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 F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

If a sheet is for multiple days it shows a conversion table to convert from weekday to date and back.

If the obstructing object provides multiple, closely spaced openings, a complex pattern of varying intensity can result.

If multiple symmetry axes are present, they will necessarily intersect at a single point, and this is usually taken to be the center.

It follows that there are also infinitely many solutions if c is a multiple of the greatest common divisor of a and b. If c is not a multiple of the greatest common divisor of a and b, then the Diophantine equation ax + by = c has no solutions.

If multiple transiting planets exist in one system, then this method can be used to confirm their existence.

If this sounds indulgent, it allows simultaneity, absolute space and time and a deterministic universe ( along with decoherence theory ) whilst the status-quo permits time travel / causality paradoxes, subjectivity in the measurement process and multiple universes.

If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different.

If a and b are not both zero, the greatest common divisor of a and b can be computed by using least common multiple ( lcm ) of a and b:

If we are considering multiple operations on a set, then all operations must be preserved for a function to be considered as a homomorphism.

In arithmetic and number theory, the least common multiple ( also called the lowest common multiple or smallest common multiple ) of two integers a and b, usually denoted by LCM ( a, b ), is the smallest positive integer that is divisible by both a and b. If either a or b is 0, LCM ( a, b ) is defined to be zero.

On the other hand, LDAP does not define transactions of multiple operations: If you read an entry and then modify it, another client may have updated the entry in the meantime.

# If p is an odd prime, then any prime q that divides 2 < sup > p </ sup > − 1 must be 1 plus a multiple of 2p.

If it is desirable to encode more text than will fit in an encoded-word of 75 characters, multiple encoded-words ( separated by CRLF SPACE ) may be used.

If the hardware provides multiple rings or CPU modes, the microkernel is the only software executing at the most privileged level ( generally referred to as supervisor or kernel mode ).

In addition, multiple continuities are visited in the comic book series What If, What The --?!

If a text ( such as this one ) discusses multiple bases, and if ambiguity exists, the base ( itself represented in base 10 ) is added in subscript to the right of the number, like this: number < sub > base </ sub >.

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

If multiple vendors agree to implement the same functionality using the same API, a shared extension may be released, using the identifier EXT.

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 a marriage includes multiple husbands and wives, it can be called group marriage.

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 adjectival meanings show relatively low retentiveness of stems, as I am confident will prove to be the case in most languages of the world, why should our basic lists include 15 per cent of these unstable forms, but only 8 per cent of animals and plants which replace much more slowly??

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

* Indicative conditional, a conditional in the form of " If A then B " in natural languages

If the page's creator and reader are both assuming some platform-specific character encoding, and the server does not send any identifying information, then the reader will nonetheless see the page as the creator intended, but other readers on different platforms or with different native languages will not see the page as intended.

If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.

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 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 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 the relations between letters and sounds are similar in both languages, a transliteration may be ( almost ) the same as a transcription.

" If the treaty is executed in multiple copies in different languages, that fact is always noted, and is followed by a stipulation that the versions in different languages are equally authentic.

If mathematics is a language, it is a different type of language than natural languages.

If grammars differ only by having different rankings of CON, then the set of possible human languages is determined by the constraints that exist.

If you're not sure how to make a clean link between the same topic in two languages, put the link in the " Problem links " section at the bottom of this list.

If you'd like to help with the process, here's a list of all pages on the English Wikipedia which include links to their Esperanto counterparts: follow the links, and if the eo page hasn't been updated, put in an en: link to the English page and any other languages which might be linked.

If you'd like to help with the process, here's a list of all pages on the English Wikipedia which include links to their Polish counterparts: follow the links, and if the pl page hasn't been updated, put in an en: link to the English page and any other languages which might be linked.

If the Son of God had been born in India, his spoken language would have had to conform itself to the structure of the Indian languages.

If the duration of note is to be doubled, the letter is either capitalized ( if using Roman script ) or lengthened by a diacritic ( in Indian languages ).

If the association of Battle Axe cultures with Indo-European languages is to prove correct, then Fatyanovo would be a culture with an Indo-European superstrata over a Uralic substrata, and may account for some of the linguistic borrowings identified in the Indo-Uralic thesis.

In natural languages, an indicative conditional is the logical operation given by statements of the form " If A then B ".

In the novel, Faria, an Italian, is a prisoner of the Château d ' If who instructs Edmond Dantès, the protagonist and a fellow prisoner, in a number of fields including mathematics, the sciences, and foreign languages, and eventually helps him to escape from the island prison.

If the earlier England of Anglo-Saxons and Norse was tied to indigenous traditions, the England emerging from the Conquest owed a debt to the Romance languages and the culture of ancient Rome, that was not so important before the Conquest, but was maintained at a high level by the English catholic church and the clerks of England.

If an ISO 639-2 code that covers a group of languages is used, it might be overridden for some specific languages by a new ISO 639-1 code.