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.
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.
But ecclesiastical politics gave him an infinity of trouble.
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.
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.
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.
- 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.
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.
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.
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.
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.
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.
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.
Property that the line at infinity is a tangent.
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.
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.
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.
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.
If in a central orbit the velocity is equal to the velocity from infinity, we have, from (5),
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 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.
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.
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.
Infinity in relation to time and space which from one point of view is parallel to the Ontological argument.
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.
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.
+X) happens to be zero, X lies at infinity in a determinate direction; unless - aA is the barycentre of (3B, yC, ...
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.
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.
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.
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.
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'.
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.
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.
He points out the contradiction between the attributes of infinity and individuality.
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.
The symbol for infinity, o°, was invented by him.
It has the important property that it tends to infinity with x, but more slowly than any power of x, 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 Diogenes went much farther than Anaximenes by attributing to air not only infinity and eternity but also intelligence.
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 A or B vanish we have an equiangular spiral, and the velocity at infinity is zero.
Clarke appeals to the immensity of time and space as involving infinity in God.
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 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.
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.
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+?
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.
Pierced by an infinity of ancient cave-dwellings, some of which are still occupied.
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.