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Often assumptions are made which lead to equations in x which cannot be solved "rationally," i.e.

93I buy something because I have certain assumptions about how much happiness it will bring me.

72These assumptions marked a definite rejection of all allegiance to Rome.

77When the assumptions on which it rests are proved to be baseless, the particular scepticism is also overcome.

67There is no subject of human study which may not be at some time or other of economic significance, and anything which affects the character, the ideals or the environment of man may make it necessary to modify our assumptions and our reasoning with regard to his conduct in economic affairs.

42His assumptions are based upon ordinary observation and experience, and are usually accurate in proportion to his practical shrewdness and sagacity, so that he is not interested in the speculative flights of philosophy, except in so far as they influence or have influenced conduct.

22But the modern conception of society or the state owes more to biology than philosophy, and actual research has destroyed more frequently than it has justified the assumptions of the older philosophical school.

22As a matter of fact, discussions of method and the criticism of hypotheses and assumptions are very rarely found in early economic works.

22All the assumptions we require are furnished by observation of people in the mass and the larger generalizations of statistics.

22Morphology becomes a farce when such assumptions are made.

22I know that sounds preposterous—but only based on our assumptions that the future will be like the past.

22He also gives us " natural law " 2 - a Stoic inheritance, preserving the form of an idealist appeal to systematic requirements of reason, while practically limiting its assumptions to those of intuitionalism.

11It rested on a mass of legal assumptions and subtleties, fallacious indeed, but ingenious, and, as the result proved, effective.

11The assumptions, the definitions, the reasoning, the conclusions of the classical writers have been ruthlessly overhauled.

11We may talk of the assumptions implicitly involved in Ricardo's works.

11Although Kekule founded his famous benzene formula in 1865 on the assumptions that the six hydrogen atoms in benzene are equivalent and that the molecule is symmetrical, i.e.

11Regarding it as important that all reasoning with reference to magnetism should be conducted without any uncertain assumptions, he worked out a mathematical theory upon the sole foundation of a few wellknown facts and principles.

11That it formed the starting-point, and largely prescribed the course of thought on the subject of planetary origin is due to the simplicity of its assumptions, and the clearness of the mechanical principles involved, rather than to any cogent evidence of its truth.

11This theory, however, depended upon unverified assumptions, such as the supposed silence of theologians about the creed at the beginning of the 9th century; the suggestion that the completed creed would have been useful to them if they had known it as a weapon against the heresy of Adoptianism; the assertion that no MS. containing the complete text was of earlier date than c. 813.

11Since the volume at constant pressure is exactly proportional to the absolute temperature, it follows that the coefficients of expansion of all gases ought, to within the limits of error introduced by the assumptions on which we are working, to have the same value 1/273.

11But in Servetus, whose execution he approved, we find an isolated, feeble revolt against assumptions which both Catholics and Protestants of all shades accepted without question.

11The struggle with the Crown, which ended in independence, began at the foundation of the colony, with assumptions of power under the charter which the colonial government was always trying to maintain, and the crown was as assiduously endeavouring to counteract.

11Over against these sweeping assumptions and deductions, the Roman Catholic Church had to build up its own statement of the basis of belief.

11That world of the learned offers us non-dogmatic definitions, drawn up from the outside; definitions which do not share the root assumptions either of Catholicism or of post-Reformation Protestant orthodoxy.

11(a) The nature of the bounding curve or surface may not be exactly known, so that certain assumptions have to be made, a formula being then used which is adapted to these assumptions.

11The application of Simpson's rule, for instance, to a plane figure implies certain assumptions as to the nature of the bounding curve.

11In finding the line of pressure some principle such as the principle of least action must be used in determining the reactions at the crown and springings, and some assumptions must be made of not certain validity.

11These assumptions, however, were fanciful.

11- The theory of conduction of heat by diffusion in gases has a particular interest, since it is possible to predict the value on certain assumptions, if the viscosity is known.

11Since the volume at constant pressure is exactly proportional to the absolute temperature, it follows that the coefficients of expansion of all gases ought, to within the limits of error introduced by the assumptions on which we are working, to have the same value 1/273.

11But in Servetus, whose execution he approved, we find an isolated, feeble revolt against assumptions which both Catholics and Protestants of all shades accepted without question.

11- The theory of conduction of heat by diffusion in gases has a particular interest, since it is possible to predict the value on certain assumptions, if the viscosity is known.

11In areas of uncertainty, we form our opinions on the basis of assumptions in other parts of our life.

11would give negative, surd or imaginary values; Diophantus then traces how each element of the equation has arisen, and formulates the auxiliary problem of determining how the assumptions must be corrected so as to lead to an equation (in place of the "impossible" one) which can be solved rationally.

13They are repelled by the dryness of much of the matter, the unsuitableness of many of the topics discussed for poetic treatment, the arbitrary assumption of premises, the entire failure to establish the connexion between the concrete phenomena which the author professes to explain and these assumptions, and the erroneousness of many of the doctrines which are stated with dogmatic confidence.

13These assumptions are often wrong.

13To the specialists in sciences which were advancing rapidly and in divergent directions to results which often reacted on and transformed their initial assumptions, Spencer has often appeared too much of a philosopher and defective in specialist knowledge.

17To the specialists in sciences which were advancing rapidly and in divergent directions to results which often reacted on and transformed their initial assumptions, Spencer has often appeared too much of a philosopher and defective in specialist knowledge.

17In finding the abutment reactions some principle such as the principle of least action must be used, and some assumptions of doubtful validity made.

00Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load.

00Such a distinction involves the assumptions that bodily pleasures are generically different from mental ones, and that there is in practice a clearly marked dividing line, - both of which hypotheses are frequently denied.

00But there is another species of deduction which, as Cliffe Leslie has shown, seriously tainted the philosophy of Smith - in which the premises are not facts ascertained by observation, but the a priori assumptions which we found in the physiocrats.

00In his speculations as to the physical cause of the celestial motions, his mind, though not wholly emancipated from the tyranny of gratuitous assumptions, was working steadily towards the light.

00He gradually fell under the dominion of two false assumptions.

00On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

00His commentaries on the Scriptures were the first application on an extensive scale of the principle affirmed by Scaliger, that, namely, of interpretation by the rules of grammar without dogmatic assumptions.

00While it is evident that some such conclusion must follow from the attempt to regard the cognitive consciousness as made up of disconnected feelings, it is equally clear, not only that the result is selfcontradictory, but that it involves certain assumptions not in any way deducible from the fundamental view with which Hume starts.

00There can, on these assumptions, be no doubt that, from the early years of the 5th century B.C., the archonship was of practically no importance.

00China and Japan have hitherto been regarded as the chief producers of tea, and the reputed large domestic consumption of those Mongolian peoples has led to assumptions of vast internal productions.

00But in such an undertaking one is always apt to take subjective assumptions or mere fancies for established data.

00Such assumptions are not wholly unjustified.

00The obvious way of avoiding the scepticism into which rationalism is thus driven is to revise the assumptions about the nature and postulates of truth which lead to it.

00But if thus far Grote's protest against prevalent assumptions carries an immediate and unhesitating conviction, it may be doubted whether his positive statement can be accounted final.

00The Result Calculated On These Assumptions Is Given In The Last Column In Joules, And Also In Calories Of 20° C. The Heatloss In This Example Is Large, Nearly 4.5% Of The Total Supply, Owing To The Small Flow And The Large Rise Of Temperature, But This Correction Was Greatly Reduced In Subsequent Observations On The Specific Heat Of Water By The Same Method.

00and its companion a diameter of 830,000 m.; the distance between their centres cannot be deduced without making certain doubtful assumptions, but may be about 3,000,000 m.

00In a very short time he settled his fundamental assumptions.

00Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

00The simplest assumptions to make are that the vapour behaves as a perfect gas (or that p(v-w) = Re), and that L is constant.

00Plane Stalics.The statics of a rigid body rests on the following two assumptions:

00From this point of view the equation is a mere truism, its real importance resting on the fact that by attributing suitable values to the masses in, and by making simple assumptions as to the value of X in each case, we are able to frame adequate representations of whole classes of phenomena as they actually occur.

00The equation of energy for a rigid body has already been stated (in effect) as a corollary from fundamental assumptions.

00We must not suffer it to lead us into rhetoric about the deadness and the darkness of the middle ages, or hamper our inquiry with preconceived assumptions that the re-birth in question was in any true sense a return to the irrecoverable pagan past.

00He first introduced into economics on a great scale the method of deduction from a priori assumptions.

00He also pointed out more distinctly the nature of the assumptions which we must make with respect to the law of action of the particles in order to be consistent with observed phenomena.

00He was at issue, however, with the atomistic materialism of Democritus in regard to its twin assumptions of absolute atoms and infinite space.

00He reduces the opposite doctrine to three assumptions, all of which he shows to be untenable: (1) " a self-determining power in the will "; (2) " indifference, ...

00But for him the alternative was between Calvinism and Arminianism, simply because of the historical situation, and in the refutation of Arminianism on the assumptions common to both sides of the controversy, he must be considered completely successful.

00These and similar assumptions are ultimate presuppositions or working hypotheses for the sciences themselves.

00The following are the usual assumptions made in good practice for superimposed loads: Floors of dwellings and offices..

00or with the reservoir full, near the lower part of the outer face ac. The principles hitherto adopted in designing masonry dams, in which the moment of resistance depends upon the figure and weight of the masonry, involve certain assumptions, which, although not quite true, have proved useful and harmless, and are so convenient that they may be continued with due regard to the modifications which recent investigations have suggested.

00It likewise vindicated afresh the rights of the Christian laity in regard to their own beliefs and the work of the Church, against the assumptions and despotism of an arrogant clergy.

00These assumptions are probably not nearly correct and, as the stresses caused by the cooling of the casting are unknown, it is necessary to choose a low working stress of about one ton per square inch.

00It serves as a means of research, more particularly in mathematical investigations, the simple laws thus deduced being subsequently modified by introducing assumptions in order to co-ordinate actual experiences.

00Expert knowledge and judicial insight must decide the point; but, so far as the present writer can judge, it is illusory to imagine that Duns points us beyond the medieval assumptions.

00But the contribution made by psychology to the solution of the problem has taken the form not so much of a direct reinforcement of the arguments of either of the opponent systems, as of a searching criticism of the false assumptions concerning conative processes and the phenomena of choice common alike to determinists and libertarians.

00Nor is it possible to give any rational explanation of the idea of responsibility itself upon indeterminist assumptions.

00sense Socrates brought a new critical spirit, showing that these popular lecturers, in spite of their fertile eloquence, could not defend their fundamental assumptions, nor even give rational definitions of what they professed to explain.

00Not the less important is the indirect stimulus given by the Reformation towards the development of a moral philosophy independent alike of Catholic and Protestant assumptions.

00Again, the argument that " conduct is good or bad according as its total effects are pleasurable or painful," and that ultimately " pleasure-giving acts are life-sustaining acts," seems to involve Spencer in a multitude of unverified assumptions and contradictory theories.

00But further, it is becoming increasingly apparent that psychology (upon which Taylor would base morality) itself involves metaphysical assumptions; its position in fact cannot be stated except as a metaphysical position, whether that of subjective idealism or any other.

00This involves no assumptions as to the law of variation of E.M.F.

00Other Assumptions.

00It may appear at first sight astonishing that it should be possible to apply so many different assumptions to the solution of one and the same problem.

00It is not, however, necessarily implied in the reasoning or in the equations given by Thomson, which are not founded on any assumptions with regard to the seat of the E.M.F., but only on the balance of heat absorbed and evolved in all the different parts of the circuit.

00I knew neither how he found us, what information he knew nor what incorrect assumptions he'd made.

00Though both assumptions were totally incorrect, neither combatant pointed this out.

00This contradicted the assumptions about low levels of involvement of young people.

00His assumptions were predicated on this belief.

00actuarial assumptions applied to more precise data, an additional liability increase of £ 3.4m resulted.

00Its assumptions are fundamentalist principles of which he is himself a faithful adherent.

00assumptions of superiority and expectations of service did not endear him to locals.

00assumptions of consistent rationality is not difficult to cut through.

00Earlier studies have used Bayesian inference under simplifying assumptions.

00This is a book which is not afraid to challenge assumptions.

00Don't make assumptions or put us into boxes.

00I have therefore examined the underlying assumptions made by both sides.

00However, for Hardin's tragedy to occur several erroneous assumptions about the commons must be made (Shiva, 2002 ).

00The baseline assumptions in these simulations are tabulated below.

00based on unproved assumptions.

00No amount of chest beating can conceal how wrong these assumptions were.

00However this does not mean that we do not make calculated assisted assumptions to help enable us effectively explore new frontiers.

00cautious assumptions, the initial package of reforms 5 is estimated to increase labor supply by 160,000 people.

00The reliability of this proof obviously depends on several prior assumptions: (1) Paul must have written Colossians, and from Rome.

00Parsons proposes an essentially consensual theory of power, in accord with the assumptions of his overall scheme.

00conservative assumptions about migration.

00In order to address these issues two assumptions of social constructivism need to be made explicit.

00Are there any assumptions you have made which you have not double-checked via your research?

00draughtn doing so they have to make a variety of assumptions about your chimney draft, fuel and method of operation.

00facile assumptions most computer stores may not realize.

00framing assumptions.

00In their form and design, suburbs are also gendered spaces, shaped by assumptions about home, work and family.

00implausible assumptions.

00inaccurate assumptions about people if they are unaware that a person has a hearing problem.

00inbuilt assumptions appear to be that firms are either product providers or commission driven product sellers.

00inbuilt flexibility in the system - making assumptions using approximate, rather than precise rules.

00Earlier studies have used Bayesian inference under simplifying assumptions.

00interrogate these assumptions by describing the results of research on a number of case studies of actual work situations.

00These were a result of weak assumptions made in the original interpretation of the robot system kinematics.

00lidar signals were then compared and the assumptions in the microphysical model refined.

00Many assumptions made, especially that the reader knows Scripture, church, etc. Too much managerial speak.

00many of the assumptions and discursive maneuvers of postcolonialism.

00Without the assumptions of biblical monotheism much that has been achieved under the influence of those assumptions may not be able to stand.

00achieving open ness or high levels of flexibility present difficulties because both notions turn current educational assumptions upside down.

00notional rent certain assumptions are made.

00odel can be approximated by a series of ODEs given simplifying assumptions.

00optimism bias assumptions we suggest.

00These are based on no prior assumptions about disease pathogenesis.

00pessimistic assumptions which would not apply to the vast majority of staff.

00Ecological assumptions entered into the models that were then used to predict evapotranspiration and net photosynthesis.

00playwriting in a European way and there are all sorts of assumptions there that are not necessarily relevant.

00Most of our assumptions about human development and political plurality and choice are rooted in the print era.

00preconceived assumptions about the information needs of its users.

00prejudicial assumptions by staff lead to very real health needs being overlooked.

00prudence of assumptions ).

00prudent assumptions.

00questionable assumptions.

00However this explanation rests on some rather questionable assumptions.

00They claim that their ' high-precision radiocarbon dating is liberating us from chronological assumptions based on Biblical research ' (Levy et al.

00reconsider some basic assumptions underlying all approaches to the frame problem.

00Estimates are presented for women with and without first-degree relatives with breast cancer and the sensitivity of the results to various assumptions investigated.

00relying on assumptions.

00rethink basic assumptions.

00That such assumptions can be made self-consistent is doubtful.

00shareholders ' funds are around £ 290 million lower than they would have been under the 2001 assumptions.

00simplifying assumptions.

00Many assumptions have to be made to make practical engineering problems solvable, leading to loss of information.

00sphericity assumptions have been violated, and independent contrasts cannot be computed.

00staffers ' assumptions about.

00stereotypical assumptions about the capabilities of disabled people.

00It thus stresses the link between theory and practice, and examines the often tacit assumptions which underlie translation practice.

00theorize concerning the origin of the universe that he sees on the basis of assumptions made.

00An observer in the present can only theorize concerning the origin of the universe that he sees on the basis of assumptions made.

00To some, the Horse seems so typical of La TÃ¨ne art that a Bronze Age dating de-stabilised some widely held cultural assumptions.

00typologylogies based solely on pottery typologies, with all the built-in temporal assumptions, are not, by themselves, sufficient anymore.

00Part of my job is to constantly uncouple these assumptions.

00underlines just what assumptions we make about ' the other ' with so little evidence.

00underlying assumptions made by both sides.

00unfounded assumptions ', said the Government.

00uniformitarian assumptions answer the many difficulties Venus present us?

00The view that religion is a private matter without political implications is one of the almost unquestioned assumptions of modern British culture.

00But by the early 1980s it was clear that the assumptions on which loans were based were hopelessly unrealistic.

00Many workers,make a lot of assumptions about users and feel unskilled in working with them.

00unthinking assumptions?

00unwritten assumptions.

00validity of the underlying assumptions.

00The fact that the old designs were successful lends weight to the usefulness of the design assumptions.

00worst-case assumptions are a reasonable component of screening calculations, to ensure that the stack height will not be under-estimated.

00this - to try to bring unity and harmony into the scattered thoughts of our general culture, to trace them to their primary assumptions and follow them into their ultimate consequences, to connect them all together, to remodel, curtail or amplify them, so as to remove their apparent contradictions, and to combine them in the unity of an harmonious view of things, and especially to investigate those conceptions which form the initial assumptions of the several sciences, and to fix the limits of their applicability.

00He also gives us " natural law " 2 - a Stoic inheritance, preserving the form of an idealist appeal to systematic requirements of reason, while practically limiting its assumptions to those of intuitionalism.

00It rested on a mass of legal assumptions and subtleties, fallacious indeed, but ingenious, and, as the result proved, effective.

00With one symbol for an unknown, it will easily be understood what scope there is foradroit assumptions, for the required numbers, of expressions in the one unknown which are at once seen to satisfy some of the conditions, leaving only one or two to be satisfied by the particular value of x to be determined.

00Often assumptions are made which lead to equations in x which cannot be solved "rationally," i.e.

00would give negative, surd or imaginary values; Diophantus then traces how each element of the equation has arisen, and formulates the auxiliary problem of determining how the assumptions must be corrected so as to lead to an equation (in place of the "impossible" one) which can be solved rationally.

00There is no subject of human study which may not be at some time or other of economic significance, and anything which affects the character, the ideals or the environment of man may make it necessary to modify our assumptions and our reasoning with regard to his conduct in economic affairs.

00His assumptions are based upon ordinary observation and experience, and are usually accurate in proportion to his practical shrewdness and sagacity, so that he is not interested in the speculative flights of philosophy, except in so far as they influence or have influenced conduct.

00But the modern conception of society or the state owes more to biology than philosophy, and actual research has destroyed more frequently than it has justified the assumptions of the older philosophical school.

00As a matter of fact, discussions of method and the criticism of hypotheses and assumptions are very rarely found in early economic works.

00In all economic investigation assumptions must be made, but we must see that they are legitimate in view of the actual life and character of the community or communities which are the subject of investigation.

00All the assumptions we require are furnished by observation of people in the mass and the larger generalizations of statistics.

00The assumptions, the definitions, the reasoning, the conclusions of the classical writers have been ruthlessly overhauled.

00We may talk of the assumptions implicitly involved in Ricardo's works.

00= tions were; we only know what assumptions we should make in order to reach the same conclusions, and they may be very different from " the mind of Ricardo."

00The conclusions of such a work are of wider significance than the assumptions we attribute to the author would warrant.

00These assumptions marked a definite rejection of all allegiance to Rome.

00In addition to empirical and molecular formulae, chemists are in the habit of employing various kinds of rational formulae, called structural, constitutional or graphic formulae, &c., which not only express the molecular composition of the compounds to which they apply, but also embody certain assumptions as to the manner in which the constituent atoms are arranged, and convey more or less information with regard to the nature of the compound itself, viz.

00Although Kekule founded his famous benzene formula in 1865 on the assumptions that the six hydrogen atoms in benzene are equivalent and that the molecule is symmetrical, i.e.

00that two pairs of hydrogen atoms are symmetrically situated with reference to any specified hydrogen atom, the absolute demonstration of the validity of OH these assumptions was first given by A.

00Ewing has himself also shown how satisfactorily this theory accords with many other obscure and complicated phenomena, such as those presented by coercive force, differences of magnetic quality, and the effects of vibration, temperature and stress; while as regards simplicity and freedom from arbitrary assumptions it leaves little to be desired.

00Regarding it as important that all reasoning with reference to magnetism should be conducted without any uncertain assumptions, he worked out a mathematical theory upon the sole foundation of a few wellknown facts and principles.

00Morphology becomes a farce when such assumptions are made.

00That it formed the starting-point, and largely prescribed the course of thought on the subject of planetary origin is due to the simplicity of its assumptions, and the clearness of the mechanical principles involved, rather than to any cogent evidence of its truth.

00But, as applied to lower and more obscure forms of life, teleology presented alfnost insurmountable difficulties; and consequently, in place of exact experiment and demonstration, the most reckless though ingenious assumptions were made as to the utility of the parts and organs of lower animals.

00Many zoologists - prominent among them in Great Britain being Huxley - had been repelled by the airy fancies and assumptions of the " philosophical " morphologists.

00His methods, however, were not free from tentative assumptions, and were considerably improved by Edmund Halley (Phil.

00They are repelled by the dryness of much of the matter, the unsuitableness of many of the topics discussed for poetic treatment, the arbitrary assumption of premises, the entire failure to establish the connexion between the concrete phenomena which the author professes to explain and these assumptions, and the erroneousness of many of the doctrines which are stated with dogmatic confidence.

00In this form it stands in sharp antithesis to the doctrine of evolution, both because the former views the world of particular things and events as essentially unreal and illusory, and because the latter, so far as it goes, looks on matter as eternal, and seeks to explain the general forms of things as we perceive them by help of simpler assumptions.

00Meyer, on slightly different assumptions, it should be 41/2 times, the actual volume of the molecules.

00This theory, however, depended upon unverified assumptions, such as the supposed silence of theologians about the creed at the beginning of the 9th century; the suggestion that the completed creed would have been useful to them if they had known it as a weapon against the heresy of Adoptianism; the assertion that no MS. containing the complete text was of earlier date than c. 813.

00From the standpoint of the history of enlightenment, as Harnack has observed, " Socinianism with its systematic criticism (tentative and imperfect as it may now seem) and its rejection of all the assumptions based upon mere ecclesiastical tradition, can scarcely be rated too highly.

00Yet the divergent uses that have been made of it witness to the ambiguity of his statement which is traceable to the fact that Kant was himself too deeply rooted in the thought of his predecessors and carried with him too much of their spirit to be able entirely to free himself from their assumptions and abstractions.

00The struggle with the Crown, which ended in independence, began at the foundation of the colony, with assumptions of power under the charter which the colonial government was always trying to maintain, and the crown was as assiduously endeavouring to counteract.

00Over against these sweeping assumptions and deductions, the Roman Catholic Church had to build up its own statement of the basis of belief.

00That world of the learned offers us non-dogmatic definitions, drawn up from the outside; definitions which do not share the root assumptions either of Catholicism or of post-Reformation Protestant orthodoxy.

00(a) The nature of the bounding curve or surface may not be exactly known, so that certain assumptions have to be made, a formula being then used which is adapted to these assumptions.

00The application of Simpson's rule, for instance, to a plane figure implies certain assumptions as to the nature of the bounding curve.

00In finding the line of pressure some principle such as the principle of least action must be used in determining the reactions at the crown and springings, and some assumptions must be made of not certain validity.

00In finding the abutment reactions some principle such as the principle of least action must be used, and some assumptions of doubtful validity made.

00Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load.

00d'Epinay's Memoirs as coloured, if not actually dictated, by the malevolent attitude of Grimm and Diderot; and her study of the documents undoubtedly qualifies a good many of the assumptions that have been made on the strength of evidence which is at least tainted by contemporary prejudice, and leaves the way open for an interpretation of the facts which would reconcile Rousseau's character as a writer with his actions as a man.

00When the assumptions on which it rests are proved to be baseless, the particular scepticism is also overcome.

00The theoretical assumptions of Newton and Euler (hypotheses magis mathematicae quam naturales) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great analytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.

00Such a distinction involves the assumptions that bodily pleasures are generically different from mental ones, and that there is in practice a clearly marked dividing line, - both of which hypotheses are frequently denied.

00These assumptions, however, were fanciful.

00But there is another species of deduction which, as Cliffe Leslie has shown, seriously tainted the philosophy of Smith - in which the premises are not facts ascertained by observation, but the a priori assumptions which we found in the physiocrats.

00This view obviates the deed for assuming the complicated flexures of the wreath which has to be done on other assumptions (see Rotifera, Encycl.

00In his speculations as to the physical cause of the celestial motions, his mind, though not wholly emancipated from the tyranny of gratuitous assumptions, was working steadily towards the light.

00The point is that neither Buchner nor Haeckel could on their assumptions recognize any force but force of body, or any mind but mind of body, or any distinct thing or substance except body.

00He gradually fell under the dominion of two false assumptions.

00Schelling was right; but he had too much affinity with Hegelian assumptions, e.g.

00Having, however, made a deduction, which is at all events consistent, that on Kantian assumptions all we know is mental phenomena, Lange proceeded to reduce the rest of Kantism to consistency.

00There is only one Neo-Kantian way out of this dilemma, but it is to alter the original assumptions of Kant's psychological idealism.

00In Part II., ch i., he makes three assumptions about the senses, and, without stopping to prove them, or even to make them consistent, deduces from them his thesis that the evidence of the senses is not a foundation of belief in Nature.

00Balfour, however, having from unproved assumptions denied the evidence of the senses, and the rational power of using them to infer things beyond oneself, has to look out for other, and non-rational, foundations of belief.

00On certain assumptions required for the extension of the methods of the kinetic theory of gases to liquids, L.

00His commentaries on the Scriptures were the first application on an extensive scale of the principle affirmed by Scaliger, that, namely, of interpretation by the rules of grammar without dogmatic assumptions.

00This theory was adopted by Edme Mariotte, Sir Isaac Newton and Thomas Young; and, although certain of their assumptions were somewhat arbitrary, yet the general validity of the theory has been demonstrated by the researches of J.

00While it is evident that some such conclusion must follow from the attempt to regard the cognitive consciousness as made up of disconnected feelings, it is equally clear, not only that the result is selfcontradictory, but that it involves certain assumptions not in any way deducible from the fundamental view with which Hume starts.

00There can, on these assumptions, be no doubt that, from the early years of the 5th century B.C., the archonship was of practically no importance.

00China and Japan have hitherto been regarded as the chief producers of tea, and the reputed large domestic consumption of those Mongolian peoples has led to assumptions of vast internal productions.

00But in such an undertaking one is always apt to take subjective assumptions or mere fancies for established data.

00Such assumptions are not wholly unjustified.

00The obvious way of avoiding the scepticism into which rationalism is thus driven is to revise the assumptions about the nature and postulates of truth which lead to it.

00But if thus far Grote's protest against prevalent assumptions carries an immediate and unhesitating conviction, it may be doubted whether his positive statement can be accounted final.

00The Result Calculated On These Assumptions Is Given In The Last Column In Joules, And Also In Calories Of 20Ã‚° C. The Heatloss In This Example Is Large, Nearly 4.5% Of The Total Supply, Owing To The Small Flow And The Large Rise Of Temperature, But This Correction Was Greatly Reduced In Subsequent Observations On The Specific Heat Of Water By The Same Method.

00and its companion a diameter of 830,000 m.; the distance between their centres cannot be deduced without making certain doubtful assumptions, but may be about 3,000,000 m.

00It we use Roman letters for mere numbers, capitals for instants of time, Greek letters for time-steps, and a parenthesis to denote a couple, the laws assumed by Hamilton as the basis of a system were as follows: (B1, B 2) - (A i, A2) = (Bi - A,, B2A 2) = (a, 13); (a, b) (a, #)= (aa - b(3, ba--+a(3).2 To show how we give, by such assumptions, a real interpretation to the ordinary algebraic imaginary, take the simple case a=o, b= r, and the second of the above formulae gives (o, 1) (a, (3) = (- 1 3, a).

00In a very short time he settled his fundamental assumptions.

00Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870Ã‚° C. instead of at 365Ã‚° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

00The simplest assumptions to make are that the vapour behaves as a perfect gas (or that p(v-w) = Re), and that L is constant.

00Plane Stalics.The statics of a rigid body rests on the following two assumptions:

00From this point of view the equation is a mere truism, its real importance resting on the fact that by attributing suitable values to the masses in, and by making simple assumptions as to the value of X in each case, we are able to frame adequate representations of whole classes of phenomena as they actually occur.

00The equation of energy for a rigid body has already been stated (in effect) as a corollary from fundamental assumptions.

00We must not suffer it to lead us into rhetoric about the deadness and the darkness of the middle ages, or hamper our inquiry with preconceived assumptions that the re-birth in question was in any true sense a return to the irrecoverable pagan past.

00He first introduced into economics on a great scale the method of deduction from a priori assumptions.

00He also pointed out more distinctly the nature of the assumptions which we must make with respect to the law of action of the particles in order to be consistent with observed phenomena.

00On these assumptions his results are certainly right, and are confirmed by the independent method of Gauss, so that the objections raised against them by Poisson fall to the ground.

00He was at issue, however, with the atomistic materialism of Democritus in regard to its twin assumptions of absolute atoms and infinite space.

00He reduces the opposite doctrine to three assumptions, all of which he shows to be untenable: (1) " a self-determining power in the will "; (2) " indifference, ...

00But for him the alternative was between Calvinism and Arminianism, simply because of the historical situation, and in the refutation of Arminianism on the assumptions common to both sides of the controversy, he must be considered completely successful.

00These and similar assumptions are ultimate presuppositions or working hypotheses for the sciences themselves.

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