Then, in the later account found in the Syriac Doctrine of Addai, a painted image of Jesus is mentioned in the story ; and even later, in the account given by Evagrius, the painted image is transformed into an image that miraculously appeared on a towel when Christ pressed the cloth to his wet face.

Then rotate the tangent screw back and forth so that the reflected image passes alternately above and below the direct view.

Then there are three basic constructions in universal algebra: homomorphic image, subalgebra, and product.

Then they were faced briefly with an image of a desperate family in a fallout shelter, which vanished and was replaced by a series of images reflecting the sweep of history, starting with the Acropolis and ending with an image of Marilyn Monroe ( but, again, including a mushroom cloud ).

Then each tile is analysed independently to find the dominant patterns in the part of the image it contains.

Then the degree of mapping is times the solid angle of the image S of with respect to the interior point of, O.

Then, the smaller the image is, the more depth of field is obtained, for the same field of view.

Then a king's royal attendant climbs up and performs the elaborate ritual of changing garments of the image as the king is chanting prayers to the deity.

Then products like Platform Builder ( an integrated environment for Windows CE OS image creation and integration, or customized operating system designs based on CE ) offered several components in source code form to the general public.

Then, using oil paints, the artists would actually use large brushes to paint the image.

Then they pressed a tissue on the clay to create an image of the outlines of the mosaic in the clay.

Even in Genesis 1: 26 " Then God said ( singular verb ), ' Let us make ( plural verb ) man in our image, after our likeness '.

( 2. 2 ), Then, the lens passes-from the object plane over onto the image plane-only that portion of the radiated spherical wave which lies inside the edge angle of the lens.

Then, if a and b are two periods of f such that < sup > a </ sup >⁄< sub > b </ sub > is not real, consider the parallelogram P whose vertices are 0, a, b and a + b. Then the image of f is equal to f ( P ).

Then the rank of T is the dimension of the image of T and the nullity of T is the dimension of the kernel of T, so we have

" Then weighing nearly 300 pounds with short brown hair, Flair scarcely resembled his future " Nature Boy " image.

Then Barlow meets with Abercrombie, who, fearing Barlow's plans to become a non-sectarian funeral pastor will further damage the image of the British enclave, pays his passage back to England.

Then as each eye sees a different image, the effect of depth is achieved in the central image of the three.

Then the closed subscheme determined by the base change is the closed image of X ′.< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 3. 2 .</ ref >

Then, on July 2, there occurred another incident which set tongues to wagging at a furious clip.

Then O'Banion was presented with a platinum watch set with rubies and diamonds.

`` Then maybe it was the shockwave we set up.

Then our choice function can choose the least element of every set under our unusual ordering.

Then, taking in on the first cable as the boat is motored into the wind and letting slack while drifting back, a second anchor is set approximately a half-scope away from the first on a line perpendicular to the wind.

Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies.

Then codenamed " Stella ," the machine was also set to utilize cartridges ; after seeing the Channel F, Atari realized they needed to release it before the market was flooded with cartridge-based machines.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then Asmund set himself to wait the agreed upon three days:

Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then an " estimator " is a function that maps the sample space to a set of sample estimates.

Then, in the grand final against Melbourne, Essendon set a grand final record score of 22. 18 ( 150 ) to Melbourne 13. 9 ( 87 ), with 7 goal centre half forward Gordon Lane.

Then one " flows " the charge by systematically redistributing the charge from a vertex to its neighboring vertices according to a set of rules, the discharging procedure.

is partially ordered by set inclusion, therefore it contains a maximal totally ordered subset P. Then the set satisfies the desired properties.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Then Lothair finally set out with a large Lombard army, but Louis had promised his sons Louis the German and Pepin of Aquitaine greater shares of the inheritance, prompting them to shift loyalties in favour of their father.

Then worship Allah and do not associate anything with Him, perform the Hajj and the ‘ Umrah, be righteous, and all affairs will be set right for you.

Then the null set automatically has measure zero because of countable additivity, because and is finite if and only if the empty set has measure zero.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

Then we can solve for f ′.

Then f = u + iv is complex-differentiable at that point if and only if the partial derivatives of u and v satisfy the Cauchy – Riemann equations ( 1a ) and ( 1b ) at that point.

Let R be a domain and f a Euclidean function on R. Then:

Then the probability density function f *( x ) of the size biased population is

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

For f a real polynomial in x, and for any a in such an algebra define f ( a ) to be the element of the algebra resulting from the obvious substitution of a into f. Then for any two such polynomials f and g, we have that ( fg ) ( a )

Then ( X × Y, ( π < sub > 1 </ sub >, π < sub > 2 </ sub >)) is a terminal morphism from Δ to the object ( X, Y ) of D × D. This is just a restatement of the above since the pair ( f, g ) represents an ( arbitrary ) morphism from Δ ( Z ) to ( X, Y ).

Then because the construction of f was uniform, this is a recursive function of two variables.

For f ∈ R, define D < sub > f </ sub > to be the set of ideals of R not containing f. Then each D < sub > f </ sub > is an open subset of Spec ( R ), and is a basis for the Zariski topology.

Then the sufficient condition for exact reconstructability from samples at a uniform sampling rate f < sub > s </ sub > ( in samples per unit time ) is:

Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good ( x, y ) in the least fuzzy Herbrand model of this program.

Then f is called an immersion if its derivative is everywhere injective.