If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.

If, however, the figure to be discerned were complicated, composed of several interlocking subfigures, and so on, even the tracing process failed him, and he could not focus even relatively simple shapes among its parts.

If, on the other hand, they opted for representation, it had to be representation per se -- representation as image pure and simple, without connotations ( at least, without more than schematic ones ) of the three-dimensional space in which the objects represented originally existed.

If he foresaw any problem because of the quality of the hymen, it was recommended that simple procedures be undertaken at once to incise the hymen or, preferably, to dilate it.

If we have not thought and made a decision entirely in these terms, then we need to submit ourselves to the following `` simple test '': `` Have we decided how we are to kill the other members of our household in the event of our being less injured than they are ''??

If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function.

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

If sections of the frame move in a simple manner, the compressor emits a ( slightly longer ) command that tells the decompresser to shift, rotate, lighten, or darken the copy: a longer command, but still much shorter than intraframe compression.

If is a constant, the solution is particularly simple, and describes, e. g., if, the exponential decay of radioactive material at the macroscopic level.

If the deficit is not financed through a loan it is enough with a simple majority to approve the budget ( 50 % of the votes plus 1 ).

If the outcomes x < sub > i </ sub > are not equiprobable, then the simple average ought to be replaced with the weighted average, which takes into account the fact that some outcomes are more likely than the others.

If it is unaffected, then it is a simple partial seizure ; otherwise it is a complex partial ( psychomotor ) seizure.

If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency ( which does not depend on the amplitude ).

If it were simple to ascertain the properties required to develop a lead discovered in vitro to one that is active in vivo, drug discovery would be as reliable as drug manufacturing.

If the true function is simple, then an " inflexible " learning algorithm with high bias and low variance will be able to learn it from a small amount of data.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.

If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon.

If chitin is detected, they then produce enzymes to digest it by cleaving the glycosidic bonds in order to convert it to simple sugars and ammonia.

If they both used the Attic stadion of about 185 meters, then the older estimate is 1 / 6 too large, and Ptolemy's value is 1 / 6 too small, a difference explained as due to ancient scientists ' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5 / 6, due to air's bending of horizontal light rays by 1 / 6 of the Earth's curvature.

If adding that detail only altered things slightly then it would not have been too bad, but disaster struck when it was found that the simple correction mentioned above led to infinite probability amplitudes.

If W isn't irreducible, then the dominant species ( or quasispecies ) that develops can depend on the initial population, as is the case in the simple example given below.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

If they had any significant level of non-organic parts then something as simple as an x-ray scan would show them not to be human ( unless their creators designed the non-organic parts to have almost exactly the same structure and density as the organic components they were replacing, which would be both infeasible and highly improbable but not completely out of the question ).

If Russian pupils have to take these languages, how come American students have a choice whether or not to take a language, but have to face so many exceptions??

If the Czech ethnic origin was to be stressed, combinations like " Bohemian of Bohemian language "( Čech českého jazyka ), " a real Bohemian " ( pravý Čech ) etc.

If names be not correct, language is not in accordance with the truth of things.

If language be not in accordance with the truth of things, affairs cannot be carried on to success.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.

If these two features of the language coincide too frequently, they overemphasize each other and the hexameter becomes sing-songy.

If Solomon was the author, the book underwent a later modernization of language.

If this is the case, the non-Pauline language and style are not indications of pseudonymity.

If someone sees something completely different than another, our language prevents us from acknowledging the other's point of view by limiting our perception to fixed states.

* If the entire language does not allow side-effects, then any evaluation strategy can be used ; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program ( for example, using deforestation ).

If Language A borrowed a word from Language B, or both borrowed the word from a third language or inherited it from a common ancestor, and later the word shifted in meaning or acquired additional meanings in at least one of these languages, a native speaker of one language will face a false friend when learning the other.

If the facts are related, this would be a unique case of a tradition that endured for more than a thousand years and that actually pre-dates most of the major splits in the Germanic language family.

# If the borrowed word happens to have a suffix that the borrowing language uses as a gender marker, the suffix tends to dictate gender.

If V is a formal language, then V < sub > i </ sub >, the i-th power of the set V, is a shorthand for the concatenation of set V with itself i times.

If negation is cyclic and "∨" is a " max operator ", then the law can be expressed in the object language by ( P ∨ ~ P ∨ ~~ P ∨ ... ∨ ~...~ P ), where "~...~" represents n − 1 negation signs and "∨ ... ∨" n − 1 disjunction signs.

If such a language existed, Zamenhof postulated, it could play the role of a neutral communication tool between people of different ethnic and linguistic backgrounds.

If something was already there with no conflict, he used it without changes in language, he reordered and ruled on where there was conflict, and clarified where context was not given.

If a model for a language moreover satisfies a particular sentence or theory ( set of sentences satisfying special conditions ), it is called a model of the sentence or theory.

If they express much more than this, they are usually considered to be a hardware description language such as Verilog, VHDL, or any one of several specific languages designed for input to simulators.

If a language uses multiple writing systems, it may have distinct orthographies, as is the case with Kurdish, Uyghur, Serbian, Inuktitut and Turkish.

It is this emphasis on becoming attentive to the social backdrop against which language is rendered intelligible that explains Wittgenstein's elliptical comment that " If a lion could talk, we could not understand him.

If the assumption of a " Proto-Human " language is accepted, its date may be set anywhere between 200, 000 years ago ( the age of Homo sapiens ) and 50, 000 years ago ( the age of behavioral modernity ).

Many of his stories, such as Gulf, If This Goes On —, and Stranger in a Strange Land, depend strongly on the premise, related to the well-known Sapir – Whorf hypothesis, that by using a correctly designed language, one can change or improve oneself mentally, or even realize untapped potential ( as in the case of Joe Green in Gulf ).

Klement returned his bicycle to the manufacturers, Seidel and Naumann, with a letter, in Czech, asking them to carry out repairs, only to receive a reply, in German, stating: " If you would like an answer to your inquiry, you should try writing in a language we can understand ".