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 to be a Christian means to say yes where I otherwise say no, or where I do not have the right to say anything at all, then my only choice is to refuse to be a Christian.

If the answer isn't yes, they should get rid of it.

If the remainder is zero the answer produced is ' yes ', otherwise it is ' no '.

If the elements of S are pairwise orthogonal, the answer is always yes: for any such set there exists a measurement which will ascertain the exact state of the system without disturbing it, and once we know the state we can prepare another system in the same state.

If they voted " yes ", then an ostracism would be held two months later.

If the reply is yes, it would be stating that it is " no ", as the reply was yes.

If I speak in an almost worshipful sense about this music, it is not because I have lost perspective, it is precisely because I have found it, within music, yes, that was made five years ago.

If yes, it goes on to the next point.

If there exists no hyperplane that can split the " yes " and " no " examples, the Soft Margin method will choose a hyperplane that splits the examples as cleanly as possible, while still maximizing the distance to the nearest cleanly split examples.

If yes, then parentheticals may clarify how those sources individually contribute to the argument.

If yes, then a parenthetical that points to the correct and specific information might be helpful.

Irving claimed on the basis of what he called the index books that, " Because the experts can look at a tattoo and say ' Oh yes, 181, 219 that means you entered Auschwitz in March 1943 " and he warned Auschwitz survivors " If you want to go and have a tattoo put on your arm, as a lot of them do, I am afraid to say, and claim subsequently that you were in Auschwitz, you have to make sure a ) that it fits in with the month you said you went to Auschwitz and b ) it is not a number which anyone used before ".

If yes, then no, and if no, then yes.

If yes was answered to two or more questions, the person may have a mild case of orthorexia.

If the requirement for the countable chain condition is replaced with the requirement that R contains a countable dense subset ( i. e., R is a separable space ) then the answer is indeed yes: any such set R is necessarily isomorphic to R.

When asked during an interview in February 2009 about becoming Prime Minister, Straw said: " If someone came and said " Sign on the dotted line ", yes, I'd sign.

If the answer is ' yes ', " heterological " is heterological.

*" If Australia as a whole says yes to returning a Liberal government, I think our democracy is dead.

If the response option is yes / no then you will only know how many or what percent of your sample answered yes / no.

If the question is asked of the knave and the knave's path leads to freedom he will say " no " since the knight would say " yes " it does lead to freedom.

If you ask the knight if their path leads to freedom, they will answer truthfully, with " yes " if it does, and " no " if it does not.