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deduce

Locke, however, fails to " deduce " his categories.

7657This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds.

2923The more logical method of procedure is to determine the specific heat independently of the total heat, and then to deduce the variations of total heat by equation (52).

2931Recently Hermann Walther Nernst has been able to deduce the transitionpoint in the case of sulphur from the specific heat and the heat developed in the transition only.

2629He attempts to grasp the national character as a whole, and thence to deduce practical conclusions.

2527By the vibration experiment we obtain the value of the product of the magnetic moment (M) of the magnet into the horizontal component (H), while by the deflexion experiment we can deduce the value of the ratio of M to H, and hence the two combined give both M and H.

2323It is easy to deduce the modes of vibration from stationary waves as in the previous cases.

2117All this, however, must necessarily be of the nature of the purest speculation, and the only facts which we are able to deduce in the present state of our knowledge of the subject may be summed up as follows: (a) That the Malays ethnologically belong to a race which is allied to the Polynesians; (b) that the theory formerly current to the effect that the Sakai and other similar races of the peninsula and archipelago belonged to the Malayan stock cannot be maintained, since recent investigations tend to identify them with the Mon-Annam or Mon-Khmer family of races; (c) that the Malays are, comparatively speaking, newcomers in the lands which they now inhabit; (d) that it is almost certain that their emigration took place from the south; (e) and that, at some remote period of their history, they came into close contact with the Polynesian race, probably before its dispersion over the extensive area which it now occupies.

2022We shall then show that on certain limitations two trains of disturbance may be superposed so that stationary waves may be formed, and thence we shall deduce the modes of vibration as with pipes.

1920Since the induction B is equal to H 47rI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction.

1921From this we can deduce successively X - 3s.= 26s., X= 29s.

1819Nor shall we stop here: but we shall further compare the readings of X and Y with each other and with those of A, and thus deduce the readings of a still more remote ancestor which we may call Z.

1819Descartes's own attempts to deduce the different qualities and actions of bodies in this way are not of much value.

1820Descartes's own attempts to deduce the different qualities and actions of bodies in this way are not of much value.

1820The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.

1719The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.

1719Whether we should deduce from its common occurrence in Babylonia the existence of an Elamite population there in early times, later displaced by the Sumerians, we do not know.

1618In the last resort, therefore, Spencer fails to deduce philosophically not only the necessity of progress, but also its compatibility with the evolution-dissolution oscillation, and even the general possibility of conceiving the world as a process.

1618For instance, having found that (x+a)2=x2+2axda2, we can deduce that (x+b+c) 2 = }xd(b+c)}2=x2+2(b+c)x+ (b+c)2.

1519But 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.

1415Having thus confused contradiction and difference, independence and solitariness, experience and inference, Bradley is able to deduce finally that reality is not different substances, experienced and inferred, as Aristotle thought it, but is one absolute super-personal experience, to which the socalled plurality of things, including all bodies, all souls, and even a personal God, is appearance - an appearance, as ordinarily understood, self-contradictory, but, as appearing to one spiritual reality, somehow reconciled.

1415But 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.

1415It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.

1416For example, as he says, the sphericity of the moon is the real ground of the fact of its light waxing; but we can deduce either from the other, as follows: - i.

1416Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).

1417Friar Odoric was despatched to the East, where a remarkable extension of missionary action was then taking place, about 1316-1318, and did not return till the end of 1329 or beginning of 1330; but, as regards intermediate dates, all that we can deduce from his narrative or other evidence is that he was in western India soon after 1321 (pretty certainly in 1322) and that he spent three years in China between the opening of 1323 and the close of 1328.

1313He was a man of science - one who by the vigorous study of his subject matter sought from that subjectmatter itself to deduce laws.

1314From the formula for log e (p/q) we may deduce the following very convergent series for log e 2, log e 3 and log e 5, viz.: log e 2=2(7P +5Q +3R), log e 3 =2(11P+8Q +5R), log e 5=2(16P+12Q+7R), where P 1 +3?1) 3 5 s (31) &C.

1314His principal discovery is concerned with equations, which he showed to be derived from the continued multiplication of as many simple factors as the highest power of the unknown, and he was thus enabled to deduce relations between the coefficients and various functions of the roots.

1315On the 2nd of February Loisy wrote to the archbishop: "I condemn, as a matter of course, all the errors which men have been able to deduce from my book, by placing themselves in interpreting it at a point of view entirely different from that which I had to occupy in composing it."

1316Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.

1316Thus To Deduce The New Moon Of Tisri, For The Year Immediately Following Any Given Year (Y), When Y Is Ordinary, Subtract (1 1 °) Days 15 Hours Ii Min.

1213For only 88 of them has it been possible as yet to deduce a period, and at least half even of these periods are very doubtful.

1214Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.

1214The value of the specific heat s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).

1112We shall deduce the modes of vibration of the air column in a cylindrical pipe from the consideration that the air in motion within the pipe forms some part of a system of stationary waves, one train being formed by the exciter of the disturbance, and the other being formed by the reflection of the train at the end of the pipe.

1112Before we deduce results from such abstract ideas as cause, substance, matter, we must ask what in reality do these mean - what is the actual content of consciousness which corresponds to these words?

1112The radical thought of this movement was voiced in the demand of Reinhold 2 that philosophy should " deduce " it all from a single principle and by a single method.

1112The radical thought of this movement was voiced in the demand of Reinhold 2 that philosophy should " deduce " it all from a single principle and by a single method.

1112Finally, Schopenhauer's voluntarism has had a profound effect on psychology inside and outside Germany, and to a less degree produced attempts to deduce from voluntaristic psychology new systems of voluntaristic metaphysics, such as those of Paulsen and Wundt.

1113the height of the mercury in the wide tube and the top of f he narrow tube represents the pressure due to the mercury column, and this must be added to the barometric pressure in order to deduce the total pressure on the vapour.

1011The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.

1011Both, however, used this influence freely; and, whereas Lotze used the Leibnitzian argument from indivisibility to deduce indivisible elements and souls, Fechner used the Leibnitzian hypotheses of universal perception and parallelism of motions and perceptions, in the light of the .Schellingian identification of physical and psychical, to evolve a world-view (Weltansicht) containing something which was neither Leibnitz nor Schelling.

1012Birkeland (19), who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.

1012All M is P. Proceeding from one order to the other, by converting one of the premises, and substituting the conclusion as premise for the other premise, so as to deduce the latter as conclusion, is what he calls circular inference; and he remarked that the process is fallacious unless it contains propositions which are convertible, as in mathematical equations.

1012..) In order to deduce the complete variation of the specific heats from these equations, it is necessary to make some assumption with regard to the variation of the specific heats with temperature.

9103), without pretending, like Plato, to deduce from any common principle the special principles of each science (Post.

910By imagining that a dilute solution is put through a thermodynamic cycle we may deduce directly relations between its osmotic pressure and its freezing point.

911The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences.

911From the former we deduce Ho, and from the latter the corresponding value of I, using the formulae Ho = 47rin/l and I - X s, (d (-- 11)2n7rr 2 i where s is the deflection in scale-divisions, n the distance in scaledivisions between the scale and the mirror, and r the radius of the wire.

912From the former we deduce Ho, and from the latter the corresponding value of I, using the formulae Ho = 47rin/l and I - X s, (d (-- 11)2n7rr 2 i where s is the deflection in scale-divisions, n the distance in scaledivisions between the scale and the mirror, and r the radius of the wire.

912We can deduce a remarkable expression for the energy stored up in an electric field containing electrified bodies as follows:' Let V denote the potential at any point in the field.

89the historic frontiers of the Czechoslovak State it would indeed have been difficult, with justice, to deduce a right of self-determination, that is to say, the right, in this case, of retaining all the fruits of misused power.

89Hence if the readings of the verniers on the azimuth circle are made when the transit is observed we can deduce the reading corresponding to the geographical meridian.

89Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.

810Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

810Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.

810After an analysis of the religious consciousness, which yields the doctrine of an absolute personal and spiritual God, Rothe proceeds to deduce from his idea of God the process and history of creative development, which is eternally proceeding and bringing forth, as its unending purpose, worlds of spirits, partially self-creative and sharing the absolute personality of the Creator.

79Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductivedeductive inference which might be called " perduction."

79Coulomb, 2 however, by using long and thin steel rods, symmetrically magnetized, and so arranged that disturbing influences became negligibly small, was enabled to deduce from his experiments with reasonable certainty the law that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them.

68deduce the meaning of most of the READIUE parameters from the example above.

11deduce the implications of these imperfections.

11deduce which water source is the cleanest.

11deduce who did what, when, where and how!

11deduce what the word is supposed to be.

11deduce where each of these numbers must be placed in every cell of a puzzle.

11What then may we logically deduce from this state of affairs?

11I can only applaud this man's ability to deduce.

00The function of Naturphilosophie is to exhibit the ideal as springing from the real, not to deduce the real from the ideal.

00(20) from which we deduce that the ratio 0'/0" of the temperatures at which the vapour-pressures are the same is a linear function of the temperature 0' of one of the substances.

001887) to deduce the vapour-pressures of any substance from those of a standard substance by means of two observations.

00By assuming suitable forms of the characteristic equation to represent the variations of the specific volume within certain limits of pressure and temperature, we may therefore with propriety deduce equations to represent the saturation-pressure, which will certainly be thermodynamically consistent, and will probably give correct numerical results within the assigned limits.

00But in order to deduce the values of c by the Joule-Thomson method, it is necessary to assume an empirical formula, and the type c=co(6019) n is chosen as being the simplest.

00A similar method of calculation might be applied to deduce the thermodynamical properties of other vapours, but the required experimental data are in most cases very imperfect or even entirely wanting.

00But in any case it is characteristic of theosophy that it starts with an explication of the Divine essence, and endeavours to deduce the phenomenal universe from the play of forces within the Divine nature itself.

00It is a classical problem in the calculus of variations to deduce the equation (9) from the condition that the depth of the centre of gravity of a, chain of given length hanging I I between fixed points must be catenary; it determines the scale of the curve, all cate } stationary (~ 9).

00Since I~=Ii., I~=o, we deduce 100=3/4Ma2, ~ =4MaZ; hence the value of the squared radius of gyration isfora diameter 3/4ai, and for the axis of symmetry 3/4af.

00The method of homogeneous strain can be applied to deduce the corresponding results for an ellipsoid of semi-axes a, b, c. If the co-ordinate axes coincide with the principal axes, we find l0=1/2Ma2, I9=~Mb2, I~ = ~ Me2, whence Ii.~ =3/4M (b1 +ci), &c.

00We can hence deduce the condition of steady precessional motion in a top. A solid of revolution is supposed to be free to turn about a fixed point 0 on its axis of symmetry, its masscentre G being in this axis at a distance h from 0.

00The result, owing to its symmetry, must still hold if we interchange accented and unaccented Greek letters, and by comparison we deduce (15) and (16), provided cr2 and Cr~2 are unequal.

00It is usefu in practice, by enabling the engineer easily to deduce the condition of equilibrium and stability of structures of complex and unsym metrical figures from those of structures of simple and symnietrica figures.

00In the absence of a religious census it is not possible to deduce from statistics supplied by the churches themselves any trustworthy conclusion as to the percentage of the population adhering to each church.

00Starting from the fact that if an electrified globe, placed within two hemispheres which fit over it without touching, is brought in contact with these hemispheres, it gives up the whole of its charge to them - in other words, that the charge on an electrified body is wholly on the surface - he was able to deduce by most ingenious reasoning the law that electric force varies inversely as the square of the distance.

00Nothing is more remarkable in the history of discovery than the manner in which Ampere seized upon the right clue which enabled him to disentangle the complicated phenomena of electrodynamics and to deduce them all as a consequence of one simple fundamental law, which occupies in electrodynamics the position of the Newtonian law of gravitation in physical astronomy.

00The first deals with the prehistoric period of the world, before the rise of religion; the second was to be an endeavour to deduce a universal law from known historical facts; the third to sketch the ultimate state of perfection to which humanity is moving.

00We cannot deduce from them a conquest of Iran from Babylon: for the Babylonians never set foot in Iran and even the Assyrians merely conquered the western portior of Media.

00From motion he proceeds to deduce time, space and the categories of mechanics and natural science.

00Various attempts have also been made to deduce these laws from particular hypotheses as to the action between the molecules of the elastic substance.

00The second part endeavours to deduce the facts of the elasticity of a finite portion of the substance from hypotheses as to the motion of its constituent molecules and the forces acting between them.

00In like manner we may by experiment ascertain the general fact that the surface of a liquid is in a state of tension similar to that of a membrane stretched equally in all directions, and prove that this tension depends only on the nature and temperature of the liquid and not on its form, and from this as a secondary physical principle we may deduce all the phenomena of capillary action.

00The next step is to deduce this surface-tension from a hypothesis as to the molecular constitution of the liquid and of the bodies that surround it.

00He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how from these two principles to deduce the phenomena of capillary action.

00Having applied the secondary principle of surface-tension to the various particular cases of capillary action, Young proceeded to deduce this surface-tension from ulterior principles.

00Before going further we may deduce from equation 9 the nature of all the figures of revolution which a liquid film can assume.

00The laws are formulated in general terms, and the decisions in particular cases relegated to the sphere of juris prudence; and the canonists have definitely lost the function which fell to them in the 12th and 13th centuries: they receive the law on authority and no longer have to deduce it from the texts.

00Thirdly, it is objected that in order to deduce the conditioned, Cousin makes his absolute a relative; for he makes it an absolute cause, i.e.

00by the method of reciprocal polars) deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (x, y, z.) instead of meaning point-co-ordinates pay, mean line-co-ordinates, and the demonstration is then in every step of it a demonstration of the correlative theorem.

00It was this: from the observed perturbations of a known planet to deduce by calculation, assuming only Newton's law of gravitation, the mass and orbit of an unknown disturbing body.

00But in spite of the intense conviction with which he thus identified metaphysical speculation and practical wisdom, we find in his writings no serious attempt to deduce the particulars of human well-being from his knowledge of absolute good, still less to unfold from it the particular cognitions of the special arts and sciences.

00It remains to consider how, from the doctrine that affection is the proper object of approbation, we are to deduce moral rules or " natural laws " prescribing or prohibiting outward acts.

00Spencer looked to ideas derived from the biological sciences to provide a solution of all the enigmas of morality, as of most other departments of life; and he conceived it " to be the business of moral science to deduce from the laws of life and the conditions of existence what kinds of action necessarily tend to produce happiness and what kinds to produce unhappiness."

00Bossert was enabled to deduce 2675 proper motions, published at Paris in four successive memoirs, 1887-1902; and the sum-total of those ascertained probably now exceeds 6000.

00He assails them on twenty points of their mixed physical and metaphysical peripateticism, from the statement of which, in spite of his pretended scepticism, we can deduce some very positive metaphysical opinions of his own.

00From the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed numerical aperture can be perceived.

00I can only applaud this man's ability to deduce.

00You can, however, deduce it fairly easily if you know the mechanism for the addition of pure bromine.

00deduce the sequence of a DNA chain.

00deduce the existence of a being from the idea of that being.

00deduce all mathematical truths and derive all mathematical objects.

00hence deduce how the pre-exponential factor for the radical reaction should depend on temperature.

00thus deduce the direction of the vorticity vector which may be generated.

00deduce from this simple observation that tree planting is in line with Nature's own efforts to improve ecological health.

00You can work out much of these from judicious sniffing of traffic on the network; others you can deduce with some simple heuristics.

00ladyere was no ladies ' underwear in the car, from which the archeologist can deduce that the driver was no longer young.

00Thus we deduce one of the fundamental rules for successful work with numerical workbenches: prefer compiled functions over interpreted code.

00From this we deduce for the charge p per cubic centimetre (I/41r)Xio-5 (volt/cm 2), or 2.7 X 101 electrostatic units.

00Holfmann, from observations on the amplitude of saturation currents, deduce q =4 as a mean value.

00man), we could from that alone, by reasons entirely mathematical and certain, deduce the whole figure and conformation of each of its members, and, conversely, if we knew several peculiarities of this conformation, we could from these deduce the nature of its seed."

00He attempted to deduce the existence of spirit, apart from, and yet entering from time to time into connexion with, the phenomena of the senses, by an examination of the relation between the ego of thought and the age of sensible experience as understood by Kant.

00All this, however, must necessarily be of the nature of the purest speculation, and the only facts which we are able to deduce in the present state of our knowledge of the subject may be summed up as follows: (a) That the Malays ethnologically belong to a race which is allied to the Polynesians; (b) that the theory formerly current to the effect that the Sakai and other similar races of the peninsula and archipelago belonged to the Malayan stock cannot be maintained, since recent investigations tend to identify them with the Mon-Annam or Mon-Khmer family of races; (c) that the Malays are, comparatively speaking, newcomers in the lands which they now inhabit; (d) that it is almost certain that their emigration took place from the south; (e) and that, at some remote period of their history, they came into close contact with the Polynesian race, probably before its dispersion over the extensive area which it now occupies.

00When chemical change is expressed with the aid of molecular formulae not only is the distribution of weight represented, but by the mere inspection of the symbols it is possible to deduce from the law of gaseous combination mentioned above, the relative volumes which the agents and resultants occupy in the state of gas if measured at the same temperature and under the same pressure.

00Whether we should deduce from its common occurrence in Babylonia the existence of an Elamite population there in early times, later displaced by the Sumerians, we do not know.

00On the 2nd of February Loisy wrote to the archbishop: "I condemn, as a matter of course, all the errors which men have been able to deduce from my book, by placing themselves in interpreting it at a point of view entirely different from that which I had to occupy in composing it."

00Since the induction B is equal to H 47rI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction.

00Coulomb, 2 however, by using long and thin steel rods, symmetrically magnetized, and so arranged that disturbing influences became negligibly small, was enabled to deduce from his experiments with reasonable certainty the law that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them.

00From this we can deduce successively X - 3s.= 26s., X= 29s.

00Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).

00For instance, having found that (x+a)2=x2+2axda2, we can deduce that (x+b+c) 2 = }xd(b+c)}2=x2+2(b+c)x+ (b+c)2.

00His principal discovery is concerned with equations, which he showed to be derived from the continued multiplication of as many simple factors as the highest power of the unknown, and he was thus enabled to deduce relations between the coefficients and various functions of the roots.

00Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.

00Friar Odoric was despatched to the East, where a remarkable extension of missionary action was then taking place, about 1316-1318, and did not return till the end of 1329 or beginning of 1330; but, as regards intermediate dates, all that we can deduce from his narrative or other evidence is that he was in western India soon after 1321 (pretty certainly in 1322) and that he spent three years in China between the opening of 1323 and the close of 1328.

00From it Spencer proceeds to deduce the indestructibility of matter and energy, the equivalence and transformation of forces, the necessity of a rhythm, of Evolution (i.e.

00In the last resort, therefore, Spencer fails to deduce philosophically not only the necessity of progress, but also its compatibility with the evolution-dissolution oscillation, and even the general possibility of conceiving the world as a process.

00We can deduce a remarkable expression for the energy stored up in an electric field containing electrified bodies as follows:' Let V denote the potential at any point in the field.

00The value of the specific heat s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).

00..) In order to deduce the complete variation of the specific heats from these equations, it is necessary to make some assumption with regard to the variation of the specific heats with temperature.

00In the case of solids we may determine the volume in some cases by direct measurement - this gives at the best a very rough and ready value; a better method is to immerse the body in a fluid (in which it must sink and be insoluble) contained in a graduated glass, and to deduce its volume from the height to which the liquid rises.

00the height of the mercury in the wide tube and the top of f he narrow tube represents the pressure due to the mercury column, and this must be added to the barometric pressure in order to deduce the total pressure on the vapour.

00He attempts to grasp the national character as a whole, and thence to deduce practical conclusions.

00He was a man of science - one who by the vigorous study of his subject matter sought from that subjectmatter itself to deduce laws.

00The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.

00We shall deduce the modes of vibration of the air column in a cylindrical pipe from the consideration that the air in motion within the pipe forms some part of a system of stationary waves, one train being formed by the exciter of the disturbance, and the other being formed by the reflection of the train at the end of the pipe.

00We shall then show that on certain limitations two trains of disturbance may be superposed so that stationary waves may be formed, and thence we shall deduce the modes of vibration as with pipes.

00It is easy to deduce the modes of vibration from stationary waves as in the previous cases.

00the historic frontiers of the Czechoslovak State it would indeed have been difficult, with justice, to deduce a right of self-determination, that is to say, the right, in this case, of retaining all the fruits of misused power.

00In both classes, accepted tradition (written or oral) was reinterpreted in order to justify or to deduce new teaching (in its widest sense), to connect the present with a hallowed past, and to be a guide for the future; and the prevalence of this process, the innumerable different examples of its working, and the particular application of the term Midrash to an important section of Rabbinical literature complicates both the study of the subject and any attempt to treat it concisely.'

00From the formula for log e (p/q) we may deduce the following very convergent series for log e 2, log e 3 and log e 5, viz.: log e 2=2(7P +5Q +3R), log e 3 =2(11P+8Q +5R), log e 5=2(16P+12Q+7R), where P 1 +3?1) 3 5 s (31) &C.

00The function of Naturphilosophie is to exhibit the ideal as springing from the real, not to deduce the real from the ideal.

00Nor shall we stop here: but we shall further compare the readings of X and Y with each other and with those of A, and thus deduce the readings of a still more remote ancestor which we may call Z.

003), without pretending, like Plato, to deduce from any common principle the special principles of each science (Post.

00Thus To Deduce The New Moon Of Tisri, For The Year Immediately Following Any Given Year (Y), When Y Is Ordinary, Subtract (1 1 Ã‚°) Days 15 Hours Ii Min.

00Before we deduce results from such abstract ideas as cause, substance, matter, we must ask what in reality do these mean - what is the actual content of consciousness which corresponds to these words?

00Hence Schelling objected to the Hegelian dialectic on the ground that, although reason by itself can apprehend notions or essences, and even that of God, it cannot deduce a priori the existence either of God or of Nature, for the apprehension of which experience is required.

00Finally, Schopenhauer's voluntarism has had a profound effect on psychology inside and outside Germany, and to a less degree produced attempts to deduce from voluntaristic psychology new systems of voluntaristic metaphysics, such as those of Paulsen and Wundt.

00Both, however, used this influence freely; and, whereas Lotze used the Leibnitzian argument from indivisibility to deduce indivisible elements and souls, Fechner used the Leibnitzian hypotheses of universal perception and parallelism of motions and perceptions, in the light of the .Schellingian identification of physical and psychical, to evolve a world-view (Weltansicht) containing something which was neither Leibnitz nor Schelling.

00Having thus confused contradiction and difference, independence and solitariness, experience and inference, Bradley is able to deduce finally that reality is not different substances, experienced and inferred, as Aristotle thought it, but is one absolute super-personal experience, to which the socalled plurality of things, including all bodies, all souls, and even a personal God, is appearance - an appearance, as ordinarily understood, self-contradictory, but, as appearing to one spiritual reality, somehow reconciled.

00Hence if the readings of the verniers on the azimuth circle are made when the transit is observed we can deduce the reading corresponding to the geographical meridian.

00By the vibration experiment we obtain the value of the product of the magnetic moment (M) of the magnet into the horizontal component (H), while by the deflexion experiment we can deduce the value of the ratio of M to H, and hence the two combined give both M and H.

00By imagining that a dilute solution is put through a thermodynamic cycle we may deduce directly relations between its osmotic pressure and its freezing point.

00This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds.

00Recently Hermann Walther Nernst has been able to deduce the transitionpoint in the case of sulphur from the specific heat and the heat developed in the transition only.

00After an analysis of the religious consciousness, which yields the doctrine of an absolute personal and spiritual God, Rothe proceeds to deduce from his idea of God the process and history of creative development, which is eternally proceeding and bringing forth, as its unending purpose, worlds of spirits, partially self-creative and sharing the absolute personality of the Creator.

00Birkeland (19), who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.

00It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.

00For only 88 of them has it been possible as yet to deduce a period, and at least half even of these periods are very doubtful.

00Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductivedeductive inference which might be called " perduction."

00It is likely that man began with particular inference and with particular language; and that, gradually generalizing thought and language, he learnt at last to think and say " all," to infer universally, to induce and deduce, to reason, in short, and raise himself above other animals.

00All M is P. Proceeding from one order to the other, by converting one of the premises, and substituting the conclusion as premise for the other premise, so as to deduce the latter as conclusion, is what he calls circular inference; and he remarked that the process is fallacious unless it contains propositions which are convertible, as in mathematical equations.

00For example, as he says, the sphericity of the moon is the real ground of the fact of its light waxing; but we can deduce either from the other, as follows: - i.

00Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.

00Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.

00Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

00The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences.

00Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.

00Locke, however, fails to " deduce " his categories.

00They are agreed, however, in the rejection, on the one hand, of of the subjectivist logic with its intrinsic implication that knowledge veils rather than reveals the real world, and, on the other hand, of the logic of the speculative construction with its pretension to " deduce," to determine, and finally at once to cancel and conserve any antithesis in its all-embracing dialectic. They agree, then, in a maintenance of the critical point of view, while all alike recognize the necessity of bringing the thoughtfunction in knowledge into more intimate relation with its " other " than Kant had done, by means of some formula of correlation or parallelism.

00The more logical method of procedure is to determine the specific heat independently of the total heat, and then to deduce the variations of total heat by equation (52).

00(20) from which we deduce that the ratio 0'/0" of the temperatures at which the vapour-pressures are the same is a linear function of the temperature 0' of one of the substances.

001887) to deduce the vapour-pressures of any substance from those of a standard substance by means of two observations.

00By assuming suitable forms of the characteristic equation to represent the variations of the specific volume within certain limits of pressure and temperature, we may therefore with propriety deduce equations to represent the saturation-pressure, which will certainly be thermodynamically consistent, and will probably give correct numerical results within the assigned limits.

00But in order to deduce the values of c by the Joule-Thomson method, it is necessary to assume an empirical formula, and the type c=co(6019) n is chosen as being the simplest.

00A similar method of calculation might be applied to deduce the thermodynamical properties of other vapours, but the required experimental data are in most cases very imperfect or even entirely wanting.

00But in any case it is characteristic of theosophy that it starts with an explication of the Divine essence, and endeavours to deduce the phenomenal universe from the play of forces within the Divine nature itself.

00It is a classical problem in the calculus of variations to deduce the equation (9) from the condition that the depth of the centre of gravity of a, chain of given length hanging I I between fixed points must be catenary; it determines the scale of the curve, all cate } stationary (~ 9).

00Since I~=Ii., I~=o, we deduce 100=3/4Ma2, ~ =4MaZ; hence the value of the squared radius of gyration isfora diameter 3/4ai, and for the axis of symmetry 3/4af.

00The method of homogeneous strain can be applied to deduce the corresponding results for an ellipsoid of semi-axes a, b, c. If the co-ordinate axes coincide with the principal axes, we find l0=1/2Ma2, I9=~Mb2, I~ = ~ Me2, whence Ii.~ =3/4M (b1 +ci), &c.

00We can hence deduce the condition of steady precessional motion in a top. A solid of revolution is supposed to be free to turn about a fixed point 0 on its axis of symmetry, its masscentre G being in this axis at a distance h from 0.

00The result, owing to its symmetry, must still hold if we interchange accented and unaccented Greek letters, and by comparison we deduce (15) and (16), provided cr2 and Cr~2 are unequal.

00It is usefu in practice, by enabling the engineer easily to deduce the condition of equilibrium and stability of structures of complex and unsym metrical figures from those of structures of simple and symnietrica figures.

00In the absence of a religious census it is not possible to deduce from statistics supplied by the churches themselves any trustworthy conclusion as to the percentage of the population adhering to each church.

00Starting from the fact that if an electrified globe, placed within two hemispheres which fit over it without touching, is brought in contact with these hemispheres, it gives up the whole of its charge to them - in other words, that the charge on an electrified body is wholly on the surface - he was able to deduce by most ingenious reasoning the law that electric force varies inversely as the square of the distance.

00Nothing is more remarkable in the history of discovery than the manner in which Ampere seized upon the right clue which enabled him to disentangle the complicated phenomena of electrodynamics and to deduce them all as a consequence of one simple fundamental law, which occupies in electrodynamics the position of the Newtonian law of gravitation in physical astronomy.

00The first deals with the prehistoric period of the world, before the rise of religion; the second was to be an endeavour to deduce a universal law from known historical facts; the third to sketch the ultimate state of perfection to which humanity is moving.

00We cannot deduce from them a conquest of Iran from Babylon: for the Babylonians never set foot in Iran and even the Assyrians merely conquered the western portior of Media.

00From motion he proceeds to deduce time, space and the categories of mechanics and natural science.

00Various attempts have also been made to deduce these laws from particular hypotheses as to the action between the molecules of the elastic substance.

00The second part endeavours to deduce the facts of the elasticity of a finite portion of the substance from hypotheses as to the motion of its constituent molecules and the forces acting between them.

00In like manner we may by experiment ascertain the general fact that the surface of a liquid is in a state of tension similar to that of a membrane stretched equally in all directions, and prove that this tension depends only on the nature and temperature of the liquid and not on its form, and from this as a secondary physical principle we may deduce all the phenomena of capillary action.

00The next step is to deduce this surface-tension from a hypothesis as to the molecular constitution of the liquid and of the bodies that surround it.

00He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how from these two principles to deduce the phenomena of capillary action.

00Having applied the secondary principle of surface-tension to the various particular cases of capillary action, Young proceeded to deduce this surface-tension from ulterior principles.

00Before going further we may deduce from equation 9 the nature of all the figures of revolution which a liquid film can assume.

00The laws are formulated in general terms, and the decisions in particular cases relegated to the sphere of juris prudence; and the canonists have definitely lost the function which fell to them in the 12th and 13th centuries: they receive the law on authority and no longer have to deduce it from the texts.

00Thirdly, it is objected that in order to deduce the conditioned, Cousin makes his absolute a relative; for he makes it an absolute cause, i.e.

00by the method of reciprocal polars) deduce from it the other, but we do at one and the same time demonstrate the two theorems; our (x, y, z.) instead of meaning point-co-ordinates pay, mean line-co-ordinates, and the demonstration is then in every step of it a demonstration of the correlative theorem.

00It was this: from the observed perturbations of a known planet to deduce by calculation, assuming only Newton's law of gravitation, the mass and orbit of an unknown disturbing body.

00But in spite of the intense conviction with which he thus identified metaphysical speculation and practical wisdom, we find in his writings no serious attempt to deduce the particulars of human well-being from his knowledge of absolute good, still less to unfold from it the particular cognitions of the special arts and sciences.

00It remains to consider how, from the doctrine that affection is the proper object of approbation, we are to deduce moral rules or " natural laws " prescribing or prohibiting outward acts.

00Spencer looked to ideas derived from the biological sciences to provide a solution of all the enigmas of morality, as of most other departments of life; and he conceived it " to be the business of moral science to deduce from the laws of life and the conditions of existence what kinds of action necessarily tend to produce happiness and what kinds to produce unhappiness."

00Bossert was enabled to deduce 2675 proper motions, published at Paris in four successive memoirs, 1887-1902; and the sum-total of those ascertained probably now exceeds 6000.

00He assails them on twenty points of their mixed physical and metaphysical peripateticism, from the statement of which, in spite of his pretended scepticism, we can deduce some very positive metaphysical opinions of his own.

00From the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed numerical aperture can be perceived.

00Thus we deduce one of the fundamental rules for successful work with numerical workbenches: prefer compiled functions over interpreted code.

00Based on figures at the end of 2004, we can deduce that the Xbox reached around twenty million.

00Using what you deduce from these clues, you can hold the control key and click on weapons or people to delete them from a room.

00Using what you can deduce from these clues, you can hold the control key and click on weapons or people to delete them from a room.

00No studies have been able to deduce definitively any kind of neurological basis for the syndrome.

00He began to deduce that the magnetron had caused the candy bar to melt and to test his theory he tried out some popcorn.

00More mature Geminis have learned how to use their analytical mind to deduce the right course of action.

00Though researchers struggle to understand just how protein helps control hunger, they deduce it may be due to the brain receiving lower levels of appetite stimulating hormones when more protein is consumed.

00As you may deduce by the prefix "un" the Unseelie Court includes fairies who, unlike the Seelie Court fairies, are nasty toward humans.

00

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