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  • 2) showed that one at least of the fundamental myths of Mani was borrowed from the Avesta, namely, that which recounts how through the manifestation of the virgin of light and of the messenger of salvation to the libidinous princes of darkness the vital substance or light held captive in their limbs was liberated and recovered for the realm of light.

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  • They were formerly regarded as older thaii the schists and were designated on this account primitive, fundamental, &c. They have also been called Laurenlian, a name which is still sometimes applied to them.

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  • They have now become very long and elaborate documents, seven, eight or ten times as long as the Federal Constitution, and containing a vast number of provisions on all sorts of subjects, many of them partaking of the nature of ordinary statutes passed by a legislature rather than safeguards suitable to a fundamental instrument.

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  • It is a fundamental principle of the American system that the national government possesses a direct and immediate authority over all its citizens, quite irrespective of their allegiance and duty to their own state.

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  • Following what was then deemed a fundamental maxim of political science, they divided the government into three departments, the legislative, the executive and the judicial, and sought to keep each of these as far as possible detached from and independent of the other two.

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  • The fundamental properties of coaxal systems may be summarized: 1.

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  • To compare it on this score with the fundamental proposition of Archimedes, the latter must be put into a form similar to Snell's.

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  • he claims only that the generation of the curves and their fundamental properties in Book i.

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  • The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the Cartesian equation referred to oblique axes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity.

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  • It is clearly the form of the fundamental property (expressed in the terminology of the "application of areas") which led him to call the curves for the first time by the names parabola, ellipse, hyperbola.

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  • It must, however, be distinctly borne in mind that there is a fundamental difference between the eye of Vertebrates and of all other groups in the fact that in the Vertebrata the retinal body is itself a part of the central nervous system, and not a separate C E k e FIG.

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  • Bekker, Berlin, 1831, the pages of which we use for our quotations), we find, instead of the general dialogues of Plato, special didactic treatises, and a fundamental difference of philosophy, so great as to have divided philosophers into opposite camps, and made Coleridge say that everybody is born either a Platonist or an Aristotelian.

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  • Accordingly in this dialogue he attacked Plato's fundamental position, both in its written and in its unwritten presentment, as a.

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  • On either alternative, however, " the first discourses " mentioned may have originally been a separate discourse; for Book F begins quite fresh with the definition of the science of being, long afterwards called " Metaphysics," and Book Z begins Aristotle's fundamental doctrine of substance.

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  • - This short discourse turns on Aristotle's fundamental doctrine of individual substances, without which there is nothing.

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  • Things are individual substances, without which there is nothing - this is the fundamental point of Aristotelianism, as against Platonism, of which the fundamental point is that things are universal forms without which there becomes nothing.

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  • In brief then the common ground of the Categories and the Metaphysics is the fundamental position that all things are substances having belonging to them universals and attributes, which have no separate being as Plato falsely supposed.

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  • Throughout his whole subsequent life, however, he retained the fundamental doctrine, which he had learnt from Plato, and Plato from Socrates, that virtue is essential to happiness.

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  • On the other hand, there are still more fundamental points in which the first three books of the Eudemian Ethics are a very inadequate preparation for the common books.

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  • Aristotle then wrote three moral treatises, which agree in the fundamental doctrines that happiness requires external fortune, but is activity of soul according to virtue, rising from morality through prudence to wisdom, or that science of the divine which constitutes the theology of his Metaphysics.

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  • But at bottom there remains the fundamental position of Aristotelianism, that all things are substances, individuals separate though related; that some things are attributes, real only as being some individual substance somehow affected, or, as we should say, modified or determined; and that without individual substances there is nothing, and nothing universal apart from individuals.

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  • These three currents combined to produce the three fundamental ideas of Bolshevism: the conquest of society by the proletariat class, the power of revolutionary instinct and the dictatorship of a compact minority.

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  • " For us, therefore, Socialism without democracy is unthinkable."Kautsky had no difficulty in showing that, in consequence of this fundamental flaw, the practical results of Soviet rule were deplorable.

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  • In the pursuit of this inquiry he rashly invaded other departments of science, and much of the Common Place Book is occupied with a polemic, as vigorous as it is ignorant, against the fundamental conceptions of the infinitesimal calculus.

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  • To Berkeley, however, the difference is fundamental; sense ideas are not due to our own activity; they must therefore be produced by some other will - by the divine intelligence.

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  • As a piece of consecutive reasoning upon a fundamental Christian doctrine it deservedly attracted great attention.

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  • The fundamental objection to empiricism is that it fails to give an accurate explanation of experience; individual impressions as such are momentary, and their connexion into a body of coherent knowledge presupposes mental action distinct from mere receptivity.

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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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  • The quantity N may serve to fix the third fundamental unit.

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  • The objections raised from the Nonconformist point of view were numerous and varied, but they were thoroughly discussed between the first meeting on the 15th of April and the last on the 24th of July 1661; the bishops agreeing to meet the Puritan wishes on a few minor points but on none of fundamental importance.

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  • The average American citizen is only too prone to carry his national political predilections into local elections, and to vote for the local nominees of his party, without regard to the question of fitness of candidates and the fundamental difference of issues involved.

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  • The fundamental idea of this work is that human life is in reality only a great education, of which perfection is the aim.

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  • As to the origin of knowledge, Kant's position is that sense, outer and inner, affected by things in themselves, receives mere sensations or sensible ideas (Vorstellungen) as the matter which sense itself places in the a priori forms of space and time; that thereupon understanding, by means of the synthetic unity of apperception, " I think " - an act of spontaneity beyond sense, in all consciousness one and the same, and combining all my ideas as mine in one universal consciousness - and under a priori categories, or fundamental notions, such as substance and attribute, cause and effect, &c., unites groups of sensations or sensible ideas into objects and events, e.g.

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  • Here he was for the first time grappling with a fundamental difficulty in metaphysical idealism which is absent from realism, namely, the difficulty of explaining the identity of a thing, e.g.

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  • But, while he fully recognized his indebtedness to his master, he differed from him profoundly in one fundamental respect.

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  • But while he was in fundamental agreement with the first two positions of Kant, he differed from the third; he did not believe that the causes of sensible phenomena can be unknown things in themselves.

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  • Here he appeals to Schopenhauer's doctrine that will of some sort is the fundamental fact of mental life.

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  • He agrees with Schopenhauer that will is the fundamental form of the spiritual.

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  • Like these predecessors, and like his younger contemporary Paulsen, in calling will fundamental he includes impulse (Trieb).

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  • He agrees with Hegel that there are two fundamental identities, the identity of all reason, and the identity of all reason and all being.

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  • Hence his personal or pluralistic idealism is the view that the world is a plurality of many coexisting and interacting centres of experience, while will is the most fundamental form of experience.'

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  • The chief results we have found against materialism are that bodies evolving account neither for the origin of themselves, their nature, and their fundamental order of resemblance and difference, nor for the nature and origin of consciousness, nor even as yet for their becoming good for conscious beings.