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 symptoms develop during the acute phase, they usually resolve spontaneously within three to eight weeks in approximately 90 % of individuals.

If the judiciary decides in favor of the government because the country is secular, they would be considered to be Muslim individuals acting under compelling circumstances.

If the DNA sequence at a particular locus varies between individuals, the different forms of this sequence are called alleles.

) If semantic externalism is true, then the meaning of a word or sentence is not wholly determined by what individuals think those words mean.

Cafiero explains in Anarchy and Communism ( 1880 ) that private property in the product of labor will lead to unequal accumulation of capital and, therefore, the reappearance of social classes and their antagonisms, and thus the resurrection of the state: " If we preserve the individual appropriation of the products of labour, we would be forced to preserve money, leaving more or less accumulation of wealth according to more or less merit rather than need of individuals.

If 12 individuals each take one month before they start a new job, the aggregate unemployment statistics will record this as a single unemployed worker.

If the traits that give these individuals a reproductive advantage are also heritable, that is, passed from parent to child, then there will be a slightly higher proportion of fast rabbits or efficient algae in the next generation.

If the exposure to antibiotics is short, these individuals will survive the treatment.

If a new mutation reduces their susceptibility to an antibiotic, these individuals are more likely to survive when next confronted with that antibiotic.

If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem ( MacLeod & Rubenstein, 2006, § 3d ).

If resemblances between individuals are asserted, conceptualism becomes moderate realism ; if they are denied, it collapses into nominalism.

If the two houses choose different individuals, then a joint committee of both houses is appointed to agree on a common candidate.

If it is accepted as morally wrong to deliberately inflict suffering upon innocent human creatures, then it is only logical to also regard it as wrong to inflict suffering on innocent individuals of other species.

If individuals experience diminishing returns from income, then the optimum distribution of income for society involves a progressive income tax.

If no individual had a majority, then the House of Representatives would choose from the five individuals with the greatest number of electoral votes.

If " good " coins have a face value below that of their metallic content, individuals may be motivated to melt them down and sell the metal for its higher intrinsic value, even if such destruction is illegal.

" I do not refer to real estate, or to personal property or to cold cash, but rather to that in life which tends to make these tangible substances count for most in the daily lives of people, namely, goodwill, fellowship, mutual sympathy and social intercourse among a group of individuals and families who make up a social unit … If he may come into contact with his neighbor, and they with other neighbors, there will be an accumulation of social capital, which may immediately satisfy his social needs and which may bear a social potentiality sufficient to the substantial improvement of living conditions in the whole community.

If tens of thousands of emails are sent every day by thousands of individuals, it doesn't take a very high success rate to be worthwhile.

If these individuals cannot communicate with their family and caregivers it makes it very difficult for them to participate in daily activities as they also have severe physical difficulties.

If we accept that " mental illness " is a euphemism for behaviors that are disapproved of, then the state has no right to force psychiatric " treatment " on these individuals.

If the exposure is singular and all of the affected individuals develop the disease over a single exposure and incubation course, it can be termed a point source outbreak.

If AA and BB individuals ( homozygotes ) show different forms of the trait ( phenotype ), and AB individuals ( heterozygotes ) show the same phenotype as AA individuals, then allele A is said to dominate or be dominant to or show dominance to allele B, and B is said to be recessive to A.