On the sphere, the solution is significantly more complex, e. g., in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc, i. e. the geodesic.

On July 1, 2005, the United States reportedly deployed troops and aircraft to the large military airfield of Mariscal Estigarribia as part of a bid to extend control of strategic interests in the Latin American sphere, particularly in Bolivia.

On the surface of a sphere there are no parallel line s. Euclid's Elements contained five postulates that form the basis for Euclidean geometry.

On the sphere, points are defined in the usual sense, but the analogue of " line " may not be immediately apparent.

On the surface of each sphere is a checkerboard pattern of inwards and outwards going magnetic field lines.

On an infinite-radius celestial sphere, all observers see the same things in the same direction.

On the celestial sphere, positions are located by latitude and longitude.

On the one hand the Netherlands wanted to use New Guinea as a Dutch sphere of influence in the region.

On a sphere, the sum of the angles of a triangle is not equal to 180 °.

On the celestial sphere, this star lies about half a degree from the 4th magnitude star Eta Cygni.

On a sphere, the images of geodesics are the great circles.

On some occasions when William was absent ( back in Normandy ), he served as de facto regent of England, and at times he led the royal forces against rebellions ( e. g. the Revolt of the Earls ): the precise sphere of his powers is not certain, however.

On the standard sphere, where the curvature is everywhere 1, we see that the angle sum of geodesic triangles is always bigger than π.

On the disk, the latter has nearly four times the area as the former ; if one uses finer and finer grids on the sphere, then the ratio of the areas approaches exactly 4.

On 10 October he issued an order ( known as the " Reichenau Order ") headed Conduct of the Troops in the East, in which he said: " The primary goal of the campaign against the Jewish-Bolshevist system is the absolute destruction of the means of power and the eradication of the Asian influence in the European cultural sphere ...

On the left, a mathematical function defining a bump map simulates a crumbling surface on a sphere, but the object's outline and shadow remain those of a perfect sphere.

On the right, the same function is used to modify the surface of a sphere by generating an isosurface.

On a sphere, the sum of the angles of a triangle is not equal to 180 °.

On the sphere, points are defined in the usual sense.

On the sphere the geodesics are the great circles ; other geometric concepts are defined as in plane geometry but with straight lines replaced by great circles.

Within these circular rings is a small terrestrial globe J, fixed on an axis K, which extends from the north and south poles of the globe at n and s, to those of the celestial sphere at N and S. On this axis is fixed the flat celestial meridian L L, which may be set directly over the meridian of any place on the globe, so as to keep over the same meridian upon it.

On the other hand, others see globalization as a social phenomenon expanding the sphere of classical liberal values, which inevitably led to a larger role for civil society at the expense of politically derived state institutions.

On the sphere one of these cuts runs longitudinally through the southern hemisphere, connecting a point on the equator ( z

On the other hand, we cannot regard artistic invention as pure, uncaused, and unrelated to the times in which it occurs.

`` On each side of the Hoogli, where we are now sailing, are the Hindoo cottages, as thick together as the houses in our seaports.

On the eve of the `` great debate '' on the proposal to give the President broad powers to make across-the-board tariff concessions which could practically bring us into the Atlantic Community, we should face the alternatives on this proposition.

On Thursday evening we may go out of town together by some stage or mail about the distance of ten or twelve miles.

On the contrary, if this be an apocalyptic era as is commonly said, we see it as an era of opportunity.

On the basis of what they give us we can know how the young Caruso sang, appreciate the distinctive qualities of Parsifal under Karl Muck's baton, or sense the type of ensemble Toscanini created in his years with the New York Philharmonic.

On the following pages and in the following issues we take you every step of the way to your vacation cottage, from choosing the proper site to applying the final trim.

On the basis of its life history, we like to think that Andrena is more primitive than the bumblebees.

On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.

On the one hand do we argue the Supreme Court decision required only that a child not be denied admission to a school on account of his race??

On this giddy and oscillating platform over fifty feet from the floor, after a first dusting, we began to wash.

On that cold, but bright, April day we were guests of your government in the reviewing stand of Red Square to witness the poeple's celebration for Yuri Gagarin and later on that day we attended the somewhat more exclusive reception for him in one of the impressive palaces of the Kremlin.

On the one side we have the university professors and their students, trained in Teutonic methods of research, who have sought out, collected and studied the true products of the oral traditions of the ethnic, regional and occupational groups that make up this nation.

On the other we have the flag-wavers and the national sentimentalists who have been willing to use any patriotic, `` frontier western '' or colonial material willy-nilly.

On arriving in Tokyo later we were met by Masu who took us immediately to her university, the Japanese Women's University.

On more than one occasion, Judge told the writers that one of their ideas for an episode of King of the Hill would work well for Beavis and Butt-Head ; eventually he concluded, " Maybe we should just actually make some good Beavis and Butt-Head episodes.

On this topic, Malachi deals with divorce both as a social problem (" Why then are we faithless to one another ...

On the day of the Berlin Blockade, a Soviet representative told the other occupying powers " We are warning both you and the population of Berlin that we shall apply economic and administrative sanctions that will lead to circulation in Berlin exclusively of the currency of the Soviet occupation zone.

On top of this there are many non-European clowning traditions ( including clown-like figures in Japanese Kabuki theatre ), North American native shaman traditions to consider which may or may not have influenced what we now think of as a clown in the Western world.

The whole, however, may be judged from this fragment: " We Irish, though dwelling at the far ends of the earth, are all disciples of St. Peter and St. Paul ... we are bound to the Chair of Peter, and although Rome is great and renowned, through that Chair alone is she looked on as great and illustrious among us ... On account of the two Apostles of Christ, you pope are almost celestial, and Rome is the head of the whole world, and of the Churches ".

On October 7, Cuban President Osvaldo Dorticós spoke at the UN General Assembly: " If ... we are attacked, we will defend ourselves.

Following the influence of Malthus and concerns stemming from his An Essay On The Principle Of Population the UK census as we know it today started in 1801.

On the other hand, to the extent that our society is out of sync with the actualizing tendency, and we are forced to live with conditions of worth that are out of step with organismic valuing, and receive only conditional positive regard and self-regard, we develop instead an " ideal self ".