Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;

Then, in terms of P < sub > n </ sub >( x ), the remainder

Then all the terms in the asymptotic series can be expressed in terms of elementary functions.

Then to define multiplication, it suffices by the distributive law to describe the product of any two such terms, which is given by the rule

Then each production department met to determine what each episode needed in terms of costumes, lights, and sets.

Then he heads the embassy that negotiates the terms of capitulation to the Spartans.

Then the unit prices could be grouped in terms of the product type, say " clothing " and " food ".

Then he desperately needed new taxes, so Charles I called a Parliament again and it would only help him if he agreed to some terms, which ultimately made Charles I a constitutional monarch.

Then looking for the expansion of the integrand into two terms

Then he reduced the chief propositions of the Mutakallamin, to prove the unity of God, to ten in number, describing them at length, and concluding in these terms: " Does the Kalam give us more information concerning God and His attributes than the prophet did?

Then he reduced the chief propositions of the Mutakallamin, to prove the unity of God, to ten in number, describing them at length, and concluding in these terms: " Does the Kalam give us more information concerning God and His attributes than the prophet did?

Then came Napoleon's contemptuous violation of Prussian territory by marching three French corps through Ansbach ; King Frederick William's pride overcame his weakness, and on November 3 he signed with Tsar Alexander I of Russia the terms of an ultimatum to be laid before the French emperor.

Then the quotient sheaf consists of equivalence classes of functions which vanish on the diagonal modulo higher order terms.

Then the problem might be to rank these alternatives in terms of how attractive they are to the decision maker ( s ) when all the criteria are considered simultaneously.

Then the two terms which contain time derivatives can be combined into a single term.

:" Then you shall hear my reas ' nable terms ,"

Then express it in lowest possible terms ( i. e., as a fully reduced fraction ) as < sup > m </ sup >⁄< sub > n </ sub > for natural numbers m and n, and let q be the largest integer no greater than √ k.

Then the intersection number of two closed curves on X has a simple definition in terms of an integral.

Then divide the sequence into an initial segment, and a tail of small terms: given any ε > 0 we can take M large enough to make the initial segment of terms up to c < sub > N </ sub > average to at most ε / 2, while each term in the tail is bounded by ε / 2 so that the average is also.

Then on 6 November 2008 Freightlink went into voluntary administration after failing to reach agreement with creditors on the terms of a sale of the business.

Then continue the sequence, where each subsequent term is the sum of the previous n terms.

Then he or she states the Omer-count in terms of both total days and weeks and days.

Then, all but blind, he said there was nothing in Back to Methuselah --, -- `` G.B.S. ought to have known that '', -- and `` I look at my bookshelves despairingly, knowing that I can have nothing more to do with them ''.

Then you can do the finishing touches at your leisure.

Then during washing, the greasy soil rolls back at the edges so that emulsified droplets can disengage themselves from the sorbed oil mass, with the aid of mechanical action, and enter the aqueous phase.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

Then the enthusiasm and energy of all elements can be channeled to produce cumulative progress toward a common objective.

Then, after I'm back, another fifty so you can put some mileage on yourself and have a solid alibi somewhere while I take care of your seat cover boy ''.

Then, with the hymn writer of old, you can say:

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

Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.

Then the momentum equation can be expressed as

Then the mass balance equation can be written as

Then the mass balance equation can be expressed as

Then one can rewrite the field in the form

Then nodules of blue earth have to be removed and an opaque crust must be cleaned off, which can be done in revolving barrels containing sand and water.

Then, in 1828, Friedrich Wöhler published a paper on the synthesis of urea, proving that organic compounds can be created artificially.

Then the bra can be computed by normal matrix multiplication.

Then the reservists have to serve up to three weeks a year and can be called up to serve two weeks during a non-military crisis.

Then we can solve for f ′.

Then it can be shown that one can write a thermodynamic version of the above calorimetric rules:

Then, according to Adkins ( 1975 ), it can be shown that one can write a further thermodynamic version of the above calorimetric rules:

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 each point p of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains p.

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 >.