Sin sentence example
His main sin appears to be his poor timing.
It is not a sin to want your child.
Sin is the contradiction of that purpose, and guilt is alienation from the family.
The impressiveness and the stimulating power of the mystic ceremonies, the consciousness of being the privileged possessor of the secret wisdom of the ancients, the sense of purification from sin, and the expectation of a better life where there was to be compensation for the sufferings of this world - were all strong appeals to human nature.
Ogling a spouse couldn't be a sin – especially when he derived such obvious pleasure from it.Advertisement
His system declared that holiness and sin are free voluntary exercises; that men act freely under the divine agency; that the slightest transgression deserves eternal punishment; that it is through God's mere grace that the penitent believer is pardoned and justified; that, in spite of total depravity, sinners ought to repent; and that regeneration is active, not passive, with the believer.
The sacrament of the most Holy Eucharist shall be freely administered in the two kinds, that is bread and wine, to all the faithful in Christ who are not precluded by mortal sin - according to the word and disposition of Our Saviour.
Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.
Of the quadratic axe+2bxy+cy2, he discovered the two invariants ac-b 2, a-2b cos w+c, and it may be verified that, if the transformed of the quadratic be AX2=2BXY+CY2, sin w 2 AC -B 2 =) (ac-b2), sin w A-2B cos w'+C = (sin w'1 2(a - 2bcosw+c).
This made it a grave sin in the priest to refuse absolution, whenever there was some good reason for giving it even when there were other and better reasons for refusing it.Advertisement
If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.
If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.
If P is the weight of the magnet, l the length of each of the two threads, 2a the distance between their upper points of attachment, and 2b that between the lower points, then, approximately, MH = P(ab/l) sin 0.
Let 0 be the angle which the standard magnet M makes with the meridian, then M'/R = sin 0, and M/R = cos 0, whence M' = M tan 0.
From that time Conselheiro was a victim of remorse, and to expiate his sin became a missionary in the sertao or interior of Brazil among the wild Jagunco people.Advertisement
If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).
The directed line whose length is a, and which makes an angle 0 with the real (positive) unit line, is expressed by a (cos 0+i sin e), where i is regarded as +1,/ - 1.
If, as is usually most convenient, the two assigned directions are at right angles, the two components of a force P will be P cos 0, P sin 0, where 0 is the inclination of P to the direction of the p former component.
If the origin of rectangular axes fixed in the lamina be shifted through a space whose projections on the original directions of the axes are X, u, and if the axes are simultaneously turned through an angle e, the coordinates of a point of the lamina, relative to the original axes, are changed from x, y to X+x cos ey sin e, u+x sin e+y cos e, or X + x ye, u + Xe + y, ultimately.
If the forces are all parallel, making say an angle 0 with Ox, we may write Xi = Pi cos 0, Vi = P1 sin 0, Xi = P2 cos 0, VI = Pi sin 0,.Advertisement
The displacement of the point H in the figure, resolved in the direction of R, is r cos 0sh sin 0.
The work is therefore R(r cos 0sh sin 0)+ G cos 8
The factor (P+P) cos 0h sin 0 is called the vIrtual coefficient of the two screws which define the types of the wrench and twist, respectively.
The solution is x=A cos nl+B sinai, y=C cos nt-ED sin at, (9)
Fi(sin 1/811), (18)Advertisement
Again, in the equiangular spiral we have p =r sin a, and therefore P = u/ri, if u =hh/sinh a.
Thus the centre of a sphere rolling under gravity on a plane of inclination a describes a parabola with an acceleration g sin a/(I+C/Ma)
Baptism entirely destroys original sin.
If now you married again with the object of bearing children, your sin might be forgiven.
The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.Advertisement
The second and third factors of (3) being each of the form sin 2u/u2, we have to examine the character of this function.
The maxima occur when u=tan u, (4), and then sin 2 u/u 2 = cos 2 u (5).
In the direction (suppose horizontal) for which n=o, /f=sin 0, the phases of the secondary waves range over a complete period when sin 0 =X/a, and, since all parts of the horizontal aperture are equally effective, there is in this direction a complete compensation and consequent absence of illumination.
When sin 0 = 2A/a, the phases range one and a half periods, and there is revival of illumination.
In like manner we may find the illumination in any other direction, and it is obvious that it vanishes when sin 0 is any multiple of A/a.Advertisement
Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 18.104.22.168.1.3.5 5 () 3 1 22.214.171.124 1 3 cos(z - ?r) 8 ' z (z) 126.96.36.199.188.8.131.52.7 1 5 + 184.108.40.206.40 (z
Now since AP is very small, AL' - PL'= AP sin a, where a is the angular semi-aperture L'AB.
In like manner PL - AL has the same value, so that PL - PL' = 2AP sin a.
Calling the refractive index µ, we have as the critical value of e=2Xo/ µ sin a, (1).
The denominator sin a is the quantity well known (after Abbe) as the " numerical aperture."Advertisement
If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.
A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').
In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.
For this purpose Rowland places the eye-piece at 0, so that 0 =o, and then by (11) the value of '" in the m th spectrum is o- sin $' = tmX.
If w now relate to the edge of the grating, on which there are altogether n lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.Advertisement
If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .
By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 220.127.116.11 18.104.22.168.9.11 These series are convergent for all values of v, but are practically useful only when v is small .
The intensity may be expressed by 12= (2+Cv) 2 +(2+Sv) 2 and the maxima and minima occur when dC dS (z+Cv)a`j+(2+Sv)dV=0, whence sin rV 2 +cos27rV 2 =G..
Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).
The occurrence of sin 4 as a factor in (6) shows that the relative intensities of the primary light and of that diffracted in the direction B depend upon the condition of the former as regards polarization.Advertisement
Its connexion with a is expressed by a =c4'/dr; so that TZ sin 05 e'(at - kr) 47b 2 where the factor e int is restored.
Retaining only the real part of (16), we find, as the result of a local application of force equal to DTZ cos nt (17), the disturbance expressed by TZ sin 4, cos(nt - kr) ?
We will now apply (18) to the investigation of a law of secondary disturbance, when a primary wave = sin (nt - kx) (19) is supposed to be broken up in passing the plane x = o.
According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).
The proportionality of the secondary disturbance to sin 43 is common to the present law and to that given by Stokes, but here there is no dependence upon the angle 0 between the primary and secondary rays.
Now, both the Korahite and Asaphic groups of psalms are remarkable that they hardly contain any recognition of present sin on the part of the community of Jewish faith - though they do confess the sin of Israel in the past - but are exercised with the observation that prosperity does not follow righteousness either in the case of the individual (xlix., lxxiii.) or in that of the nation, which suffers notwithstanding its loyalty to God, or even on account thereof (xliv., lxxix.).
Malachi, Ezra and Nehemiah, like Haggai and Zechariah, are still very far from holding that the sin of Israel lies all in the past.
They no doubt deferred the baptism which is death to sin, perhaps because, like the Cathars, they held post-baptismal sin to be unforgivable.
The Key of Truth regards the water as a washing of the body, and sees in the rite no opus operatum, but an essentially spiritual rite in which "the king releases certain rulers a from the prison of sin, the Son calls them to himself and comforts them with great words, and the Holy Spirit of the king forthwith comes and crowns them, and dwells in them for ever."
He held a prominent place in the New School branch of the Presbyterians, to which he adhered on the division of the denomination in 1837; he had been tried (but not convicted) for heresy in 1836, the charge being particularly against the views expressed by him in Notes on Romans (1835) of the imputation of the sin of Adam, original sin and the atonement; the bitterness stirred up by this trial contributed towards widening the breach between the conservative and the progressive elements in the church.
His extraordinary thinness is commemorated, among other things, by the very poor but well-known epigram attributed to Young, and identifying him at once with "Satan, Death and Sin."
The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.
Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.
For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.
Consider the motion given by w=U(z+a2/z), (I) 4,=U(r+- r) cos 0= U + a1x, so that (2) = U (r-)sin 0= U(i -¢) y.
Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ¢2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).
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.
When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?
Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2 r 2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2 r 2 cos 2 0 +mr1 sin 0) (Ua 2 r 2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2 r 2 cos 30), (8) and with b tan r =b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU.
Consider the streaming motion given by w =m =a+si, (5) 4=m ch (n -a)cos(-0), p=m sh(n-a)sin(-13).
An ellipse interior to n = a will move in a direction opposite to the exterior current; and when n = o, U = oo, but V = (m/c) sh a sin 13.
The resultant hydrostatic thrust across any diametral plane of the cylinder will be modified, but the only term in the loss of head which exerts a resultant thrust on the whole cylinder is 2mU sin Olga, and its thrust is 27rpmU absolute units in the direction Cy, to be counteracted by a support at the centre C; the liquid is streaming past r=a with velocity U reversed, and the cylinder is surrounded by a vortex.
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.
The polar equation of the cross-section being rI cos 19 =al, or r + x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(r-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.
Similarly, with the function (19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?
For instance, with n = I in equation (9), the relative stream function is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(r 2 -a 3 /r) sin?
In the absolute path in space cos Ili = (2 - 3 sin 2 6)/1/ (4-sin 2 6), and sin 3 B = (y 3 -c 2 y)/a 3, (19) which leads to no simple relation.
If there are more B corners than one, either on xA or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1!
For the body alone the resultant of the components of momentum W V -cos andW V sin 0 is W V -sec. lb, acting along 00', and so is unaltered.
Another son was high-priest of the city of Tutu, and in the name of his daughter, Lipus-Eaum, a priestess of Sin some ur dynasty.
The last king of Assyria was probably the brother of Assur-etil-ilani, Sin - sar - iskun (Sin-sarra-uzur), who seems to have been the Sarakos (Saracus) of Berossus.
The moon-god Sin is written by a sign which has the force of " thirty," and is a distinct reference to the monthly course of the planet; or the name is written by two signs to be pronounced EN-ZU, which describe the god as the " lord of wisdom."
The book treats of the Messiah and the Messianic kingdom, the woes of Israel in the past and the destruction of Jerusalem in the present, as well as of theological questions relating to original sin, free will, works, &c. The views expressed on several of these subjects are often conflicting.
It is possible for a regenerate man to live without sin.
But, while Samaria is summarily dismissed, the sin of Judah is analysed at length in chs.
At last the power and influence of the spirits of darkness, with whom man associates himself by his sin, became so great that the existence of the human race was threatened, and Jehovah was necessitated to descend into nature to restore the connexion between Himself and man.
The romantic school was supported by Sin Otetchestva (1812), " Son of the Fatherland," united in 1825 to the Severnoi Arkhiv (1822), which dwindled and came to an end soon after 1839.
Its preaching is practical and direct, asseverating the reality of Sin, "the everlasting punishment of the wicked," and Redemption.
It ex pounded in terse and significant teaching the doctrine (1) of God, (2) of original sin, (3) of the Son of God, (4) of justification..
It deals with the Bible as the final appeal in controversy, the doctrines of God, man, sin, the Incarnation, the Resurrection of our Lord Jesus Christ, " both the Son of man and the Son of God," the work of the Holy Spirit, justification by faith, the perpetual obligation of Baptism and the Lord's Supper, final judgment, the law of Christian fellowship. The same principles have been lucidly stated in the Evangelical Free Church catechism.
He knows that the great object of all my preaching and writing was to convert men from sin.
The church key reminds him that "it is my sin that locks his handes," and the stones of the floor are patience and humility, while the cement that binds them together is love and.
Of in Jesus Christ the Saviour, who delivers from the bondage of sin by his life, doctrine and death; in the operation of the Holy Ghost; in a holy, universal, Christian church; in forgiveness of sins and the life everlasting.
The Cathars even held it necessary, in case a bishop fell into mortal sin, to repeat his ba p tisms and ordinations, for they had been vitiated by his sins.
Although they surrendered transubstantiation, the loss of one mystery was amply compensated by the stupendous doctrines of original sin, redemption, faith, grace and predestination upon which they founded their theory of salvation.
If he be once approved as a true prophet, his words and acts are not to be criticized; for this is the sin that shall not be forgiven.
The Lombard sect went farther in (3) and (4), holding that no one in mortal sin could consecrate the sacrament, and that the Roman Church was the scarlet woman of the Apocalypse, whose precepts ought not to be obeyed, especially those appointing fast-days.
Let a be the radius of a circle, and 0 (circular measure) the unknown angle subtended by an arc. Then, if we divide 0 into m equal parts, and L 1 denotes the sum of the corresponding chords, so that L i =2ma sin (0/2m), the true length of the arc is L1 +a9 3 - 5 + ..., where cp. =B/2m.
Jesus, they say, was sent to save sinners; was he not sent to help those who have kept themselves free from sin?
There are twenty-nine letters, one more than in Arabic, Samech and Sin being distinct forms, as in Hebrew.
The moon-god Sin appears on an inscription of Shahwat; but, according to Hamdani, Haubas, " the drier," was the Sabaean moon-god.
On the Shabwat inscription `Athtar is the father of Sin, and it is noteworthy that these two deities also appear as nearly related in the Babylonian legend of 'Ishtar's descent to Hades, where `Ishtar is conversely the daughter of the god Sin.
The simplest form of wave, so far as our sensation goes - that is, the one giving rise to a pure tone - is, we have every reason to suppose, one in which the displacement is represented by a harmonic curve or a curve of sines, y=a sin m(x - e).
If we put this in the form y=a sin (x - e), we see that y=o, for x =e, e +aX, e+2A, e+;X, and so on, that y is + from x=e to x=e+iX, - from e+zX to e+?A, and so on, and that it alternates between the values+a and - a.
If we transfer 0 to A, e=o, and the curve may be represented by y=a sin A x.
If now the curve moves along unchanged in form in the direction ABC with uniform velocity U, the epoch e =OA at any time t will be Ut, so that the value of y may be represented as 2 y=a sin T (x - Ut).
Putting A /M =n 2 the equation becomes x+n 2 x=o, whence x =A sin nt, and the period is 27r/n.
Repre - senting it by -P sin pt, the equation of motion is now 2 -M sin pt=o.
We may represent the displacement due to one of the trains by y l =a sin 2 i (24) where x is measured as in equation (16) from an ascending node as A in fig.
If we measure t from an instant at which the two trains exactly coincide, then as U for the other train has the opposite sign, its displacement is represented by y2= a sin (x+Ut).
But the tension at P is T, parallel to the tangent, and T sin 4 parallel to PM, and through this - T sin is the momentum passing out at P per second.
If then y=a sin (x - Ut),, t=2,ro-ra cos (x - Ut).
If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(n i - n 2)t sin ir(nl-t-n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(n i - n 2)t slowly varying with the time.
Let us suppose that with constant excess of pressure, p, in the wind-chest, the amplitude produced is proportional to the pressure, so that the two tones issuing may be represented by pa sin 27-nit and pb sin 21rn 2 t.
Suppose now that F =a sin 22rn i t+b sin 21rn 2 t, the second term will evidently produce a series of combination tones of periodicities 2n 1, 2772, n, - n2, and n 1 -1-n 2, as in the first method.
But certainly the myth does help us to imagine a story in which, for some sin against the gods, some favoured hero was hurled down from the divine abode, and such a story may some day be discovered.
It is held that, but for his sin, Adam would have been immortal.
Truly, a worthy development of the seed-thoughts of the original narrator, and (must we not add ?) entirely opposed to any doctrine of Original Sin.
One is that Adam is said to have had from the first a wicked heart, owing to which he fell, and his posterity likewise, into sin and guilt.
All men have the same seed of evil in them that Adam had; they sin and die, like him.
The first ended with the Flood, so that any consequences of Adam's sin were, strictly speaking, of limited duration.
On the belief in the Fall, see Tennant, The Sources of the Doctrine of the Fall and Original Sin (1903).
In later times Ate is regarded as the avenger of sin (Sophocles, Antigone, 614, 625).
It refers not to an accusation, but to sin actually committed (after baptism); and it denotes the setting of the sinner free from the guilt of the sin, or from its ecclesiastical penalty (excommunication), or from both.
The Old Testament has no theory of sacrifice; in connexion with sin the sacrifice was popularly regarded as payment of penalty or compensation.
The idea of vicarious atonement appears in the Old Testament in different forms. The nation suffers for the sin of the individual; 8 and the individual for the sin of his kinsfolk 7 or of the nation.
Christ suffering on behalf of sinners satisfies the divine righteousness, which was outraged by their sin.'3 His work is an expression of God's love to man; 14 the redeeming power of Christ's death is also explained by his solidarity with humanity as the second Adam," - the redeemed sinner has " died with Christ."
For instance, it has been held that Christ atoned for man k ind not by enduring the penalty of sin, but by identify views.
Y Y ing Himself with the sinner in perfect sympathy, and feeling for him an " equivalent repentance " for his sin.
At present the belief in an objective atonement is still widely held; whether in the form of penal theories - the old forensic view that the death of Christ atones by paying the penalty of man's sin - or in the form of governmental theories; that the Passion fulfilled a necessity of divine government by expressing and vindicating God's righteousness.
After the fall of Ayuthia a great general, Phaya Takh Sin, collected the remains of the army and restored the fortunes of the kingdom, establishing his capital at Bangkok; but, becoming insane, he was put to death, and was succeeded by another successful general, Phaya Chakkri, who founded the present dynasty.
Meanwhile in the Western Church the subject of sin and grace, and the relation of divine and human activity in salvation, received especial attention; and finally, at the second council of Orange in 529, after both Pelagianism and semi-Pelagianism had been repudiated, a moderate form of Augustinianism was adopted,, involving the theory that every man as a result of the fall is in such a condition that he can take no steps in the direction of salvation until he has been renewed by the divine grace given in baptism, and that he cannot continue in the good thus begun except by the constant assistance of that grace, which is mediated only by the Catholic Church.
Since the landed proprietors disposed of churches and convents, and the kings of bishoprics and abbeys, it became possible for them too to commit the sin of simony; hence a final expansion, in the iith century, of the meaning of the term.
It was answered that sin had not totally destroyed man's ethical nature, and that grace changed what was morally insensitive into what was morally sensitive, so that there could be a cooperation between God's grace and man's will.
For some purposes it is preferable to retain the circular measure, i radians, as being undistinguishable from sin i and tan i when i is small as in direct fire.
In this table (93) sin 20=Ca, where a is a function tabulated for the two arguments, V the initial velocity, and R/C the reduced range in yards.
The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of expressions, however complicated - nay, the more complicated they were the more he seemed to revel in them - provided they did not sin against the ruling spirit of all his work - symmetry.
Jeremiah was keenly conscious of his people's sin; and the aim of most of his earlier prophecies is to bring his countrymen, if possible, to a better mind, in the hope that thereby the doom which he sees impending may be averted - an end which eventually he saw clearly to be unattainable.
The dominant theory at the time when Job was written was that all suffering was a punishment of sin; and the aim of the book is to controvert this theory.
As a presumptive ruler of England she was, like Cecil, and for that matter the future archbishop Parker also, too shrewd to commit herself to passive or active resistance to the law; and they merely anticipated Hobbes in holding that the individual committed no sin in subordinating his conscience to the will of the state, for the responsibility for the law was not his but the state's.
To the mass these signs are unintelligible, because they deem it impossible that Yahweh should utterly cast off His chosen nation; but to those who know His absolute righteousness, and confront it with the people's sin, the impending approach of the Assyrian can have only one meaning and can point to only one issue, viz.
The author of the Otbaxr7 goes so far as to assert that whoever does this is guilty of the sin against the Holy Ghost.
By means of ascetic observances the man becomes once more a spiritual and enduring being, free from all sin.
The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.
It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.
Under these heads it discusses respectively the sin and misery of men, the redemption wrought by Christ (here are included the Creed and the Sacraments), and the grateful service of the new life (the Decalogue).
The last book of the Laws of Manu deals with karmaplialam, " the fruit of karma," and gives many curious details of the way in which sin is punished and merit rewarded.
From this it is clear that only in doubtful cases concerning sin should an inferior try to submit his judgment to that of his superior,to be not only one who would not order what is clearly sinful, but also a competent judge who knows and unds, better than the inferior, the nature and aspect of the command.
Alexander condemned in 1690 the doctrines of so-called philosophic sin, taught in the Jesuit schools.
The bread and wine are indeed an offering to God of what is his own, pure because offered in purity of heart; but they are not interpreted of the sacrifice of Jesus' body broken on the cross, or of his blood shed for the remission of sin.
And this food is called by us Eucharistia, and of it none may partake save those who believe our teachings to be true and have been washed in the bath which is for remission of sin and rebirth, and who so live as We should probably omit the words bracketed.
In these centuries baptism was the rite for the remission of sin, not the Eucharist; it is the prophet in the Didache who presides at the Lord's Supper, not the Levitically conceived priest; nor as yet has the Table become an Altar.
This reconstruction of its meaning seems to have been the peculiar revelation of the Lord to Paul, who viewed Christ's crucifixion and death as an atoning sacrifice, liberating by its grace mankind from bonds of sin which the law, far from snapping, only made more sensible and grievous.
The first man, Adam, was engendered by Satan in conjunction with "sin," "cupidity," "desire."
Instead of the subtle Catholic theories concerning divine predestination and human freedom, and instead of a difficult theodicaea, it offered an exceedingly simple conception of sin and goodness.
As a thinker he was not original, and even as a theologian he has produced but few schemes of doctrine, except his doctrine of sin.
A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants.
Glancing over its pages, however, it seemed to him a sin that a book so holy - and so saleable - should be destroyed.
Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.
In its most simple and attractive form - one at the same time invested with the authority of the reputed holy author - their account of the creation of the world and of man; the origin of sin and redemption, the history of the Cross, and the disputes between body and soul, right and wrong, heaven and hell, were embodied either in "Historiated Bibles" (Paleya 1) or in special dialogues held between Christ and his disciples, or between renowned Fathers of the Church who expounded these views in a simple manner adapted to the understanding of the people (Lucidaria).
The importance of IIarran was doubtless due not only to its fame as a seat of the Moon-god Sin, honoured also west of the Euphrates, and to its political position, but also to its trade relations.
Before long, however, the overthrow of Astyages by Cyrus cleared Mesopotamia, and Nabonidus (Nabu-naid) was able, drawing on the resources of the whole of Syria for the purpose, to restore the famous temple of Sin at Harran, where a few years later he erected in memory of his mother, who seems to have been a priestess there, the stele published in 1907 by Pognon.
It was a medicine of sin that could only be used once and not a second time.
Occasionally we know what the name was; the Baal of Tyre was Melqarth (Melkarth), which again means merely " king of the city "; similarly among the Aramaeans the Ba'al of Harran was the moon-god Sin.
His writings are described by Harnack as a curious mixture of Catholic orthodoxy and unconscious tendencies to Protestantism; their most noticeable point is the great importance they attach to the fact of sin, both original and actual.
Following Parmenides, Philolaus regarded the soul as a "mixture and harmony" of the bodily parts; he also assumed a substantial soul, whose existence in the body is an exile on account of sin.
The prophets had an ethical conception of Yahweh; the sin of His own people and of other nations called for His intervention in judgment as the moral ruler of the world.
Julian of Indiana, were nominated for the presidency and the vice-presidency respectively, on a platform which declared slavery "a sin against God and a crime against man," denounced the Compromise Measures of 1850,1850, the fugitive slave law in particular, and again opposed the extension of slavery in the Territories.
On some other points, as the nature of matter, the immortality of the soul and the principle of sin, his views are interesting.
Mysticism may broadly be described as the effort to give effect to the craving for a union of the soul with the Deity already in this life; and asceticism as the effort to give effect to the hankering after an ever-progressive purification of the soul and an atoning for sin by renunciation and self-denial in things lawful.
I); "He hath not given any man licence to sin" (xv.
To illustrate the main features of the calculation, we may suppose that the surface is subject to a simple-harmonic cycle of temperature variation, so that the temperature at any time t is given by an equation of the form 0 - 0 0 = Asin 27rnt= A sin 27rt/T, (5) where 0 0 is the mean temperature of the surface, A the amplitude of the cycle, n the frequency, and T the period.
The wave at a depth x is represented analytically by the equation 0 - 0 0 = Ae mx sin (21rnt - mx).
We thus obtain the differential equation gk(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.
Such an inference is, however, clearly at variance with the whole doctrine of sin, repentance and the atonement, as also with that of eternal reward and punishment, which postulates a real measure of human responsibility.
For in fixity and resoluteness of character he likened himself to God; and having kept himself free from sin was united with God, and was empowered to grasp as it were the power and authority of wonders.
He delivered the second series of the Croall lectures, on the Doctrine of Sin, which were afterwards published.
The word is also used for a man's evil genius, which drives him to sin without any provocation; a man so driven is sometimes called Alastor.
The process of human development Rothe regards as necessarily taking an abnormal form and passing through the phase of sin.
In consequence of His supernatural birth the Saviour, or the second Adam, was free from original sin.
Imprisoned in the garment of flesh, burdened with its sin, souls long to be clothed upon with the habitations they left in heaven.
The consolamentum removes original sin, undoes the sad effects of the primal fall, clothes upon us our habitation which is from heaven, restores to us the lost tunic of immortality.
In historic times the chisels are about I X3/4, X6 to Sin, long (34).
Abu Angar entered Abyssinia and, in August 1887, attacked Ras Adal in the plain of Debra Sin and, after a prolonged battle, defeated the Abyssinians, captured their camp, and marched on Gondar, the ancient capital of Abyssinia, which he sacked, and then returned into Gallabat.
In its present form, however, it can hardly be original, but must have been revised in accordance with the later Deuteronomic conception which represented the sin committed by the people as a breach of the 2nd commandment.
Ba11, 3 Lamech is an adaptation of the Babylonian Lamga, a title of Sin the moon god, and synonymous with Ubara in the name Ubara-Tutu, the Otiartes of Berossus, who is the ninth of the ten primitive Babylonian kings, and the father of the hero of the Babylonian flood story, just as Lamech is the ninth patriarch, and the father of Noah.
Some sects calling themselves Spirituales or Perfecti also held that the baptized cannot sin, a very ancient tenet.
It is quite in accordance with the keener consciousness of sin, which prevailed in the middle ages, that the expiatory pilgrimage took its place side by side with the pilgrimage to the glory of God.
It was the site of a famous temple, E-Nannar, "house of Nannar," and the chief seat in Babylonia of the worship of the moon-god, Nannar, later known as Sin.
It is worthy of notice that Haran, in upper Mesopotamia, which also was a home of Abraham, was likewise a famous site of worship of the god Sin, and that the name of that god also appears in Mount Sinai, which was historically connected with the origin of the Hebrew nation and religion.
Indeed, the other gods, Sin, Shamash (Samas), Adad, Ninib and Nergal, and even Ea, take on the warlike traits of Assur in the epithets and descriptions given of them in the annals and votive inscriptions of Assyrian rulers to such an extent as to make them appear like little Assurs by the side of the great one.
Besides the chief temple, the capital contained temples and chapels to Anu, Adad, Ishtar, Marduk, Gula, Sin, Shamash, so that we are to assume the existence of a sacred precinct in Assur precisely as in the religious centres of the south.
Then followed the tremendous warning, that to assign His work to Satan, and so to call good evil, was to blaspheme against the Holy Spirit - the one sin which admitted of no forgiveness.
Martin Luther and thousands of children like him were trained at home to know the creed, the ten commandments, the Lord's prayer, and such simple hymns as Ein Kindelein so lobelich, Nun bitten wir den Heiligen Geist and Crist ist erstanden; and they were taught to believe that God for Christ's sake freely pardons sin.
His theological studies, part of the convent education, told him that pardon could be had through the Sacrament of Penance, and that the first part of the sacrament was sorrow for sin.
In the earliest church life, when Christians fell into sin, they were required to make public confession before the congregation, to declare their sorrow, and to vow to perform certain acts which were regarded as evidence of the sincerity of their repentance.
But the common people did not discriminate, and believed that when they bought an Indulgence they were purchasing pardon from sin; and Luther placed himself in the position of the ordinary Christian uninstructed in the niceties of theological distinctions.
It cannot remit the divine punishment for sin; that also is in the hands of God alone.
According to the original commandment of God, marriage is between one man and one woman, and this original precept has been confirmed by our Lord; but sin brought it about that first Lamech, then the heathen, and then Abraham, took more than one wife, and this was permitted under the law.
Old-fashioned Parsis in country districts still follow these customs. To uncover the head is looked upon as a sin; hence Parsis of both sexes always wear some head covering whether indoors or out.
Associated with Marduk was his consort Sarpanit, and grouped around the pair as princes around a throne were the chief deities of the older centres, like Ea and Damkina of Eridu, Nebo and Tashmit of Borsippa, Nergal and Allatu of Kutha, Shamash and A of Sippar, Sin and Ningal of Ur, as well as pairs like Ramman (or Adad) and Shala whose central seat is unknown to us.
By the side of the first triad, consisting of Anu, Bel and Ea - disconnected in this form entirely from all local associations - we encounter a second triad composed of Shamash, Sin and Ishtar.
The personification of the two great luminaries - the sun and the moon - was the first step in the unfolding of this system, and this was followed by placing the other deities where Shamash and Sin had their seats.
If man is thought of as under the authority of God, any transgression of or want of conformity to the law of God is defined as sin.
Crime is a legal, vice a moral, and sin a religious term.
Sin is a term applied not only to actions, but also to dispositions and motives.
In the theological phrase original sin it means the inherited tendency to do wrong.
Pelagius insisted that sin was an act, not a state, an abuse of the freedom of the will, and that each man was responsible and liable to punishment only for his own acts.
To this Augustine opposed the view that Adam's sin is, as its penalty, transmitted to all his descendants, both as guilt and as weakness.
The essence and mode of operation of original sin is concupiscence, which, as of the devil, subjects man in his natural state to the devil's dominion.
Sin is a necessity in each individual, and there is a total corruption of man's nature, physically as well as morally.
As regards original sin they taught that the inclinations to evil inherited from Adam are not themselves blameworthy, and only consent to them involves real guilt.
It is not just, however, to Arminianism to identify it with Pelagianism, as it does strive to make clear man's need of divine grace to overcome sin and reach holiness.
Only after the introduction of sin did man lose his spiritual body, and acquire the animal nature with its distinction of sex.
Naturally sin is a necessary preliminary to this redemption, and Erigena has the greatest difficulty in accounting for the fact of sin.
If God is true being, then sin can have no substantive existence; it cannot be said that God knows of sin, for to God knowing and being are one.
In the universe of things, as a universe, there can be no sin; there must be perfect harmony.
Sin, in fact, results from the will of the individual who falsely represents something as good which is not so.
At an annual spiritual examination of the members, there are mutual criticisms and public confessions of sin.
From the new point of view we see at once, as it were, why it is true that (cos 0+ i sin 0) m =cos me+ i sin me.
We may state, in passing, that every quaternion can be represented as a (cos 0+ 7 sin 9), - where a is a real number, 6 a real angle, and it a directed unit line whose square is - 1.
Also, if 0 be the angle between them, and x", y", z" the direction-cosines of a line perpendicular to each of them, we have xx' +yy'+zz' =cos 0, yz' - zy" = x" sin 0, &c., so that the product of two unit lines is now expressed as - cos0+ (ix" +jy" +kz") sin 0.
In Sweden, even in the 16th century, such snakes were virtually household gods and to hurt them was a deadly sin.
Hence he attains salvation, being delivered from sin and fear and death, for the divine attributes are not ontological entities to be discussed and defined in the schools, but they are realities, entering into the practical daily life.
Even the most repulsive forms of disease and sin drew from him only loving aid, while he recognized in all other men who laboured for the welfare of their fellows the most intimate relationship to himself.
By him they felt themselves freed from sin and fear - and under the influence of a divine power.
He had gained control of man by man's sin, and Christ set man free.
Primitive man seldom connects sacrifice with notions of propitiation, indeed only in highly ethicized religions is the consciousness of sin or of guilt pre-eminent.
Participation in the mass also releases from guilt, as the Lamb of God offered up atones for sin and intercedes with the Father in our behalf.
If we write C cos =H,C sin =K, (17)
Since by the universally accepted doctrine of karman (deed) or karmavipaka (" the maturing of deeds") man himself - either in his present, or some future, existence - enjoys the fruit of, or has to atone for, his former good and bad actions, there could hardly be room in Hindu pantheism for a belief in the remission of sin by divine grace or vicarious substitution.
The banks of the great rivers such as the Ganga (Ganges), the Yamuna (Jumna), the Narbada, the Krishna (Kistna), are studded with them, and the water of these rivers is supposed to be imbued with the essence of sanctity capable of cleansing the pious bather of all sin and moral taint.
To escape from these preoccupations and prejudices except upon the path of conscious and deliberate sin was impossible for all but minds of rarest quality and courage; and these were too often reduced to the recantation of their supposed errors no less by some secret clinging sense of guilt than by the church's iron hand.
All his poetry was on sacred themes, and its unvarying aim was to turn men from sin to righteousness and the love of God.
Alvarez Pelayo, a Spanish bishop and papal penitentiary, wrote in 1332, "The clergy sin commonly in these following ways.
His views on the subject of original sin, akin a it is to that of justification, were accepted and embodied in the decree.
On the one hand, since that which is tabooed is held to punish the taboo-breaker by a sort of mystic infection, taboo comes to stand for uncleanness and sin.
No one ever thought of confessing sin, for instance, to a river.
That baptism or washing with water is the outward manifestation of dying unto sin and walking in newness of life; and therefore in no wise appertaineth to infants."
Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.
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 .
In order to obtain beatitude for her adoptive father, she resolved to become a river whose waters should purify from all sin.
He liked books and quiet corners all his days, he says; and so, when conviction of sin and visions of God's grace came to him in the medieval fashion of a dream of the anger and forgiveness of the Virgin, Florentius told him that a monk's life would suit him best, advised him to join the Augustinian order, and sent him to Zwolle to the new convent of Mount St Agnes, where his brother John was prior.
To these conflicting tendencies were probably due his self-contradictions on the problem of original sin and the conflicting claims of feeling and reason.
In these Orestes is the guilt-laden mortal who is purified from his sin by the grace of the gods, whose merciful justice is shown to all persons whose crime is mitigated by extenuating circumstances.
The claim that Apollo can in every case purify from sin is met by Athens with a counterclaim on behalf of the state.
Resolving vertically we find that the weight of the liquid raised above the level must be equal to T(sin 0 2 - sin 01), and this is therefore equal to the area P 1 P 2 A 2 A 1 multiplied by gp. The form of the capillary surface is identical with that of the " elastic curve," or the curve formed by a uniform spring originally straight, when its ends are acted on by equal and T 2 opposite forces applied either to the ends themselves or to solid pieces attached to them.
If d is the distance between the plates at the edge of the film and II the atmospheric pressure, the pressure 2T of the liquid in the film is II - d cos a, and if A is the area of the film between the plates and B its circumference, the plates will be pressed together with a force 2AT cos a +BT sin a, and this, whether the atmosphere exerts any pressure or not.
Hence dividing equation io by y sin a, we find p= T(I/R1+I /R2) (14).
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.
One form of the solution of the equation, and that which is applicable to the case of a rectangular orifice, is z =C sin px sin qy.
If the wave-length is X, the equation of the surface is y=b sin 2lrxx The pressure due to the surface tension T is p= - Td 2 = 4Ty.
His crowning sin (recorded by the poet alone) was the destruction of the Sibylline books - a sin worthy of one who had decked his wife in the spoils of Victory, the goddess who had for centuries presided over the deliberations of the senate.
His system was simplicity itself, all sin being reduced to the one form of lying.
The older school had taught that Gotama, who had propounded the doctrine of Arahatship, was a Buddha, that only a Buddha is capable of discovering that doctrine, and that a Buddha is a man who by self-denying efforts, continued through many hundreds of different births, has acquired the so-called Ten Paramitas or cardinal virtues in such perfection that he is able, when sin and ignorance have gained the upper hand throughout the world, to save the human race from impending ruin.
The belief in them probably arose out of the doctrine of the older school, which did not deny the existence of the various creations of previous mythology and speculation, but allowed of their actual existence as spiritual beings, and only deprived them of all power over the lives of men, and declared them to be temporary beings liable, like men, to sin and ignorance, and requiring, like men, the salvation of Arahatship. Among them the later Buddhists seem to have placed their numerous Bodhisats; and to have paid especial reverence to Manju-sri as the personification of wisdom, and to Avalokiteswara as the personification of overruling love.
It may be shown that if the distance of the carried point from the centre of the rolling circle be mb, the equation to the epitrochoid is x = (a+b) cos 0 - mb cos (a+b/b)0, y = (a +b) sin 9 - mb sin (a +b/b)0.
Therefore any epicycloid or hypocycloid may be represented by the equations p = A sin B+,' or p---A cos B,,G, s = A sin B11.
He is constantly admitting that on such and such an occasion he was terribly afraid; he confesses without the least shame that, when one of his followers suggested defiance of the Saracens and voluntary death, he (Joinville) paid not the least attention to him; nor does he attempt to gloss in any way his refusal to accompany St Louis on his unlucky second crusade, or his invincible conviction that it was better to be in mortal sin than to have the leprosy, or his decided preference for wine as little watered as might be, or any other weakness.
But the supersession of the law, which was bound up with the regime of sin and death, does not mean the relaxation of the moral bond.
It was said that he was so virtuous as hardly to have committed a venial sin.
Through the first sin Adam and his posterity lost Immortality, And His Will Received A Bias Towards Evil.
In this natural state man, who even before he actually sins is a sinner before God by original or inherited sin, commits manifold actual transgressions; but he is not absolutely without power of will towards good, and is not always doing evil.
He may fall from a state of grace through mortal sin.
The new birth when lost may be restored through repentance, which is not merely (I) sincere sorrow, but also (2) confession of each individual sin to the priest, and (3) the discharge of penances imposed by the priest for the removal of the temporal punishment which may have been imposed by God and the Church.
Ecclesiastical ceremonies are part of the divine service; most of them have apostolic origin; and those connected with the sacrament must not be omitted by priests under pain of mortal sin.
Grace, by enlightening, forgiving sin and strengthening his moral powers, helps man to fulfil this purpose.
The "reprobation" of the wicked is not the cause of their sin; God's foreknowledge does not make the sin necessary; how reprobation and foreknowledge are related is not made plain.
He denied that foreknowledge or predestination as temporal relations could be properly predicated of God as eternal; he described sin and its consequences as negations, neither caused by nor known to God; he maintained that as evil is only a stage in the development of good, there will ultimately be a universal return to God.
When measured R from the vertex the results may be expressed in the forms s= 4a sin 20 and s = (8ay); the total length of the curve is 8a.
The intrinsic P equation is s =4a sin 4,, and the equation to the evolute is s= 4a cos 1P, which proves the evolute to be a similar cycloid placed as in fig.
The cartesian equation in terms similar to those used above is x = a6+b sin 0; y=a-b cos 0, where a is the radius of the generating circle and b the distance of the carried point from the centre of the circle.
The cartesian equation, referred to the fixed diameter and the tangent at B as axes may be expressed in the forms x= a6, y=a(I -cos 0) and y-a=a sin (x/afir); the latter form shows that the locus is the harmonic curve.
The Doctrine of the Mean, by his grandson Tze-sze, and The Great Learning, by Tsang Sin, the most profound, perhaps, of his disciples, give us the fullest information on that subject, and contain many of his sayings.
A contemporary account of it says that in spite of Edwards's academic style of preaching, the assembly was " deeply impressed and bowed down, with an awful conviction of their sin and danger.
Emmons, like Hopkins, considered both sin and holiness " exercises " of the will.
Timothy Dwight (1752-1847) urged the use of the means of grace, thought Hopkins and Emmons pantheistic, and boldly disagreed with their theory of " exercises," reckoning virtue and sin as the result of moral choice or disposition, a position that was also upheld by Asa Burton (1752-1836), who thought that on regeneration the disposition of man got a new relish or " taste."
They accordingly rejected the form of marriage, which, they said, would never have existed but for sin, and lived in absolute lawlessness, holding that, whatever they did, their actions could be neither good nor bad.
To give up dancing on the village green was still harder; and some months elapsed before he had the fortitude to part with his darling sin.
He began to be haunted by a strange curiosity about the unpardonable sin, and by a morbid longing to commit it.
He would have thought it a sin to borrow any time from the serious business of his life, from his expositions, ' His formal pardon is dated the 13th of September 1672; but five months earlier he had received a royal licence to preach, and acted for the next three years as pastor of the nonconformist body to which he belonged, in a barn on the site of which stands the present Bunyan Meeting.
Further, he is able to purify the guilty and to cleanse from sin (here some refer the epithet iarpOyavres, in the sense of "physician of the soul").
By them the pilgrim becomes as pure from sin as when he was born, and gains for the rest of his life the honourable title of bajj.
As a result of this theory, in the case of a retaining wall supporting a vertical face of earth beneath an extended horizontal plane level with the top of the wall, we get p _ wx 2 1 - sin ii 2 I +sin P' [[Reservoir Empty Reservoir Full Ellipses Of Vertical Pressures On Horizontal Joints]].
That the pressure so given exceeds the maximum possible pressure we do not doubt; and, conversely, if we_put wx 2 I +sin 2 .I - sin ¢' we may have equal confidence that will be less than the maximum pressure which, if exerted by the wall against the earth, will be borne without disturbance.
In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by solving the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a.
The value of a is in general small, and an approximate solution may be obtained by substituting two or three terms of the expansions for sin a and cos a.
F B is the evolute of this circle, and for any radius DE at an angle a and corresponding tangent EG terminated by the evolute, the perpendicular distance of G from the line AD is c(cos a+a sin a).
If now a line be drawn from A to the bisector H of the side BC, it will meet the vertical through G in I and IJ =c(cos a+a sin a)/ur.
A circular arc, centre D and radius c/2, meets D E in K, and the perpendicular KL gives 2c sin a.
He dwells on the risk run by the sponsors, in case the candidates for whose purity they went bail should fall into sin.
Augustine's insistence on original sin, a doctrine never quite accepted in his sense in the East, hurried on the change.
Sin after baptism excluded the sinner afresh from the divine grace and from the sacraments.
As has been remarked above, the terror of postbaptismal sin and the fact that only one restoration was allowable influenced many as late as the 4th century to remain catechumens all their lives, and, like Constantine, to receive baptism on the deathbed alone.
The idea of transferring sin into another man or into an animal, and so getting it purged through him or it, was widespread in the age of Paul and long afterwards.
Baptism conveys the forgiveness of sins, and therefore ought to result in freedom from all wilful sin.
But what was to be done with the baptized Christian who fell into grievous sin?
Though nothing was as yet systematized, the governing principle is laid down that the sin of the member affects the whole body, and therefore the society is bound to deal with it both from pity for the sinner, and for the sake of its own purity.
Three groups of sins, classified as (I) idolatry, which included apostasy, (2) adultery or fornication, and (3) murder, were held to exclude the guilty person from sharing in the eucharist until death, that is to say, if he had committed the sin after baptism.
This went on for a time proportionate to the gravity of the offence, perhaps for years; then, if his sin allowed it, he was readmitted by the bishop and clergy with further laying on of hands.
Thus in the chapterhouse of a monastery there constantly took place acts of discipline that depended on the theory that the sin of the individual is the concern of the society; open confession was made, open penance exacted.
The penance was regarded (not without precedent in earlier times) as the discharge of a liability due to God or the Church; and so much sin was reckoned to involve so much debt.
Penitentials or codes defined (even invented) different degrees of guilt, and assessed the liability involved much as if a sin gave rise to an action to recover damages.
No one is allowed to receive holy communion, if guilty of "mortal" sin, without resorting to confession; only if a priest has to celebrate mass, and there is no other priest to hear his confession, may he receive "unabsolved" after mortal sin.
It is common to go to confession, even though there are only venial sins to be confessed; and in order to excite contrition people are sometimes advised to confess over again some mortal sin from which they have been previously absolved.
On the other hand, there are those who speak as if auricular confession were a necessary element in every Christian life, and hold that post-baptismal sin of a grave sort can receive forgiveness in no other way.
Even the earliest name Nigantha, which means "free from bonds," may not be without allusions to this curious belief in the sanctity of nakedness, though it also alluded to freedom from the bonds of sin and of transmigration.
He now maintained not only that it was a sin that kings should invest prelates with their spiritual insignia, the pallium, the staff, the ring, but claimed that no clerk ought to do homage to the king for the lands of his benefice, though he himself seven years before had not scrupled to make his oath to his earlier master.
His private life was grave and seemly, his court did not sin by luxury or extravagance.
The tendency to increased rigour may be discerned in the 2nd canon of the synod of Orleans (541), which declares that every Christian is bound to observe the fast of Lent, and, in case of failure to do so, is to be punished according to the laws of the church by his spiritual superior; in the 9th canon of the synod of Toledo (653), which declares the eating of flesh during Lent to be a mortal sin; in Charlemagne's law for the newly conquered Saxony, which attaches the penalty of death to wanton disregard of the holy season.'
It is extremely questionable, in particular, whether fasting be so efficient as it is sometimes supposed to be in protecting against temptation to fleshly sin.
On the 1st of May 418 a great synod ("A Council of Africa," St Augustine calls it), which assembled under the presidency of Aurelius, bishop of Carthage, to take action concerning the errors of Caelestius, a disciple of Pelagius, denounced the Pelagian doctrines of human nature, original sin, grace and perfectibility, and fully approved the contraryviews of Augustine.
They are taken as involved in redemption from sin - in the Atonement, or in the sacraments.
Whatever be the truth in the assertion that death rather than sin is the enemy dreaded by Eastern Christianity, and immortality rather than forgiveness the blessing craved, it is difficult to take the talk about deification as anything more than rhetoric. Did they not start from belief in one God ?
If early " enthusiasm " conceived the Christian as almost entirely free from acts of sin, and if Protestant Paulinism conceives the child of God as justified by faith once for all, the full Catholic theory, representing one development of Augustinianism, views the Christian as an invalid, perpetually dependent on the good offices of the Church.
If we are warranted in regarding the Second Person of the Godhead as in very deed " Himself vouchsafing to be made, " that great Becoming cannot well be suspended upon a contingency which might or might not arise; and theologians in general regard the sin of man as such a contingent event.
Those who shrink from the old confident assertion, " Christ would not have become incarnate but for man's sin," might claim to say, from reverence and not from evasiveness, ignoramus.
Under John and Charles Wesley, a system known as Evangelical Arminianism was worked out in 18th-century England, strongly Augustinian in its doctrines of sin and atonement, modern Augustinian in its doctrine of conversion, strongly anti-Augustinian in its rejection of absolute predestination.
Again Ritschl modifies the doctrine of sin.
Like Schleiermacher he substitutes collective guilt for original sin; and he attaches great dogmatic value to the assertion that sin has two stages - ignorance, in which it is pardonable, and obduracy, when it is ripe for final sentence (probably annihilation).
Horace Bushnell's last theory declared that in forgiving sin God " bore cost," as even a good man must do.
Again, Western theology, very roughly summarized, while accepting the earlier doctrinal tradition, has broken new ground for itself, in affirming as rational necessity that God must punish sin (this is at least latent in Aquinas's - doctrine of natural law), but as contingent fact of revelation that God has in Christ combined the punishment of sin with the salvation of sinners; this is the Reformation or postReformation thought.
Even if He should still be taken as the prophet of the divine goodwill, yet the loss of any serious estimate of sin makes good nature on God's part a matter of course.
A centre of his cult in Assyria was in Harran, where, because of the predominating character of the moon-cult, he is viewed as the son of the moongod Sin.
If so, parliament was told that temporal possessions ruin the church and drive out the Christian graces of faith, hope and charity; that the priesthood of the church in communion with Rome was not the priesthood Christ gave to his apostles; that the monk's vow of celibacy had for its consequence unnatural lust, and should not be imposed; that transubstantiation was a feigned miracle, and led people to idolatry; that prayers made over wine, bread, water, oil, salt, wax, incense, altars of stone, church walls, vestments, mitres, crosses, staves, were magical and should not be allowed; that kings should possess the jus episcopale, and bring good government into the church; that no special prayers should be made for the dead; that auricular confession made to the clergy, and declared to be necessary for salvation, was the root of clerical arrogance and the cause of indulgences and other abuses in pardoning sin; that all wars were against the principles of the New Testament, and were but murdering and plundering the poor to win glory for kings; that the vows of chastity laid upon nuns led to child murder; that many of the trades practised in the commonwealth, such as those of goldsmiths and armourers, were unnecessary and led to luxury and waste.
Under the pretext that a true believer could commit no sin, the Amalricians indulged in every excess, and the sect does not appear to have long survived the death of its founder.
Whatever was not of knowledge was of sin; and the distinction between right and wrong being absolute and not admitting of degrees all sins were equally sinful; whoever broke the least commandment was guilty of the whole law.
Without this grace it is impossible for man to obey the " first greatest commandment " of love to God; and, this unfulfilled, he is guilty of the whole law, and is only free to choose between degrees of sin; his apparent external virtues have no moral value, since inner rightness of intention is wanting.
For example, we find him arguing for the legitimacy of judicial punishments and military service against an over-literal interpretation of the Sermon on the Mount; and he took an important part in giving currency to the distinction between evangelical " counsels " and " commands," and so defending the life of marriage and temperate enjoyment of natural good against the attacks of the more extravagant advocate of celibacy and self-abnegation; although he fully admitted the superiority of the latter method of avoiding the contamination of sin.
Passing on to Anselrn (1033-1109), we observe that the Augustinian doctrine of original sin and man's absolute need of unmerited grace is retained in his theory of salvation; he also follows Augustine in defining freedom as the " power not to sin "; though in saying that Adam fell " spontaneously " and " by his free choice," though not " through its freedom," he has implicitly made the distinction that Peter the Lombard afterwards expressly draws between the freedom that is opposed to necessity and freedom from the slavery to sin.