With the Lombard invasion of Italy it was annexed to the Duchy of Benevento, until it was finally destroyed by the Byzantines of Constans II in 663, reducing to a small hamlet known as Quintodecimo ( referring to its distance of 15 miles from Benevento ).

With this work under his belt, Bessel was able to achieve the feat for which he is best remembered today: he is credited with being the first to use parallax in calculating the distance to a star.

With an apparent brightness of 0. 03m, this is the second brightest star of the northern hemisphere ( after Arcturus ) and the fifth brightest star in all ; its spectral class is A0 V and it lies at a distance of only 25. 3 ly.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

With the addition of a new bullpen in right field of Fenway Park, which reduced the distance from home plate from 400 feet to 380 feet, the bullpen was nicknamed " Williamsburg ", because the new addition was " obviously designed for Williams ".

With the German rulers at a distance, Avignon set up as a republic with a consular form of government, between 1135 and 1146.

With respect to one another, their relative refractive indices are, in order of distance from the core: lowest, highest, lower, higher.

With long distance rates at historic lows, using regular business lines, OUTWATS service became obsolete late in the 20th century.

With the catapult launch, the plane successfully traveled the distance outlined by the competition, but was declined the prize due to the takeoff method.

With a fixed spool, spin cast reels can cast lighter lures than bait cast reels, although friction of the nose cone against the unspooling line slightly reduces casting distance compared to spinning reels.

With maglev a vehicle is levitated a short distance away from a guideway using magnets to create both lift and thrust.

With a total distance of around 1, 850 km ( 1, 150 mi ) it is the longest historic stock route in the world.

With the triangulation method, distances, elevations and directions between objects at great distance from one another can be determined.

With repeaters in the fiber optic cable the distance from the telephone exchange can be extended much farther.

With a course that covers a distance of 829 km, it is the fourth-longest in the Iberian peninsula, and its hydrological basin extends into an area of approximately 68, 000 km² ( the majority of which lies within Spain ).

With an area of 112, 622 square kilometers, roughly the size of Pennsylvania and slightly bigger than Bulgaria, Benin extends from the Niger River in the north to the Atlantic Ocean in the south, a distance of.

With the exception of the longer, distance contests, Quarter Horse races are run flat out, with the horses running at top speed for the duration.

With the typical 5 mil scale ( each mark is 5 mil ), a lighthouse that is 3 marks high that is known to be 120 meters tall is 8000 meters distance.

With his University of Kansas teammates he also anchored a world record in the sprint medley relay ( 3: 15. 2 ) and twice in the distance medley relay ( 9: 33. 8 at the Drake Relays in 1967 and then 9: 33. 0 at the Kansas Relays in 1969, Ryan's 3: 57. 6 anchor leg for the mile being his last collegiate race on his home track ).

With this definition of distance, geodesics in a Riemannian manifold are then the locally distance-minimizing paths, in the above sense.

With no set standards, there is the tendency to promote to the next highest level when the top of a salary band is reached regardless of performance.

With each vertex we associate certain numerical values, namely the set of positive differences in the parameter T between the vertex and its corresponding forward corner points.

With the transit set up, a mirror on one of the accelerometers is sighted and the platform is turned until it is aligned.

A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

With the Academies in Europe ( second half of 16th century ) the gap between fine and applied arts was definitely set.

With their consent, he set up a rival emperor, the prefect of the city, a Greek named Priscus Attalus.

Among other composers who set Housman songs were John Ireland ( song cycle, Land of Lost Content ), Michael Head ( e. g. ' Ludlow Fair '), Graham Peel ( a famous version of ' In Summertime on Bredon '), Ian Venables ( Songs of Eternity and Sorrow ), and the American Samuel Barber ( e. g. ' With rue my heart is laden ').

With the crystallization of church order improvisation in prayer largely gave place to set forms, and collections of prayers were made which later developed into Sacramentaries and Orationals.

With a business association established with two entrepreneurs, Edward Molton and Stephen Warwick, and with John Muggeridge from Conran serving briefly as an assistant, he set about working primarily for the music industry.

With two exceptions, some words and phrases which had become archaic were modernized ; secondly, the readings for the Epistle and Gospel at the Holy Communion, which had been set out in full since 1549, were now set to the text of the 1611 Authorized Version of the Bible.

With the Spanish New Laws of 1552 Cuban Indians were freed from encomienda, and some seven Indian towns were set up.

With his shots in the 9th and 10th innings Wrigley Field erupted and Sandberg set the stage for a comeback win that cemented the Cubs as the team to beat in the East.

With his golden ear, Porter found the studio's acoustics to be problematic, and he devised a set of acoustic baffles to hang from the ceiling, then selected positions for microphones based on resonant room modes.

With the removal of the German High Seas Fleet in 1919, Britain had no naval enemies, and at the Washington Naval Treaty of 1922 it was agreed that the USA, Britain and Japan should set their navies in a ratio of 5: 5: 3, with France and Italy maintaining smaller fleets.

With this letter, Dost Mohammad formally set the stage for British intervention in Afghanistan.

With Saville and others, he set up the New Reasoner, a journal that sought to develop a democratic socialist alternative to what its editors considered the ossified official Marxism of the Communist and Trotskyist parties and the managerialist cold war social democracy of the Labour Party and its international allies.

With the advent of the New Dawn promotion, three additional servers were set up and maintained by Ubisoft: Venril Sathir ( British ), Sebilis ( French ) and Kael Drakkal ( German ).

With the possible exception of gravitation, these interactions can usually be described in a set of calculational approximation methods known as perturbation theory, as being mediated by the exchange of gauge bosons between particles.

With the above product, the set of all homotopy classes of loops with base point x < sub > 0 </ sub > forms the fundamental group of X at the point x < sub > 0 </ sub > and is denoted

With this additional condition — the covariant divergence of the energy – momentum tensor, and hence of whatever is on the other side of the equation, is zero — the simplest set of equations are what are called Einstein's ( field ) equations:

With Conté as president, the CMRN set about dismantling Touré's oppressive regime, abolishing the authoritarian constitution, dissolving the sole political party and its mass youth and women's organizations, and announcing the establishment of the Second Republic.

With the opening of trade between England and Japan, Japanese imports, art and styles became fashionable in London, making the time ripe for an opera set in Japan.

With Jason in command of the Protector, the actors and Thermians destroy Sarris ' ship and set course back to Earth.

With a grant from the Rockefeller Foundation, Hoover set up health units to work in the flooded regions for a year.