Analytically Sentence Examples

Failing analytically to probe its nature, historically we seek relief to our perplexities by tracing its origin..

Viewed analytically in its developed nature, magic is a wonder-working recognized as such, the core of the mystery consisting in the supposed transformation of suggested idea into accomplished fact by means of that suggestion itself.

The area BCDdb under the path represents the external work done by the substance in expanding from B to D, which is analytically represented by the integral of pdv taken along the given path.

Swanton - have studied many of these languages analytically and comparatively.

Analytically, the Cartesian equation to a coaxal system can be written in the form x 2 + y 2 + tax k 2 = o, where a varies from member to member, while k is a constant.

Really, 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.

The recomposition of the secondary waves may also be treated analytically.

By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or analytically that this is a minimum.

For commercial purposes iron is universally employed and works well; but it is not available analytically, because a superficial oxidation of the empty part of the vessel (by the water and air) cannot be prevented.

The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.

The object of the above sketch has been to embrace in constructive outline the ground usually covered analytically and on a far larger scale by Introductions to the New Testament, and by Histories of the New Testament Canon.

It satisfies the condition, however, equally with logarithms, of enabling multiplication to be performed by the aid of a table of single entry; and, analytically considered, it is not so different in principle from the logarithmic method.

The wave at a depth x is represented analytically by the equation 0 - 0 0 = Ae mx sin (21rnt - mx).

Adopting a hypothetical law of the dispersion of differently coloured rays of light, he proved analytically the possibility of constructing an achromatic object-glass composed of lenses of glass and water.

Deduction 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.

Analytically we have from (5),

This connexion is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.

This may be readily accomplished geometrically or analytically, and it will be found that the envelope is a cardioid, i.e.

But it can be shown, analytically or geometrically, that if the given curve has a node, the first polar passes through this node, which therefore counts as two intersections, and that if the curve has a cusp, the first polar passes through the cusp, touching the curve there, and hence the cusp counts as three intersections.

Thirdly, for the double tangents; the points of contact of these are obtained as the intersections of the curve by a curve II = o, which has not as yet been geometrically defined, but which is found analytically to be of the order (m-2) (m 2 -9); the number of intersections is thus = m(rn - 2) (m 2 - 9); but if the given curve has a node then there is a diminution =4(m2 - m-6), and if it has a cusp then there is a diminution =6(m2 - m-6), where, however, it is to be noticed that the factor (m2 - m-6) is in the case of a curve having only a node or only a cusp the number of the tangents which can be drawn from the node or cusp to the curve, and is used as denoting the number of these tangents, and ceases to be the correct expression if the number of nodes and cusps is greater than unity.

This last quantity is analytically defined by the equation r 2 = x 2 - + y2.

Analytically the elements are determined from these data by solving the four equations just given, regarding a, b, c and d as unknown quantities, and x, y, x', y' and t as given quantities.

Analytically it is defined by an equation of the second degree of which the highest terms represent two imaginary lines.

Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically.

Starting from simple elementary propositions, Steiner advances to the solution of problems which analytically require the calculus of variation, but which at the time altogether surpassed the powers of that calculus.

That the ego to which different parts of experience are presented must be the same ego, if there is to be cognition at all, is analytically evident; but the peculiarity is that the ego must be conscious of its own unity and identity, and this unity of self-consciousness is only possible in relation to difference not contained in the ego but given to it.

The Mathematical Tripos includes Computational Project courses which train students to solve analytically intractable mathematical problems using computers.

It can be solved analytically in terms of the statistical mechanics of spin lattices.

I present a simple model of a spatially extended spiking neuron which can be studied analytically.

Projection steps in the EP iteration that cannot be done analytically are done using Gaussian quadrature.

Traditional models generally assume very simple functional forms for f i, in order to have analytically tractable expressions for g t.

Analytically, it is defined by an equation of the second degree, of which the highest terms have real roots (see Conic Section).

But when the rate of change of aethereal strain - that is, of (f,g,h) specified as Maxwell's electric displacement in free aether - is added to it, an analytically convenient vector (u,v,w) is obtained which possesses the characteristic property of being circuital like the flow of an incompressible fluid, and has therefore been made fundamental in the theory by Maxwell under the name of the total electric current.

The schismatic nature of the contemporary community raises the question of whether a single Jewish voluntary sector is either analytically or practically valid.

After the normal form for the equations has been derived, the extent to which the equations may be solved analytically is covered.

Rather than panic and overreact when you're surprised by events, you can deal with it objectively and analytically.

Analytically expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the focal point) was equal to A 2 /X 2 f2.

Newton 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).