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 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.
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.
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.
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.
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.
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.
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.
Infinity in relation to time and space which from one point of view is parallel to the Ontological argument.
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.
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.
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 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.
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.
+X) happens to be zero, X lies at infinity in a determinate direction; unless - aA is the barycentre of (3B, yC, ...
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.
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.
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.