We have intuitions of cause, of infinity, of good and Flint.
The process by which the mind is thus stored consists of an infinity of individual impressions.
The line la+ma+ny is the radical axis, and since as+43 c-y =o is the line infinity, it is obvious that equation (I) represents a conic passing through the circular points, i.e.
God does not seem to find much place in the Wissenschaftslehre, where mankind is the absolute and nature mankind's product, and where God neither could be an absolute Ego which posits objects in the non-Ego to infinity without ever completing the process, nor could be even known to exist apart from the moral order which is man's destination.
But ecclesiastical politics gave him an infinity of trouble.
The symbol for infinity, o°, was invented by him.
The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.
property that the line at infinity is a tangent.
Thus his pantheistic is also a teleological idealism, which in its emphasis on free activity and moral order recalls Leibnitz and Fichte, but in its emphasis on the infinity of God has more affinity to Spinoza, Schelling and Hegel.
If in a central orbit the velocity is equal to the velocity from infinity, we have, from (5),
Here, according to Alexander the commentator, he first brought: against Plato the argument of " the third man " (6 Tp ir os & vBpcvrros); that, if there is the form, one man beyond many men, there will be a third man predicated of both man and men, and a fourth predicated of all three, and so on to infinity (Fragm.
He accepts an ultimate antinomy as to the finiteness or infinity of " the unconditioned," yet applies the law of the excluded middle to insist that one of the two alternatives must be true, wherefore we must make the choice.
there were several hundreds of them at Versailles, and within a generation or two they had taken an infinity of forms - columns, tripods, termini and mythological figures.
- N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.
As a special case A the three points A, B, C may be in a straight line; J is then at infinity and the displacement is equivalent to FIG 10 a pure translation, since every point of the lamina is now displaced parallel to AB through a space equal to AB.
The general equation to the circle in trilinear co-ordinates is readily deduced from the fact that the circle is the only curve which intersects the line infinity in the circular points.
infinity in relation to time and space which from one point of view is parallel to the Ontological argument.
If we now imagine the point 0 to recede to infinity, the forces P, Q and the resultant R are parallel, and we have R=P+Q, P.AC=Q.CB.
If a is negative the frequency passes through infinity and the maximum distance between the lines occurs there.
A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.
138) imagined it merely "to contain an infinity of nerves, disposed like net-work, all of which lead immediately to the nostrils," and add to the olfactory faculty.
It has the important property that it tends to infinity with x, but more slowly than any power of x, i.e.
From the religious point of view there are two main problems. The first is to establish any real relation between the individual and God without destroying personality and with it the whole idea of human responsibility and free will: the second is to explain the infinity of God without destroying his personality.
The essence of God, for instance, he held to be love; God, he said, can love nothing inferior to himself; but he cannot be an object of love to himself without going out, so to speak, of himself, without manifesting his infinity in a finite form; in other words, by becoming man.
Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.
In these tribes the bold and active habits, the striking colours, or the fantastic diversities of structure,have so long attracted remark that recent investigations, while adding a multitude of new species and supplying the specialist with an infinity of new details, have not materially altered the scientific standpoint.
Religion therefore is "nothing else than the consciousness of the infinity of the consciousness; or, in the consciousness of the infinite, the conscious subject has for his object the infinity of his own.
He points out the contradiction between the attributes of infinity and individuality.
The terms of 0 may be determined one at a time, and this problem is purely kinematical; thus to determine 4)1, the component U alone is taken to exist, and then 1, m, n, denoting the direction cosines of the normal of the surface drawn into the exterior liquid, the function 01 must be determined to satisfy the conditions v 2 0 1 = o, throughout the liquid; (ii.) ' = -1, the gradient of 0 down the normal at the surface of the moving solid; 1 =0, over a fixed boundary, or at infinity; similarly for 02 and 03.
If a+$+y+~=O, G is at infinity; if a = fi =~ =~, G bisects the lines joining the middle points of opposite edges of the tetrahedron ABCD; if a: ~: 7: = M3CD: z~CDA: ~DAB: L~ABC, G is at the centre of the inscribed sphere.
The question presents itself whether ther then is any other law of force, giving a finite velocity from infinity, under which all finite orbits are necessarily closed curves.
In projective geometry it may be defined as the conic which intersects the line at infinity in two real points, or to which it is possible to draw two real tangents from the centre.
Whatever one may think of the cogency of such arguments, it seems safe to conclude that thinkers, who dislike constructive idealism, but accept time and space as boundless given quanta, reach in that way the thought of infinity, and if they are theists, necessarily connect their theism with reflexions on the nature of Time and Space.
When cut open, it displays an infinity of tiny leaf-buds and stems, and at intervals there exudes from it an aromatic resin, which from its astringent properties is used by the shepherds as a vulnerary, but has not been converted to any commercial purpose.
Thus with a' =o, a stream is split symmetrically by a wedge of angle ' zr/n as in Bobyleff's problem; and, by making a = oo, the wedge extends to infinity; then chnS2= u, sh nS2= b n u.
To determine x i the angular velocity P alone is introduced, and the conditions to be satisfied are (i.) 0 2 x1 = o, throughout the liquid; y l =mz - ny, at the surface of the moving body, but zero over a fixed surface, and at :infinity; the same for x 2 and x3.
Clarke appeals to the immensity of time and space as involving infinity in God.
+X) happens to be zero, X lies at infinity in a determinate direction; unless - aA is the barycentre of (3B, yC, ...
ZUy2BB0 Bll; reducing, when the liquid extends to infinity and B 3 =0, to = xA o' _ - zUy 2B o so that in the relative motion past the body, as when fixed in the current U parallel to xO, A 4)'=ZUx(I+Bo), 4)'= zUy2(I-B o) (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting b 2 =pa, A = A'a, and proceeding to the limit where a = oo, we find for a paraboloid of revolution P B - p (7) B = 2p +A/' Bo p+A y2 i =p+A'- 2x, (8) p+?
When the source S is inside the sphere and H outside, the line sink must extend from H to infinity in the image system; to realize physically the condition of zero flow across the sphere, an equal sink must be introduced at some other internal point S'.
so that a+f~=o, the point C is at infinity, and the effect is a translation perpendicular to tire plane of the two given axes, of amount a.
When b = o, U 1 =00; and when b = oo, U 1 = -U, so that at infinity the liquid is streaming in the direction xO with velocity U.
pierced by an infinity of ancient cave-dwellings, some of which are still occupied.
If a+~+7 =0, G is at infinity; if a=~=y, G is at the intersection of the median lines ofthetriangle; jfa:: y=a: b: c,Gisatthecentreofthe inscribed circle.
No~ it appears from (6) that 2/s/r is the square of the velocity whici would be acquired by a particle faffing from rest at infinity to the distance r.
Hence the character of the orbit depends on whether the velocity at any point is, less than, equal to, or greater than the velocity from infinity, as it is called.
If the liquid is reduced to rest at infinity by the superposition of an opposite stream given by w = - Uz, we are left with w = Ua2/z, (6) =U(a 2 /r) cos 0= Ua2x/(x2+y2), (7) 4, = -U(a 2 /r) sin 0= -Ua2y/( x2+y2), (8) giving the motion due to the passage of the cylinder r=a with velocity U through the origin 0 in the direction Ox.
Beginning with a single body in liquid extending to infinity, and denoting by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest.
Another important conception connected with the preceding is the infinity of philosophy, which arises out of history and is as it were a reflection from history, varying at every moment and always solving a problem by placing alongside its solution the premise of a new history and therefore of a new problem and a new philosophy.
If A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.
No ruins are visible, the mounds of the old city being for the most part hidden under modern buildings; but the slopes of the limestone hills behind it are pierced with an infinity of rock-cut tombs, some of which were large and decorated with sculptures, paintings and long inscriptions.
But Diogenes went much farther than Anaximenes by attributing to air not only infinity and eternity but also intelligence.
However, looking over the whole field of North American achievement, architectural and non-architectural, composite and monolithic, the palm for boldness, magnitude of proportions and infinity of labour, must go to the sculptured mosaics of Yucatan.
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a: b: c, where a, b, c are the lengths of the sides, this becomes the line at infinity, and the forces reduce to a couple.
While resembling the parabola in extending to infinity, the curve has closest affinities to the ellipse.
As regards the so-called hyperbolisms, observe that (besides the single asymptote) we have in the case of those of the hyperbola two parallel asymptotes; in the case of those of the ellipse the two parallel asymptotes become imaginary, that is, they disappear; and in the case of those of the parabola they become coincident, that is, there is here an ordinary asymptote, and a special asymptote answering to a cusp at infinity.
We may consider in relation to a curve, not only the line infinity, but also the circular points at infinity; assuming the curve to be real, these present themselves always conjointly; thus a circle is a conic passing through the two circular points, and is thereby distinguished from other conics.
There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.
axiom of infinity - that there is an infinite set?
Hiroshima, visited by a bomb of exponential power, reached an infinity of destruction in seconds.
Diamond infinity rings are beautiful designs as rich with symbolism as they are with precious stones and sparkle.
HYPERBOLA, a conic section, consisting of two open branches, each extending to infinity.
The direction of magnetic induction may be indicated by lines of induction; a line of induction is always a closed curve, though it may possibly extend to and return from infinity.
Take caution, though, a wide band infinity ring may overshadow a simpler engagement ring.
The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.
Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.
concentric circles have double contact at the circular points, the chord of contact being the line at infinity.
The term "Nature" is put more into the foreground in the Treatise, a point which might be urged as evidence of Bruno's influence - the dialogues, moreover, being specially concerned to establish the unity, infinity and selfcontainedness of Nature 2; but the two opposed Cartesian attributes, thought and extension, and the absolutely infinite substance whose attributes they are - substance constituted by infinite attributes - appear here as in the Ethics.
Here we have u„+1 =2un+(2nI)2un-lr whence uh+1 -(2n +I)ac„= -(2n-I)(un-(2n-I)un_1}, and we readily find that p n I I I I 2 n I whence the value of the fraction taken to infinity is t r.
Here the fraction converges to the sum to infinity of the series.
infinity of minute prescriptions, injunctions on purity and the like, is well known.
At first the tension will diminish, but if the process be continued the tension will reach a minimum value and will afterwards increase to infinity as the chain between A and B approaches to the form of a straight line.
The small might become great, the point be enlarged to infinity (iv.
Thus mathematics assumes space as an existent infinite, without investigating in what sense the existence or the infinity of this Unding, as Kant called it, can be asserted.
The frank recognition that local income taxes are impossible, and that taxation on property for local purposes can only be applied to real property, where it becomes, usually or frequently, in the nature of a rent-charge, would have saved the legislature and the public an infinity of laborious discussion.
The sun is a small target for a meteorite coming from infinity to hit, and if this considerable quantity reaches its mark, a much greater amount will circulate round the sun in parabolas, and there is no evidence of it where it would certainly make itself felt, in perturbations of the planets.
Beyond mention, there is little to be said, owing to the absence of general principles in an infinity of specific details, mostly domestic and apparently trivial.
We have, in the case just referred to, to take account of a point at infinity on the line y=0; the two intersections are the point (x=110, y=0), and the point at infinity on the line y= 0.
It is, moreover, to be noticed that the points at infinity may be all or any of them imaginary, and that the points of intersection, whether finite or at infinity, real or imaginary, may coincide two or more of them together, and have to be counted accordingly; to support the theorem in its universality, it is necessary to take account of these various circumstances.
The foregoing notion of a point at infinity is a very important one in modern geometry; and we have also to consider the paradoxical statement that in plane geometry, or say as regards the plane, infinity is a right line.
Say the projection is always a line, then if the figure is such that the two planes are parallel, the projection is the intersection of the given plane by a parallel plane, or it is the system of points at infinity on the given plane, that is, these points at infinity are regarded as situate on a given line, the line infinity of the given plane.
1 1 In solid geometry infinity is a plane - its intersection with any given plane being the right line which iš the infinity of this given plane.
Reverting to the purely plane theory, infinity is a line, related like any other right line to the curve, and thus intersecting it in m points, real or imaginary, distinct or coincident.
ont idealement deux points imaginaires communs a l'infini "; that is, a circle qua curve of the second order is met by the line infinity in two points; but, more than this, they are the same two points for any circle whatever.
The points in question have since been called (it is believed first by Dr George Salmon) the circular points at infinity, or they may be called the circular points; these are also frequently spoken of as the points I, J; and we have thus the circle characterized as a conic which passes through the two circular points at infinity; the number of conditions thus imposed upon the conic is = 2, and there remain three arbitrary constants, which is the right number for the circle.
Poncelet throughout his work makes continual use of the foregoing theories of imaginaries and infinity, and also of the before-mentioned theory of reciprocal polars.
A branch is either re-entrant, or it extends both ways to infinity, and in this case, we may regard it as consisting of two legs (crura, Newton), each extending one way to infinity, but without any definite separation.
Names may also be used for the different forms of infinite branches, but we have first to consider the distinction of hyperbolic and parabolic. The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other.
If a line S2 cut an arc aa at b, so that the two segments ab, ba lie on opposite sides of the line, then projecting the figure so that the line Sl goes off to infinity, the tangent at b is projected into the asymptote, and the arc ab is projected into a hyperbolic leg touching the asymptote at one extremity; the arc ba will at the same time be projected into a hyperbolic leg touching the same asymptote at the other extremity (and on the opposite side), but so that the two hyperbolic legs may or may not belong to one and the same branch.
And we thus see that the two hyperbolic legs belong to a simple intersection of the curve by the line infinity.
Next, if the line S2 touch at b the arc aa so that the two portions ab, ba lie on the same side of the line Sl, then projecting the figure as before, the tangent at b, that is, the line S2 itself, is projected to infinity; the arc ab is projected into a parabolic leg, and at the same time the arc ba is projected into a parabolic leg, having at infinity the same direction as the other leg, but so that the two legs may or may not belong to the same branch.
And we thus see that the two parabolic legs represent a contact of the line infinity with the curve, - the point of contact being of course the point at infinity determined by the common direction of the two legs.
The foregoing considerations also show (what is very important) how different branches are connected together at infinity, and lead to the notion of a complete branch or circuit.
The genera may be arranged as follows: 1,2,3,4 redundant hyperbolas 5,6 defective hyperbolas 7,8 parabolic hyperbolas 9 hyperbolisms of hyperbola To „ II „ „ parabola 12 trident curve 13 divergent parabolas 14 cubic parabola; and thus arranged they correspond to the different relations of the line infinity to the curve.
First, if the three intersections by the line infinity are all distinct, we have the hyperbolas; if the points are real, the redundant hyperbolas, with three hyperbolic branches; but if only one of them is real, the defective hyperbolas, with one hyperbolic branch.
Secondly, if two of the intersections coincide, say if the line infinity meets the curve in a onefold point and a twofold point, both of them real, then there is always one asymptote: the line infinity may at the twofold point touch the curve, and we have the parabolic hyperbolas; or the twofold point may be a singular point, - viz., a crunode giving the hyperbolisms of the hyperbola; an acnode, giving the hyperbolisms of the ellipse; or a cusp, giving the hyperbolisms of the parabola.
Thirdly, the three intersections by the line infinity may be coincident and real; or say we have a threefold point: this may be an inflection, a crunode or a cusp, that is, the line infinity may be a tangent at an inflection, and we have the divergent parabolas; a tangent at a crunode to one branch, and we have the trident curve; or lastly, a tangent at a cusp, and we have the cubical parabola.
(See Parabola.) Drawing a line to cut any one of these curves and projecting the line to infinity, it would not be difficult to show how the line should be drawn in order to obtain a curve of any given species.
But although we thus arrive by projection at the notion of a circuit, it is not necessary to go out of the plane, and we may (with Zeuthen, using the shorter term circuit for his complete branch) define a circuit as any portion (of a curve) capable of description by the continuous motion of a point, it being understood that a passage through infinity is permitted.
On submitting a complex substance of this character to destructive distillation, it will be found that the yield and quality of the products will vary very considerably with the temperature existing in the retorts, with the size of the charge of coal used, with its distribution in the retort, with the length of time the distillation has been going on, and with an infinity of other factors of a more or less complex nature.
These have now to pass down the heated retort on their way to the ascension pipe, and the contact with the heated sides of the retort, and the baking from the radiant heat in the retort, set up an infinity of changes.
Concurrently, there was a speculative or philosophical interest; and some prefer to defend Trinitarianism as a reconciliation of the personality with the infinity of God.
For these inferences there is indeed no actual physical evidence: infinity is a mental concept.
This is Spinoza's theory of the infinitely infinite," the limiting notion of infinity being of a numerical, quantitative series, each term of which is a qualitative determination itself quantitatively little, e.g.
The doctrine of geometrical continuity and the application of algebra to geometry, developed in the 16th and 17th centuries mainly by Kepler and Descartes, led to the discovery of many properties which gave to the notion of infinity, as a localized space conception, a predominant importance.
A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.
The infinity of real existence, in contrast with the necessary finitude of human understanding and experience, is always in his thoughts.
To prove this, our thoughts of space, time, infinity, power, substance, personal identity, causality, and others which " seem most remote from the supposed original " are examined in a " plain historical method," and shown to depend either on (a) perception of things external, through the five senses, or on (b) reflection upon operations of the mind within.
the line at infinity intersects the hyperbola in real points, the ellipse in imaginary points, and the parabola in coincident real points.
If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.
13 and 14, so that its image, the entrance pupil, lies at infinity, all the principal rays in the object-space are parallel to the axis, and we have on the object-side " telecentric " transmission.
The eyepiece, which by means of narrow pencils represents the relatively large real image at infinity, transmits from all points of this real image parallel pencils, whereby the inclination of the principal rays becomes further increased.
The entrance window is then the real image of this diaphragm projected by the objective in the surface conjugate to the plane focused for, and the exit window is the image projected by the eyepiece; this happens with the image of the object lying at infinity.
Its purpose in a microscope is by means of narrow cones of rays to represent at infinity the real magnified image which the objective produces.
that the source falls approximately at the front focus of this lens and consequently is represented at infinity through the illuminating lens.
allegorical representation of Infinity.
arc of infinity featured Amsterdam.
autofocus function and set the camera at infinity.
It will satisfy Infinity and Choice if the original model of TST satisfies these axioms.
CCD chip are at the common infinity focus of the lens.
complicated by the presence of lawyer media assumed to extend to infinity.
damped oscillator, at M 4, the oscillations continue into infinity.
In fact, the infinity fryer has been scientifically proven to produce food with up to 25% less fat.
His first novel, To hold infinity, was one of the Daily Telegraph's ' Books of the Year ' .
It reaches the minimum in a circular object and approaches infinity in thin, complex objects.
Confidence intervals for nausea included infinity suggesting the point estimate (9.9) is unreliable.
Martin 1983 among others assigns this a value of negative infinity.
The permitted range of the argument is from minus infinity to plus infinity.
If the argument is positive infinity, then positive infinity is returned.
Malebranche himself maintains that his view of God follows from divine infinity, which of course has a scriptural basis.
This is why Craig rejects the notion of actual infinity in statement 2.1.
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As the list of harmful things approaches infinity, I have found something new to fear, take note of this warning.
By claiming that one of those moments earlier nolan project infinity.
infinity in the palm of your hand And eternity in an hour ' .
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The lowest order contributions to the partition function will come from metrics with a U1 isometry, and given behavior at infinity.
Now we can continue the sequence ` beyond infinity ' by using the basic lemma repeatedly, starting at t w.
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omnipotence cannot be exalted; Infinity cannot be amplified; Perfection cannot be improved.
At M 4, the system is a damped oscillator, at M 4, the oscillations continue into infinity.
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Her words caught Daniel's senses a glancing blow and then ricocheted away into infinity.
singularitycomputer simulations can help, many algorithms fail when they address regions near black hole singularities where the gravitational fields theoretically approach infinity.
FACILITIES infinity swimming pools are set overlooking the ocean, where, in winter, the whales arrive to mate and calve.
The in solido definition as the section of a cone by a plane at a less inclination to the axis than the generator brings out the existence of the two infinite branches if we imagine the cone to be double and to extend to infinity.
If a rectangle be constructed about AA' and BB', the diagonals of this figure are the "asymptotes" of the curve; they are the tangents from the centre, and hence touch the curve at infinity.
The Ontological argument, though not wholly rejected as a proof, is taken rather as pointing to God's attribute of infinity; thought rather than experience making affirmation that the intuition in question must be attached to God.
One might prefer as a theist to hold (1) that we need a philosophical doctrine of the nature of reality - the " Absolute "; given in popular form in the Cosmological argument; (2) that we take the risk of attaching a higher degree of significance and authority to the revelations of the moral consciousness, which, although moulded or educed by society, do not terminate in the authority of society, but point beyond it to God; this position has its popular form in the moral argument; possibly (3) that necessities of thought shut us up to belief in omnipotence or infinity; (4) that divine help is the supreme revelation.
When the upper limit is infinity, so that the limits correspond to the inclusion of half the primary wave, C and S are both equal to by a known formula; and on account of the rapid fluctuation of sign the parts of the range beyond very moderate values of v contribute but little to the result.
Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.
At infinity U = -me a cos (i = a m b oos (3, V= -me a sin 1 3 - C7,1 sin 0, (9) a and b denoting the semi-axes of the ellipse a; so that the liquid is streaming at infinity with velocity Q = m/(a+b) in the direction of the asymptote of the hyperbola (3.
Similarly, parallel to Oy, the increase of effective inertia is NT'/th n th(n-a), reducing to M'/th n=M' (a/b), when a= oo, and the liquid extends to infinity.
acf aZpa, a ball or globe), in geometry, the solid or surface traced out by the revolution of a semicircle about its diameter; this is essentially Euclid's definition; 1 in the modern geometry of surfaces it is defined as the quadric surface passing through the circle at infinity.
The work done in expanding to infinity from p tons per sq.
The symbol for infinity, oÃ‚°, was invented by him.
No other hand could have ventured to render the hair and beard of a sitter, as it was the habit of this inveterate linearist to do, not by indication of masses, but by means of an infinity of single lines swept, with a miraculous certainty and fineness of touch, in the richest amd most intricate of decorative curves.
A fundamental property of the curve is that the line at infinity is a tangent (see Geometry, Projective), and it follows that the centre and the second real focus and directrix are at infinity.
The equation to a parabola in triangular co-ordinates is generally derived by expressing the condition that the line at infinity is a tangent in the equation to the general conic. For example, in trilinear co-ordinates, the equation to the general conic circumscribing the triangle of reference is 113y+mya+naf3=o; for this to be a parabola the line as + b/ + cy = o must be a tangent.
If we imagine 0 to recede to infinity in any direction we learn that a system of parallel forces proportional to nh, mi,.
It will be seen that unless the conditions be exactly adjusted for a circular orbit the particle will either recede to infinity or approach the pole asymptotically.
The metaphysical and theological conception is open to the agnostic objection that the finite mind of man is by hypothesis unable to cognize or apprehend not only an infinite object, but even the very conception of infinity itself; from this standpoint the infinite is regarded as merely a postulate, as it were an unknown quantity (cf.
Kepler's greatest contribution to geometry lies in his formulation of the "principle of continuity" which enabled him to show that a parabola has a "caecus (or blind) focus" at infinity, and that all lines through this focus are parallel (see Geometrical Continuity).
Above him again was the same lofty sky with clouds that had risen and were floating still higher, and between them gleamed blue infinity.
If y is an infinity, rem returns x.
Her words caught Daniel 's senses a glancing blow and then ricocheted away into infinity.
Although computer simulations can help, many algorithms fail when they address regions near black hole singularities where the gravitational fields theoretically approach infinity.
FACILITIES Infinity swimming pools are set overlooking the ocean, where, in winter, the whales arrive to mate and calve.
With shadows now tending to infinity, the sun teetered just above the horizon as the train worked slowly round the curve.
Their very names, however, bear witness to the star treatment they offer: Zenith, Summit, Mercury, Infinity, Galaxy, Constellation, Millennium, Century, Celebrity Journey, Celebrity Quest, and Celebrity Xpedition.
Celebrity Cruises - Has family ocean view staterooms on three of its ships: the Infinity, Constellation and Millennium.
Claddagh icons combined with other Celtic knots such as trinity or infinity designs for added symbolism.
In that same year, they published Marathon: Infinity for the Mac.
Successfully beat story mode to unlock "Infinity" level.
NOTE that the Vulcan isn't found until Infinity Mode and any of the launchers may be ineffective on the Enforcer's later incarnations.
The complex philosophies of the yin yang concepts may change based on Daoism, Buddhism or the western culture, but the basic concepts of polarity, duality, infinity and balance of yin yang theory remains the same throughout belief systems.
While the Tao symbol is probably better known as the yin yang symbol, the encircled symbol represents the never-ending energy of chi, which is the concept of infinity.
The number eight creates a pattern of two circles with no end and is considered a symbol of infinity.
Since the number eight is associated with wealth and power, the infinity aspects means a limitless source of the energies this number will bring to you.
It's created by tying six infinity knots together.
Many universally recognize the figure eight as the symbol for infinity.
The double happiness symbol can be combined with an infinity symbol, known as the mystic knot.
This knot is always created by using a series of six infinity knots (figure eight) tied together.
It's comprised of six infinity knots (the figure eight turned on its side) entwined together.
You can vary your look with more current blouses and accessories, like a silk infinity scarf.
The reading should output as INFINITY when you have the door open and "0" when the door is closed.
When you test the leads, the reading should begin with a low ohms number and gradually rise toward INFINITY.
Simple trinity, infinity, or lover's knots, often used as the focal point of the ring instead of a gemstone.
A diamond infinity ring (also known as an eternity ring) has diamonds encircling the entire band.
Another infinity style uses the infinity symbol as part of the design.
Both styles have a loop that represents infinity and has a symbolic meaning when given as a special gift.
Show that your love will never end by giving an infinity ring in a style that reflects her personality and taste.
In addition to infinity eternity bands, there are rings that have the infinity symbol incorporated into the design.
The meaning behind the symbol, that resembles a knot, is that love is eternal and for infinity.
Diamond Infinity Symbol Ring: Found at Apples of Gold, this ring has rows of infinity symbols encrusted with diamonds on the edges and set in 10K white or yellow gold.
Sterling Silver Diamond Infinity Ring: Set in sleek sterling silver, this ring from LeVaron Jewelers uses diamonds on half of the knot design.
Diamond Accent Infinity Knot Ring: Zales features this ring set in sterling silver with two diamond accents within the design.
There are many different options for infinity ring designs.
At Wedding Bands.com, you can find a variety of infinity style bands with diamonds.
Eternity Wedding Bands specializes in infinity rings done in the eternity style.
Enhanced Black and White Diamond Infinity Ring in 10K White Gold: This unique ring design has the infinity symbol done on half diamonds and half black diamonds.
Sun Jewelry has a good selection of infinity eternity styles, especially in terms of bridal sets.
This shop also carries a 1.88 Carat Infinity Diamond style in white gold that has the infinity symbol encircling a center diamond.
Many women wear diamond infinity rings as an elegant wedding ring because not only are they beautiful bands, but they also coordinate well with any diamond engagement ring.
An infinity ring may also make the combined set disproportionately wide for the woman's finger, in which case the band should be worn by itself on whichever hand is most comfortable.
If the infinity band ring has open edges, such as with a pave setting, it should not be worn against other rings that it could scratch or the delicate edges of the diamonds may be chipped.
Diamond Infinity Rings: Eternity-style rings with elaborate accents are characteristic Beaudry style, and floral patterns give these bands even more uniqueness.
Knots: The basic Celtic knots representing infinity and romance are popular, or couples with a personal Celtic history may choose specific knots with a family connection.
Glyph: Cancer's glyph looks a little like the symbol for infinity and a little like yin and yang intertwined.
A recent article in Baseball America raved about the 9-Spike Pro Limited cleats, saying that their Infinity Wave Technology would set new standards of comfort in professional play.
Rocker Pink's designs include the infinity symbol, an Asian dragon and the Japanese symbol for luck.
When the two rings are connected they also create the symbol for "infinity" as there is no end in the union of the two.
Infinity: The rapid-fire beat of a hummingbird's wings form a pattern much like the infinity symbol.
Other top rated atomic clock manufacturers include Equity Skyscan, Oregon Scientific and Infinity Instruments.
Thanks to Citizen's ongoing technical innovations, your Eco-Drive watch will keep you on time and in fashion for infinity.
Every other concomitant is a rational integral function of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.
Such are modes of quantity in space, and time and number, under which Locke reports that we find ourselves mentally impelled towards immensity, eternity and the innumerable - in a word, towards Infinity which seems to transcend quantity; then there is the complex thought of Substance, to which we find ourselves mysteriously impelled, when the simple phenomena of the senses come to be regarded as qualities of " something "; again there is the obscure idea of the identity of persons, notwithstanding their constant changes of state; and there is, above all, the inevitable tendency we somehow have to refund a change into what we call its " Cause," with the associated idea of active power.
The question is rather that of the infinity of forms that matter may assume, including that most attenuated form found in the nebulae, which seem to be composed of matter more refined than even the atoms supposed to make up the matter around us.
The "infinity" of the premise is an infinity of subdivisions of a distance which is finite; the "infinity" of the conclusion is an infinity of distance.
But one may well believe that there was in his mind at any rate a foreshadowing of some of the ideas by which modern mathematicians have finally laid to rest the traditional difficulties connected with infinity and continuity."
Other geometrical definitions are: it is the oblique projection of a circle; the polar reciprocal of a circle for a point within it; and the conic which intersects the line at infinity in two imaginary points.
When light from an extended source is made to converge upon the crystal, the phenomenon of rings and brushes localized at infinity is obtained.The exact calculation of the intensity in this case is very complicated and the resulting expression is too unwieldy to be of any use, but as an approximation the formula for the case of a parallel beam may be employed, the quantities and p therein occurring being regarded as functions of the angle and plane of incidence and consequently as variables.
In the case of the circle, the centre is the focus, and the line at infinity the directrix; we therefore see that a circle is a conic of zero eccentricity.
When a = b, a = o, and the stream is very broad compared with he wedge or lamina; so, putting w=w' (a-b)la in the penultimate ase, and A B A (7) When the polygon is closed by the walls joining, instead of reaching back to infinity at xx', the liquid motion must be due to a source, and this modification has been worked out by B.
The feng shui symbol of unlimited happiness, the symbol for infinity, brings good luck, happiness and prosperity as it attracts positive energy bringing balance to your life.
Diamond Infinity Ring in 10K White Gold: This ring has the symbol done in 1/4 carat diamonds in a softly looping design.
The 2007 release Infinity on High has pushed the popularity of Fall Out Boy even higher, and the album's first single, This Ain't a Scene, It's an Arms Race, saw the band make serious in roads in the UK charts as well.
The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.