For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For example Darrell Schweitzer writing to the New York Review of Science Fiction in 1999 quoted a passage from the original van Vogt novelette “ The Mixed Men ”, which he was then reading, and remarked:

Also, supporters of this view would characterize Luke ’ s portrayal of the Roman Empire as positive because they believe Luke “ glosses over negative aspects of the empire and presents imperial power positively .” For example, when Paul is before the council defending himself, Paul says that he is “ on trial concerning the hope of the resurrection of the dead ” ( Acts 23: 6 ).

Many who side with this view disagree that Luke portrays Christianity or the Roman Empire as harmless and thus reject the apologetic view because “ Acts does not present Christians as politically harmless or law abiding for there are a large number of public controversies concerning Christianity, particularly featuring Paul .” For example, to support this view Cassidy references how Paul is accused of going against the Emperor because he is “ saying that there is another king named Jesus .” ( Acts 17: 7 ) Furthermore, there are multiple examples of Paul ’ s preaching causing uprisings in various cities ( Acts 14: 2 ; 14: 19 ; 16: 19-23 ; 17: 5 ; 17: 13-14 ; 19: 28-40 ; 21: 27 ).

For Immanuel Kant the aesthetic experience of beauty is a judgment of a subjective but similar human truth, since all people should agree that “ this rose is beautiful ” if it in fact is.

For this last case, the cohesive fracture can be said to be “ cohesive near the interface ”.

Likewise, Jeremiah ’ s exclamation “ For I hear the whispering of many: Terror is all around !” ( Jer.

In Chapter nine, Job recognizes the chasm that exists between him and God: “ For he is not a man, as I am, that I might answer him, that we should come to trial together .” Job ’ s regret is that he has no arbiter to act as a go-between ; that Job cannot reconcile himself with God anticipates the need for the Messiah to become incarnate.

“ For she said, I will go after my lovers ...” ( Hosea 2: 5 ).

“ For the day of the Lord upon all the nations is near … But on Mount Zion there shall be deliverance ”

For example, the inhabitants of Beth-le-aphrah (“ house of dust ”) are told to “ roll yourselves in the dust .” 1: 14.

For instance, in 1962, Bob Jones, Sr. warned the Greenville City Council that he had “ four hundred votes in his pocket and in any election he would have control over who would be elected .”

For decades, medical personnel and others have fought, and continue to fight, to define the circumstances for which a patient is “ dead ”.

For example, although a patient may be “ brain dead ”, they may still be considered alive because they can still grow and even reproduce.

For an atemporal interpretation that “ makes no attempt to give a ‘ local ’ account on the level of determinate particles ”, the conjugate wavefunction, (" advanced " or time-reversed ) of the relativistic version of the wavefunction, and the so-called " retarded " or time-forward version are both regarded as real and the transactional interpretation results.

For instance, a professor of formal logic called Chin Yueh-lin – who was then regarded as China ’ s leading authority on his subject – was induced to write: “ The new philosophy Marxism-Leninism, being scientific, is the supreme truth ”.

For example, it has been suggested that, in the early 20th century Shanghai, “ Western food, and in particular identifiably nourishing items like milk, became a symbol of a neo-traditional Chinese notion of family .”

Nonetheless, Wilson believed that, in all cases, corporations “ should be erected with caution, and inspected with care .” The actions of corporations were clearly circumscribed: “ To every corporation a name must be assigned ; and by that name alone it can perform legal acts .” For non-binding external actions or transactions, corporations enjoyed the same latitude as private individuals ; but it was with an eye to internal affairs that many saw principal advantage in incorporation.

For example in the mid 350 ’ s the city of Jerusalem was hit with drastic food shortages at which point church historians Sozomen and Theodoret reported “ Cyril secretly sold sacramental ornaments of the church and a valuable holy robe, fashioned with gold thread that the emperor Constantine had once donated for the bishop to wear when he performed the rite of Baptism ”.

For example Cyril writes “ I gave my back to those who beat me and my cheeks to blows ; and my face I did not shield from the shame of spitting ”.

For instance, there is no instruction to load an arbitrary “ immediate ” value into an accumulator ( although memory reference instructions do encode such a value to form an effective address ).

For this, and other, reasons mathematical historian Kurt Vogel writes: “ Diophantus was not, as he has often been called, the father of algebra.

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

Moreland fixed us each another drink, and said, `` For God's sake, tell me something truly amusing ''.

For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For an object with a fixed mass that is rotating about a fixed symmetry axis,

For instance an arbitrageur would first buy a convertible bond, then sell fixed income securities or interest rate futures ( to hedge the interest rate exposure ) and buy some credit protection ( to hedge the risk of credit deterioration ).

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For example, if function div stands for the division operation x / y, then div with the parameter x fixed at 1 ( i. e., div 1 ) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv ( y )

For that reason most democratic constitutions provide that elections are held at fixed regular intervals.

Limit functor: For a fixed index category J, if every functor J → C has a limit ( for instance if C is complete ), then the limit functor C < sup > J </ sup >→ C assigns to each functor its limit.

For example, a field called " Length of Stay " could invoke a MUMPS expression that would process the various dates, transfers, and discharges that would then be returned as if it were stored as a fixed data element.

For example, the German and Austrian schuhplattling dance consists of slapping the body and shoes in a fixed pattern, a feature that few other countries ' dances have.

For example, generally German-style games do not have a fixed number of players like chess or bridge ; though there is a sizable body of German-style games that are designed for exactly two players, most games can accommodate anywhere from two to six players ( with varying degrees of suitability ).

( For example, in the 1970s in the United Kingdom inflation reached 25 % per annum, yet interest rates did not rise above 15 % – and then only briefly – and many fixed interest rate loans existed ).

Consider the logarithm function: For any fixed base b, the logarithm function log < sub > b </ sub > maps from the positive real numbers R < sup >+</ sup > onto the real numbers R ; formally:

A unary operation is idempotent if it maps each element of S to a fixed point of f. For a set with n elements there are

For example, the higher the fixed costs, the fewer firms the market will support.

For example, the olivine group is described by the variable formula ( Mg, Fe )< sub > 2 </ sub > SiO < sub > 4 </ sub >, which is a solid solution of two end-member species, magnesium-rich forsterite and iron-rich fayalite, which are described by a fixed chemical formula.

For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot.

For producers of homogeneous goods, when demand falls, these producers have more of an incentive to maintain output and cut prices, in order to spread out the high fixed costs these producers faced ( i. e. lowering cost per unit ) and the desire to exploit efficiencies of maximum volume production.