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Page "Gauss–Bonnet theorem" ¶ 9
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If and one
If you take the one, you'd better take both ''.
`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.
If one dancer slaps another, the victim may do a pirouette, sit down, or offer his assailant a fork and spoon.
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 we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If within one year you can make a success out of the American, you can practically name your own salary thereafter.
If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.
If one finger is raised against the authorities, all our moral power will vanish.
If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.
If he can bounce back with one of those 25 home runs years, the club will have to be better off offensively.
If they do meet and recognize one another, slap backs and embrace, the moment soon is done.
If either one ever started making promises, there is no telling where the promises would end.
If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.
Somebody, got to be somebody If I don't put my two cents in soon, somebody else will I know they're waitin only for one thing: for the bastards what done it to be nailed.
If we had, then one of us would have had to go instead.
`` If I catch you one more time down here without stockings '' --
If, for some reason such as economy, we are not going to develop aircraft nuclear propulsion with a sense of national urgency, then we should turn our effort to developing jet engines with a thrust-to-weight ratio of 12 or 15 to one.
If you don't own a planer and don't want to buy one, it's well worth renting.
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
If you have a full-time doctor now, can he be replaced with a part-time doctor or one who serves on a fee-per-case basis only??
If you use one of the new year-round cooling system fluids such as `` Dowguard '' be sure to check it.
If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.

If and bends
If the giraffe wants to bend down to drink, it either spreads its front legs or bends its knees.
If the air near the ground is warmer than that higher up, the light ray bends in a concave, upward trajectory.
If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero.
If the patient bends over the examination table, the physician will have them place their elbows on the table and squat down slightly.
If the wrist bends on impact, it can easily be sprained, dislocated or broken.
If the body has the escape velocity with respect to the Earth, this is not enough to escape the Solar System, so near the Earth the orbit resembles a parabola, but further away it bends into an elliptical orbit around the Sun.
" If the yellow line bends to the right, then straightens out, then bends to the right again, it is regarded as one curve.
Newer articulated buses feature Burma-Shave-style poetry such as " Parking got you down / Don't make Faces / Hop on the bus / There's plenty of spaces ", " This big shiny bus / Is really no riddle / But it sure is odd / How it bends in the middle ", " Getting to work / Is no trouble / When you ride / The daily double ", " There's the church / There's the steeple / And here's the bus / With all the people ", and " If you're tired of all the traffic / And could use an assist / Hop aboard a bus / With a bit of a twist ".
If any of the worldlines bends away from a geodesic path in some region, we can think of the observers as test particles that accelerate by using ideal rocket engines with a thrust equal to the magnitude of their acceleration vector.

If and deforms
If the nut is overtightened, the ferrule frequently deforms improperly causing the joint to fail.
If the strip deforms another 10 %, then one obtains the intensity of the blast stream.
If one piece flexes due to this lack of support, the edges of the opposite piece will tend to dig depressions into it a short distance in from the edge, and the edges of the opposite piece are heavily abraded by the same action-the lapping procedure assumes roughly equal pressure distribution across the whole surface at all times, and will fail in this manner if the workpiece itself deforms under that pressure.

If and surface
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If you drive greater distances than that, you'll just be skimming the surface and will never discover the enchantment, fascination and beauty which lured you in the first place to explore the hinterlands.
If, however, a layer of paper remains stuck to the surface, the adhesive has not failed.
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 the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture — there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e. g. in photography.
If rotation is arrested, the energy stored in fashioning the concave surface must be dissipated, for example through friction, before an equilibrium flat surface is restored.
If a player is unsure of whether a bet is a single or multi-roll bet, it can be noted that all single-roll bets will be displayed on the playing surface in one color ( usually red ), while all multi-roll bets will be displayed in a different color ( usually yellow ).
If the ball has a rough surface, the fluid flowing past it will make it rotate.
where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.
If the missile starts to roll, the gyroscopic force of the disk drives the control surface into the airflow, cancelling the motion.
If a particle of the beam crosses this surface, there will be some kind of interaction.
If an organism ( such as bacteria ) attaches to a valve surface and forms a vegetation, the host immune response is blunted.
If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid.
If a previous fresco was being painted over, the surface would be roughened to give a key.
If a solid surface is chilled below the dew point of the surrounding air and the surface itself is colder than freezing, frost will form on the surface.
If the solid surface is rough, and the liquid is in intimate contact with the solid asperities, the droplet is in the Wenzel state.
If the imaging surface is cleaned of contaminants and residual moisture before the second image is taken, then no image of the missing section would appear.
* If creatures similar to plesiosaurs lived in the waters of the Loch Ness, they would be seen very frequently as they would have to surface several times a day to breathe.
If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid ( for example across an orifice plate or venturi ), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.
If the universe is static and populated by an infinite number of stars, any sight line from Earth must end at the ( very bright ) surface of a star, so the night sky should be completely bright.

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