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 it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

If the administration does not succeed in passing the sales tax bill, or any other tax bill, it could very well be faced this spring at the fiscal session of the Legislature with an interesting dilemma.

If the weight is suspended off the seabed it acts as a spring or shock absorber to dampen the sudden actions that are normally transmitted to the anchor and can cause it to dislodge and drag.

If the driving member rotates in the direction that would unwind the spring the spring expands minutely and slips although with some drag.

If the barley was not ripe, or various other phenomena indicated that spring was not yet imminent, an intercalary month ( Adar II ) would be added.

If the depressive episodes are routinely during the winter and the hypomania presents in the spring / summer it is possible that the person may be diagnosed with Seasonal Affective Disorder instead of bipolar II disorder.

If done in the spring, cutting off vines must be repeated as regrowth appears to exhaust the plant's stored carbohydrate reserves.

If blood is taken from a hibernating squirrel in the winter and injected into another squirrel in the spring, the normally active squirrel will be more prone to hibernation when placed in cold dark conditions.

If the storm surge coincides with a spring tide, dangerously high water levels can occur in the Thames Estuary.

If it was spring and time for the sacrifice, she was ritually cleansed.

If a perched aquifer's flow intersects the Earth's dry surface, at a valley wall for example, the water is discharged as a spring.

If this is indeed the intended theme of the drawing, the bull would represent the zodiacal sign of Taurus, while the nude female, holding a bouqet of flowers, would be a depiction of Flora, the goddess of spring.

If these areas are overrun by wildfire they often produce a bumper crop of black morels the following spring.

If a mass m is attached to the end of such a spring, the system becomes a harmonic oscillator.

If the rod is too short, there will be excessive sideways movement between the axle and the body at the ends of the spring travel.

If an animal is drowsy or bored, it may not be as alert as it should to be prepared to spring into action.

If the water in direct contact with the pressure transfer mechanism ( diaphragm or piston and the spring balancing the internal pressure ) of the regulator freezes, the mechanism will be locked in the position at which the freezing takes place, as the ice will prevent the movement required to close.

If the blade is opened, a spark may keep the connection between blade and spring conducting.

If the input to the virtual spring is the spring displacement, x, and the output is the force that the virtual spring applies, F, then the virtual spring would be classified as an impedance.

If the input to the virtual spring is the force applied to the spring, F, and the output is the spring displacement, x, then the virtual spring would be classified as an admittance.