Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

Since all anchors that embed themselves in the bottom require the strain to be along the seabed, anchors can be broken out of the bottom by shortening the rode until the vessel is directly above the anchor ( at this point the anchor chain is " up and down " in naval parlance ).

Since one DSL termination point can support multiple ISPs, the economic feasibility of DSL is substantially improved.

Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil.

Since lead has a lower melting point than the other constituents of the brass, it tends to migrate towards the grain boundaries in the form of globules as it cools from casting.

Since 1980, each voter names three rookies: a first-place choice is given five points, a second-place choice three points, and a third-place choice one point.

Since the conclusion of Calvin and Hobbes, Watterson has taken up painting, at one point drawing landscapes of the woods with his father.

Since the Persian force obviously contained a high proportion of missile troops, a static defensive position would have made little sense for the Athenians ; the strength of the hoplite was in the melee, and the sooner that could be brought about, the better, from the Athenian point of view.

Since the second half of the 20th century, computers have been programmed to play chess with increasing success, to the point where home computers can play chess at a very high level.

Since helium remains a liquid even at absolute zero at atmospheric pressure, it has only a boiling point, and not a melting point, in conventional presentations.

Since this curl is not the same at every point, its plot is a bit more interesting:

( Since there is no citation for this exegesis, readers will need to analyse for themselves whether the " exact parallel " is addressed elsewhere and is generally accepted, or might represent a personal point of view, and readers will also need to discern for themselves what exactly is the " illumination ".

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.

Since the remainders decrease with every step but can never be negative, a remainder r < sub > N </ sub > must eventually equal zero, at which point the algorithm stops.

Since the fundamental group is a homotopy invariant, the theory of the winding number for the complex plane minus one point is the same as for the circle.

Since these people would have to be descended from Adam, they would have had to travel to the other side of the Earth at some point ; Augustine continues:

Since half of the particles at point move right and half of the particles at point move left, the net movement to the right is:

Since King Kong was seen as the bigger draw ( at the time, he was even more popular in Japan than Godzilla ), and since Godzilla was still a villain at this point in the series, it led to the decision to not only give King Kong top billing, but also to present him as the winner of the climactic fight.

Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view this situation is not tenable.

Since, by the second law of thermodynamics, this is statistically improbable to the point of exclusion, the Carnot efficiency is a theoretical upper bound on the reliable efficiency of any process.

Since honey normally exists below its melting point, it is a supercooled liquid.

Since the 2. 4 GHz band is heavily used to the point of being crowded, using the relatively unused 5 GHz band gives 802. 11a a significant advantage.

Since Odysseus seems to be the only person ( perhaps excepting Telemachus ) who can actually use the bow, it could merely have been another delaying tactic of Penelope's.

Since the 1960s, the DCMB has been a " scatter band " like every Ivy League marching band excepting Cornell's band.

Since Chinese and English both have subject – verb – object grammatical order, literally translating this first sentence is straightforwardly understandable, excepting the final particle zhě 者 " one who ; that which ", which is a nominalizer that marks a pause after a noun phrase.

Since Sunday, October 1, 2006, the Baltimore Museum of Art and the Walters Art Museum have had free admission year-round as a result of grants given by Baltimore City and Baltimore County, excepting for special exhibitions.

Since the late nineteenth century, only two brief periods of violence have marred its democratic development.

Since the debut of the prototypical superhero Superman in 1938, stories of superheroes — ranging from brief episodic adventures to continuing years-long sagas — have dominated American comic books and crossed over into other media.

Since the Treaty of Nanking was brief and with only general stipulations, the British and Chinese representatives agreed that a supplementary treaty be concluded in order to work out more detailed regulations for relations.

Since nisses are thought to be skilled in illusions and sometimes able to make themselves invisible, one was unlikely to get more than brief glimpses of him no matter what he looked like.

Since, according to the learned researches of Sir William Jones, Odin and Buddha are probably the same person, it is curious to see the names of Bondvar, Wodansdag, and Votan designating in India, Scandinavia, and in Mexico the day of a brief period.

( Since leaving office Paesel has served on the Third Regional Airport Clearinghouse and now serves as Executive Director of the South Suburban Mayor and Managers Association and served a brief period in 2006 as District 168 Board Member ).

Since then-other adaptations of the play for TV or theatre have usually left this brief mention of a largely forgotten political party intact.

Since leaving politics in 1997, McKenna served for a brief time on the Security Intelligence Review Committee.

Since Rothe's death several volumes of his sermons and of his lectures ( on dogmatics, the history of homiletics ) and a collection of brief essays and religious meditations under the title of Stille Stunden ( Wittenberg, 1872 ) have been published.

Since the 1960s it has been grade separated from all roads, but it runs more or less at street level for a brief stretch north of Clifton, between the Grasmere and Old Town stations, and from south of the Pleasant Plains station to Tottenville, the end of the line.

Since its articulation in 1998 by South Korean President Kim Dae Jung, the policy resulted in greater political contact between the two States and some historical moments for the Korean peninsula ; the two Korean summit meetings in Pyongyang ( June 2000 ) which broke ground with several high-profile business ventures, as well as brief meetings of separated family members.

Since 2000, Mirrlees ' work has undergone another resurgence in popularity, marked by new editions of her poetry, an entry in the Dictionary of National Biography and several scholarly essays by critic Julia Briggs, new introductions to Lud-in-the-Mist by writer Neil Gaiman and scholar Douglas A. Anderson, essays and a brief biography by writer Michael Swanwick, and translations of Lud-in-the-Mist into German and Spanish.

Since then, little has been heard from any of the group members, save for a brief return to promotional duties for Martyn Young in 2001, to oversee the release of the Colourbox compilation Best of Colourbox 82 / 87.

Since the loss of the war was largely blamed on democratic politicians such as Cleon and Cleophon, there was a brief reaction against democracy, aided by the Spartan army ( the rule of the Thirty Tyrants ).

Since a brief advancing period in the 1950s, most of these glaciers have been retreating.

Since the useful time-span of individual quotes is very brief, they generally had not been sent long distances ; aggregated summaries, typically for one day, were sent instead.

Since a neuron produces an output spike when many of its inputs occur within a brief period the subset of inputs that remain are those that tended to be correlated in time.

Since its inception, the brief has always been held concurrently with the offices of Prime Minister and First Lord of the Treasury ; the list of Ministers for the Civil Service is therefore identical to the list of Prime Ministers of the United Kingdom from 1968 onwards.

Since May 1, 2009, the character has been appearing on a recurring basis after a brief return in 2008.

Since Fiat withdrew from Nanjing in 2007 and SAIC took over, discontinuing the Fiat models, the Perla only had a very brief existence.

Since implementation of the Public Use Plan, following a brief closure of the entire park due to the park service's inability to manage the growing crowds of international climbers, volunteer or commercial guides are required to access more than 2 / 3 of the park's area.

Since then, Prekmurje was mostly under administration of the Habsburg Monarchy, with brief periods of Ottoman administration.

Since then, Imperial College Union has spent long periods outside the NUS, interspersed with brief periods of membership.

Since SMS messages only require an instant to send, a brief peak in radio propagation ( such as due to changing cloud cover ) is often enough to get a message sent.