Then he went to hear a Pythagorean philosopher, who demanded that he first learn music, astronomy and geometry, which he did not wish to do.

Then on Oct 23, 1972, Balliett's student, Dr. Juno Jordan, changed Numerology further and helped it to become the system known today under the title " Pythagorean ", although Pythagoras himself had nothing to do with the system.

Then m, a, and b form a Pythagorean triple.

Then it can be scaled down to give a primitive ( i. e., with no common factors ) Pythagorean triangle with the same property.

Then is a compact topological space ; this follows from the Tychonoff theorem.

Then by Arzelà – Ascoli theorem the space K is compact.

Then Goursat's theorem asserts that ƒ is analytic in an open complex domain Ω if and only if it satisfies the Cauchy – Riemann equation in the domain.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Then according to the second isomorphism theorem S ∩ T is normal in T and ST / S ≅ T /( S ∩ T ).

# Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be proved.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Then Cauchy's theorem can be stated as the integral of a function holomorphic in an open set taken around any cycle in the open set is zero.

Then use the SAS congruence theorem for triangles OPA ' and OPB ' to conclude that angles POA and POB are equal.

Then the group action is by classification of G-orbits ( also known as the orbit-stabilizer theorem ).

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Then Noether's theorem states that the following quantity is conserved,

Then by the theorem, the equation also holds for D, E and F ′.

Then they are independent, but not necessarily identically distributed, and their joint probability distribution is given by the Bapat – Beg theorem.

Then one proves that if the theorem is true for pieces resulting from a cutting of a Haken manifold, that it is true for that Haken manifold.

Then there is a cyclic cubic field inside the cyclotomic field of pth roots of unity, and a normal integral basis of periods for the integers of this field ( an instance of the Hilbert – Speiser theorem ).

Then it is a theorem that

Then, the Riemann-Roch theorem states that

Then the integral in Mercer's theorem reduces to a simple summation

Then the Riemann – Roch theorem states: if g is a genus of X,

Then the theorem states that for analytic functions f, if

Then the Radon – Nikodym theorem provides the function g, equal to the density of μ with respect to Q.

Then v ( p ) is the displacement vector of this projected point relative to p. According to the hairy ball theorem, there is a p such that v ( p )

Then Wilson's theorem says that

Then Little Billy began shouting orders to round up the ponies and fill the water buckets and for the cooks to hurry up with the meal.

Then, helpfully, as she merely stared at him in weary silence, `` Maybe you could write it down for me, huh??

Then they were tumbling again, and the big man reached into the same pocket he had gone for earlier, and came up with a vicious switchblade.

`` Then I return to the United States for engagements at the Hollywood Bowl and in Philadelphia '', he added.

Then Miriam varied the senseless psychological warfare by suddenly withdrawing a suit for separate maintenance that had been pending, and asking for divorce on the grounds of cruelty, with the understanding that Wright would not contest it.

My own stern hand has rent the ancient bond, And thereof shall the ending not have end: But not for me, that loved her, to be fond Lightly to please me with a newer friend Then hold it more than bravest-feathered song, That I affirm to thee, with heart of pride, I knew not what did to a friend belong Till I stood up, true friend, by thy true side ; ;

Then Meltzer's voice, quiet, calm, strong, started the Kaddish, the prayer for the dead.

Then they returned to their hotel and got ready for bed.

Then he kept Blackman awake for more than an hour while he did an imaginary dialogue between his wife and himself in which, discussing the evening, he was continually berated.

Then we have surviving at least one instance of a poem prepared for another, in Naturam non Pati Senium, and perhaps also the De Idea Platonica.

Then followed a period in which he wrote reviews for The New York Times Book Review, The Commonweal, Commentary, had a small piece in Partisan Review, and moved on to Hudson, The Village Voice, and Exodus.

Then a full-time planning office will be established in Rome to work with a five-member Georgia Tech research staff for development of an area planning and industrial development program.

Then Goodbody will hand over a minimum of $15.5 million for developing the spacious Graves Tract to house the center.

Then, to conclude on an indeterminate note: `` Nevertheless, if fallout increased substantially, or remained high for a long time, it would become far more important as a potential health hazard in this country and throughout the world ''.

Then, abandoning the studies in the face of their promising outlook for all concerned, B. & O. entered on-again-off-again negotiations with C. & O. which resulted in the present situation.

Then they were given 1/2 to 1-1/2 avocados per day as a substitute for part of their dietary fat consumption.

Then, after emasculation, he was eased up for a couple of weeks.

Then you'll want terry cloth towels for mopping up.

Then, for the above parasites, feed continuously at these levels: Feeder cattle -- 2-5 grams of phenothiazine daily ; ;

Then, too, European drivers have reputations for being somewhat crazy on the road and some Americans are not particularly keen on getting mixed up with them.

Then, for the first time since his arrest, a glint of spirit lit Barco's eyes.

Then, I remembered that the girls had had a banana for dessert every day for the last week.

Then, having wrapped the lot in an afghan my dog customarily slept on, you lammed out the front door, considerately leaving it open for neighbors to discover.