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 the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If the auction is passed out, i. e. no bids are made and only four passes are called, the hands are abandoned and the turn to deal passes in rotation.

If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent.

If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.

If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request using the same die if it passes the boxman's inspection.

If the line passes through the leftmost portion of the pixel, only the red subpixel is lit ; if it passes through the rightmost portion of the pixel, only the blue subpixel is lit.

If a lock passes the requirements then it is said to be California Department of Justice ( CADOJ ) approved.

If this continues far enough, the working end passes into the knot and the knot unravels and fails.

If the applied voltage is large enough, the liquid crystal molecules in the center of the layer are almost completely untwisted and the polarization of the incident light is not rotated as it passes through the liquid crystal layer.

If a physician passes the examination, then he or she can become a nephrology specialist.

If the defendant accepts these suggestions and changes his penalty proposition, the court approves it and passes the verdict according to the plea agreement.

If the football passes through your goal line, but ends up elsewhere due to further jumps, the game continues.

If a government cannot get its appropriation ( budget ) legislation passed by the House of Representatives, or the house passes a vote of " no confidence " in the government, the prime minister is bound by convention to resign immediately.

If it passes through intermediate systems during its travels, it will probably be stored on those as well, at least for some time.

If one player cannot make a valid move, play passes back to the other player.

If a skater passes inside the track, he or she is disqualified.

If in changing from one position to another the reflected image passes directly over the unreflected image, no side error exists.

If it passes to one side, side error exists.

If not initially in thermodynamic equilibrium, simple isolated thermodynamic systems, as time passes, tend to evolve naturally towards thermodynamic equilibrium.

If the service is " good ", then the receiver must make a " good " return by hitting the ball back before it bounces a second time on receiver's side of the table so that the ball passes the net and touches the opponent's court, either directly or after touching the net assembly.

If the parliament passes a resolution of no confidence, or refuses to pass an important bill such as the budget, then the government must either resign so that a different government can be appointed or seek a parliamentary dissolution so that new general elections may be held in order to re-confirm or deny the government's mandate.

If a child had a single drop of Negro blood, he would revert to the ancestral line which, except as slaves under a superior race, had not made one step of progress in 3,000 years.

If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If they give him advice when he asks it, or if they perform specified duties under his direction, the nature of the U. N. will not of necessity change.

If the Republicans and Southern Democrats join to defeat medical care for the old under the Social Security program, they will thereby erect still another barrier to GOP hopes in the cities.

If your child is under 19 or is a student you may also claim an exemption for him if he qualifies as your dependent, even though he earns $600 or more.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

If a litigant chooses to enforce a Federal right in a State court, he cannot be heard to object if he is treated exactly as are plaintiffs who press like claims arising under State law with regard to the form in which the claim must be stated -- the particularity, for instance, with which a cause of action must be described.

If the church has followed the plan of cultivation of prospects and carried through a program of membership preparation as outlined earlier in this book, the process of assimilation and growth will be well under way.

If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.

If amber is heated under the right conditions, oil of amber is produced, and in past times this was combined carefully with nitric acid to create " artificial musk " – a resin with a peculiar musky odor.

If under the existing system he could not assemble forces quickly enough to intercept mobile Viking raiders, the obvious answer was to have a standing field force.

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

* If a fighter was knocked down, he had to rise within 30 seconds under his own power to be allowed to continue.

If present, clue cells can be visualized under a microscope.

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

If debts are greater than $ 250, 000, the proposal must be filed under Division 1 of Part III of the Bankruptcy and Insolvency Act.

If the player to move has no legal moves, the game is over ; it is either a checkmate — if the king is under attack — or a stalemate — if the king is not.

" That rich island ," he wrote on 1 December 1881, " the key to the Gulf of Mexico, is, though in the hands of Spain, a part of the American commercial system … If ever ceasing to be Spanish, Cuba must necessarily become American and not fall under any other European domination.

“ If you slaughter sheep, you will be considered guilty of a crime .” He issued a regulation to that effect ... 1279 / 1280 under Qubilai all the Muslims say: “ if someone else slaughters animal we do not eat ”.

If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software should solve the rendering equation.

If a plan cannot be confirmed, the court may either convert the case to a liquidation under chapter 7, or, if in the best interests of the creditors and the estate, the case may be dismissed resulting in a return to the status quo before bankruptcy.

If we view the DFT as just a coordinate transformation which simply specifies the components of a vector in a new coordinate system, then the above is just the statement that the dot product of two vectors is preserved under a unitary DFT transformation.

If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.

* If we think of as the group of real numbers under addition, then the direct product still consists of.