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 the engine is running with clutch engaged and the transmission in neutral, the engine spins the input shaft of the transmission, but no power is transmitted to the wheels.

If the receiving partner has wounds on his genitals, or if the giving partner has wounds or open sores on or in his or her mouth, or bleeding gums, this poses an increased risk of STD transmission.

If SMS over GPRS is used, an SMS transmission speed of about 30 SMS messages per minute may be achieved.

If these bits are known ahead of transmission ( to be a certain value with absolute probability ), logic dictates that no information has been transmitted.

If an event is sent on all channels at the same time, the highest-numbered channel's transmission will be delayed by as much as 16ms.

If the central node is passive, the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way transmission time ( i. e. to and from the central node ) plus any delay generated in the central node.

If the target is thin on an atomic scale the collision cascade can reach the back side of the target and atoms can escape the surface binding energy ` in transmission '.

If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve superluminal transmission speeds.

If the automatic is placed in reverse or first gear, the transmission divides the torque 50-50 to both front and rear wheels.

If they factor out of the calculation the fact that the light-time delay of the transmission is increasing at a rate of 0. 8 seconds per second, both can work out that the other twin is aging slower, at 60 % rate.

If transmission reliability is desired, it must be implemented in the user's application.

If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion.

If the demand for power exceeds the supply, generation plants and transmission equipment can shut down which, in the worst cases, can lead to a major regional blackout, such as occurred in the US Northeast blackouts of 1965, 1977, 2003, and in 1996 and 2011.

If so, abort transmission.

* If the high and low signal levels have the same voltage with opposite polarity, coded signals have zero average DC voltage, thus reducing the necessary transmitting power and minimizing the amount of electromagnetic noise produced by the transmission line.

If a receiver is connected to the system in the middle of a frame transmission, it ignores the data until it detects a new frame synchronization sequence.

If the transmission is temporarily interrupted, or a bit slip event occurs, the receiver must re-synchronize.

If an odd number of bits is changed in transmission, the message will change parity and the error can be detected at this point.

If the central node is passive, the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way round trip transmission time ( i. e. to and from the central node ) plus any delay generated in the central node.

If two polarizers are placed atop one another at 90 ° angles to one another, there is minimal light transmission.

If packets arrive faster than the router can process them ( such as in a burst transmission ) the router puts them into the queue ( also called the buffer ) until it can get around to transmitting them.