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 pendulum has been at rest and we were to strike it with a hammer ( the " impulse "), setting it in motion, it would swing back and forth (" resonate "), say, with an amplitude of 10 cm.

If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:

If the origin of the Cartesian coordinate system is taken to be at the point of suspension of the first pendulum, then the centre of mass of this pendulum is at:

If we measure time in days, then and we see that the pendulum rotates by an angle of − 2π sin ( φ ) during one day.

If the globe is not rotating in an inertial frame, the pointer on top of the chariot will indicate the direction of swing of a Foucault pendulum that is traversing this latitude.

If a pendulum were hung upside down from a second pivot point which could be adjusted up and down on the pendulum's rod, and the second pivot were adjusted until the pendulum had the same period as it did when swinging right side up from the first pivot, the second pivot would be at the center of oscillation, and the distance between the two pivot points would be L.

If the ball is only hit within a short distance, then instead of laying the bat down, the batsman swings the bat like a pendulum and the fielder targets the swinging bat.

If the oscillation is sufficiently strong ( in terms of its acceleration and amplitude ) then the inverted pendulum can recover from perturbations in a strikingly counterintuitive manner.

If is a fast oscillation the pendulum can be kept stable around the vertical position.

If that pendulum can move about two axes ( in a circular or elliptical shape ), due to the principle of superposition, the motion of a rod connected to the bottom of the pendulum along one axes will be described by the equation

If the arc was too small the vane never left the far side of the groove, and when the pendulum swung back it pushed the block strongly downwards.

If one shakes these devices, one hears a lead ball sliding back and forth, or a pendulum striking stops as it swings.

If the support is moved, the mode of oscillation of the pendulum will change.

If the support is moved sufficiently slowly, the motion of the pendulum relative to the support will remain unchanged.

If suspended from the surface of the Earth, the bob of the pendulum would be at the center of the Earth.

If it is hanging motionless and its support is moved sideways, the bob tends to remain motionless, so the pendulum always points at the center of the Earth.

If such a pendulum were attached to the inertial platform of an inertial navigation system, the platform would remain level, facing ' North ', ' East ', and ' Down ', as it was moved about on the surface of the Earth.

If the clock is moved without immobilising the pendulum, the uncontrolled swinging of the pendulum can cause the anchor pallets to collide violently with the escape wheel.