Word Finder - infinitely

definition

In an infinite manner; as of anything growing without bounds; endlessly.

definition

To a surpassingly large extent.

example

He is infinitely more capable than John.

We don't need our computers to be infinitely fast, just a whole lot faster than they are today.

The form is infinitely finer in Matt.

Estimates of Pilate's attitude at this point have varied infinitely, from Tertullian's, that he was " already in conviction a Christian " - jam pro sua conscientia Christianus- to Bacon's " jesting Pilate," who would not stay for a reply.

It is often necessary to remind her that there are infinitely many things that the wisest people in the world cannot explain.

We can still point to much in exact science that is absolutely his; and we can indicate infinitely more which is due to his inspiration.

Truth varies infinitely under circumstances whose relative weight cannot be accurately gauged.

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.

Dubuat considered that if water were a perfect fluid, and the channels in which it flowed infinitely smooth, its motion would be continually accelerated, like that of bodies descending in an inclined plane.

We don't need miniaturization to go to infinitely small, just really, really small.

Probably I should not consciously and deliberately forsake my particular calling to do the good which society demands of me, to save the universe from annihilation; and I believe that a like but infinitely greater steadfastness elsewhere is all that now preserves it.

According to common optics, where images are absolute, the diffraction pattern is supposed to be infinitely small, and two radiant points, however near together, form separated images.

Certainly it was true of him, in a far higher degree than of John Henry Newman, that the being of God and himself were to his mind two absolutely self-luminous truths - though both his God and his self were almost infinitely remote from Newman's.

Firmness such as this secured for him the support of all constitutional elements, and after three years premiership his position was infinitely stronger than at the outset.

Although the above useful formulae, (io) to (15), are true only for an infinitely small magnet, they may be practically applied whenever the distance r is considerable compared with the length of the magnet.

Though he lacked the brilliant qualities of his rival Wallqvist, Nordin had the same alertness and penetration, and was infinitely more stable and disinterested.

By imagining the successive positions to be taken infinitely close to one another we derive the theorem stated.

An infinitely small rotation about any axis is conveniently represented geometrically by a length AB measures along the axis and proportional to the angle of rotation, with the convention that the direction from A to B shall be related to the rotation as is the direction of translation to that of rotation in a righthanded screw.

Work.The work done by a force acting on a particle, in any infinitely small displacement, is defined as the product of the force into the orthogonal projection of the displacement on the direction of the force; i.e.

In the same way, the work dne by a force acting on a rigid body in any infinitely small displacement of the body is the scalar product of the force into the displacement of any point on the line of action.

But this puts an infinitely worse face on the matter, and suggests, beside, that probably not even the other three succeed in saving their souls, but are perchance bankrupt in a worse sense than they who fail honestly.

The total work done by two concurrent forces acting on a particle, or on a rigid body, in any infinitely small displacement, is equal to the work of their resultant.

It is also evident that the total work done in two or more successive infinitely small displacements is equal to the work done in the resultant displacement.

The work of a couple in any infinitely small rotation of a rigid body about an axis perpendicular to the plane of the couple is equal to the product of the moment of the couple into the angle of rotation, proper conventions as to sign being observed.

It is evident, in the first place, that in any displacement common to the two surfaces, the work of the two equal and opposite normal pressures will cancel; moreover if, one of the surfaces being fixed, an infinitely small displacement shifts the point of contact from A to B, and if A be the new position of that point of the sliding body which was at A, the pro jectior of AA on the normal at A is of the second order.

The form (I) is deduced from it by putting itt, and taking t to be infinitely small.

For purposes of mathematical treatment a force which produces a finite change of velocity in a time too short to be appreciated is regarded as infinitely great, and the time of action as infinitely short.

The effect of ordinary finite forces during the infinitely short duraticm of this impulse is of course ignored.

The impidse of a force in any infinitely small interval of time & is the product of the force into &; it is to be regarded as a vector.

The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.

Condition of Stability of Position.If the materials of a structure were infinitely stiff and strong, stability of position at any joint would be insured simply by making the centre of resistance fall within the joint under all possible variations of load.

This expression shows that as a increases y increases until when Wa = gc, y becomes infinitely large.

These investigations led him to the announcement of the fundamental law of action between elements of current, or currents in infinitely short lengths of linear conductors, upon one another at a distance; summed up in compact expression this law states that the action is proportional to the product of the current strengths of the two elements, and the lengths of the two elements, and inversely proportional to the square of the distance between the two elements, and also directly proportional to a function of the angles which the line joining the elements makes with the directions of the two elements respectively.

If Coke's reports show completer mastery of technical details, greater knowledge of precedent, and more of the dogged grasp of the letter than do Bacon's legal writings, there can be no dispute that the latter exhibit an infinitely more comprehensive intelligence of the abstract principles of jurisprudence, with a richness and ethical fulness that more than compensate for their lack of dry legal detail.

The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e.

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their " perpendicular height of incidence," i.e.

If the object point 0 be infinitely distant, u, and u 2 are to be replaced by h l and h 2, the perpendicular heights of incidence; the " sine condition " then becomes sin u',/h 1 = sin u' 2 /h 2 .

This number is only finite if the object and aperture are assumed to be " infinitely small of a certain order"; and with each order of infinite smallness, i.e.

Each of the four co-ordinates, n', x', y are functions of %, rj, x, y; and if it be assumed that the field of view and the aperture be infinitely small, then, n, x, y are of the same order of infinitesimals; consequently by expanding ', ii', x', y in ascending powers of E, rt, x, y, series are obtained in which it is only necessary to consider the lowest powers.

Freedom from aberration for two axis points, one of which is infinitely distant, is known as " Herschel's condition."

For infinitely distant objects the radius of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra," Monochromatic Aberration of the Axis Point "); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e.

If it is a risky matter to plant out the robust young fry of trout under an age of three months, it would seem to be an infinitely more speculative proceeding to plant out the delicate week-old larvae of sea-fishes in an environment which teems with predaceous enemies.

One sage, most learned of all, assents, but intimates that the scene of this glory will be, not the paternal kingdom, but another infinitely more exalted, and that the child will adopt the faith which his father persecutes.

Laplace investigated the force acting on the fluid contained in an infinitely slender canal normal to the surface of the fluid arising from the attraction of the parts of the fluid outside the canal.

If n +4 be positive, the attraction of infinitely distant parts contributes to the result; while if n+4 be negative, the parts in immediate contiguity act with infinite power.

The Magnitude Of A Drop Delivered From A Tube, Even When The Formation Up To The Phase Of Instability Is Infinitely Slow, Cannot Be Calculated A Priori.

For Example, In The Case Of Water Delivered From A Glass Tube, Which Is Cut Off Square And Held Vertically, A Will Be The External Radius; And It Will Be Necessary To Suppose That The Ratio Of The Internal Radius To A Is Constant, The Cases Of A Ratio Infinitely Small, Or Infinitely Near Unity, Being Included.

When the ellipse differs infinitely little from a circle, the equation of the meridian line becomes approximately y = a+c sin (x/a) where c is small.

Let us conceive an infinitely long circular cylinder of liquid, at rest (a motion common to every part of the fluid is necessarily without influence upon the stability, and may therefore be left out of account for convenience of conception and expression), and inquire under what circumstances it is stable or unstable, for small displacements, symmetrical about the axis of figure.

The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

The Langobards, German in their faults and in their strength, but coarser, at least at first, than the Germans whom the Italians had known, the Goths of Theodoric and Totila, found themselves continually in the presence of a subject population very different from anything which the other Teutonic conquerors met with among the provincials - like them, exhausted, dispirited, unwarlike, but with the remains and memory of a great civilization round them, intelligent, subtle, sensitive, feeling themselves infinitely superior in experience and knowledge to the rough barbarians whom they could not fight, and capable of hatred such as only cultivated races can nourish.