Whereas Plato idealized geometry, Aristotle emphasized nature and related disciplines and therefore much of his thinking concerns living beings and their properties.

Whereas spherical geometry has a constant positive curvature, hyperbolic geometry has a negative curvature: every point in hyperbolic space is a saddle point.

Whereas several figures common to English Country Dance, e. g. arming and the straight hey, are found in the traditional dances and display dances such as morris, ECD's origins rest among the gentry, first at court, then spreading to bourgeois-London, finally moving into country manors around England.

Whereas a movie is in essence " only " filmed theatre, cinematography is an attempt to create a new language of moving images and sounds.

Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright ; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically.

Whereas location may serve as a determinant for resident processes, context may be applied more flexibly with mobile computing with any moving entities, especially with bearers of smart communicators.

Whereas Active Defense envisioned the Army units moving from one blocking position to another in a series of largely static defenses, in the counter-blitz they would be far more mobile, conducting a series of limited offensives instead.

Whereas modern country began moving to FM around this time, classic country remained ( and still remains ) one of the few formats that has proven ideal for AM radio, particularly in rural areas ; prior to this transition, country was primarily an AM radio phenomenon and was most widely popular in rural areas.

Whereas the first one had all bars moved sideways in vertical positions, this one included bars moving from different directions in horizontal positions.

Whereas in the simple moving average the past observations are weighted equally, exponential smoothing assigns exponentially decreasing weights over time.

Whereas Lineker had developed into a world class goalscorer after moving from Leicester to Everton ( along with subsequent clubs FC Barcelona and Tottenham Hotspur ), Newell's form at Goodison Park was less spectacular as he formed a three-man strikeforce with Graeme Sharp and Tony Cottee, and with three strikers in the first eleven there was little pressure on any of them to score 20 or 30 goals a season.

Whereas a high percentage of the regular students can be expected to read other texts which more or less plow the same ground in a little different direction, the married students chose whole books on specific areas and went into much greater detail in their areas of interest.

Whereas a vector is an object with both a precise numerical magnitude and direction, del does not have a precise value for either until it is allowed to operate on something.

Whereas Bézier curves evolve into only one parametric direction, usually called s or u, NURBS surfaces evolve into two parametric directions, called s and t or u and v.

Whereas in his Majesty's province of Massachuset's Bay, in New England, an attempt hath lately been made to throw off the authority of the parliament of Great Britain over the said province, and an actual and avowed resistance, by open force, to the execution of certain acts of parliament, hath been suffered to take place, uncontrouled and unpunished, ...: and whereas, in the present disordered state of the said province, it is of the utmost importance ... to the reestablishment of lawful authority throughout the same, that neither the magistrates acting in support of the laws, nor any of his Majesty's subjects aiding and assisting them therein, or in the suppression of riots and tumults, ... should be discouraged from the proper discharge of their duty, by an apprehension, that in case of their being questioned for any acts done therein, they may be liable to be brought to trial for the same before persons who do not acknowledge the validity of the laws, in the execution thereof, or the of the magistrate in support of whom, such acts had been done: in order therefore to remove every such discouragement from the minds of his Majesty's subjects, and to induce them, upon all proper occasions, to exert themselves in support of the public peace of the province, and of the authority of the King and Parliament of Great Britain over the same ; be it enacted ..., That if any inquisition or indictment shall be found, or if any appeal shall be sued or preferred against any person, for murther, or other capital offense, in the province of the Massachuset's Bay, and it shall appear, by information given upon oath to the governor ... of the said province, that the fact was committed by the person against whom such inquisition or indictment shall be found, or against whom such appeal shall be sued or preferred, as aforesaid, either in the execution of his duty as a magistrate, for the suppression of riots, or in the support of the laws of revenue, or in acting in his duty as an officer of revenue, or in acting under the direction and order of any magistrate, for the suppression of riots, or for the carrying into effect the laws of revenue, or in aiding and assisting in any of the cases aforesaid ; and if it shall also appear, to the satisfaction of the said governor ... that an indifferent trial cannot be had within the said province, in that case, it shall and may be lawful for the governor ..., to direct, with the advice and consent of the council, that the inquisition, indictment, or appeal, shall be tried in some other of his Majesty's colonies, or in Great Britain ; and for that purpose, to order the person against whom such inquisition or indictment shall be found, ... to be sent, under sufficient custody, to the place appointed for his trial, or to admit such person to bail, taking a recognizance ... from such person, with sufficient sureties, ... in such sums of money as the said governor ... shall deem reasonable, for the personal appearance of such person, if the trial shall be appointed to be had in any other colony, before the governor, ... of such colony ; and if the trial shall be appointed to be had in Great Britain, then before his Majesty's court of King's Bench, at a time to be mentioned in such recognizances ; and the governor, ... or court of King's Bench, where the trial is appointed to be had in Great Britain, upon the appearance of such person, according to such recognizance, or in custody, shall either commit such person, or admit him to bail until such trial ....

Whereas previously Baldwin could barely bounce in the direction he wanted, he eventually became more proficient at controlling his leaps and using his powers in various ways, such as to deliver impressive blows, and even to project a stream of kinetic energy from his bubble field at a distance.

Whereas Gerry Anderson had a rocket ship in Fireball XL5 that could travel to planets around other stars as though they were just a few million miles away ( a rocket ship is limited in that it forms an explosive force which is contained and then sent off in one direction so the ship travels in another direction.

Whereas there is a motorway exit named after Arona, the exit at Castelletto Ticino is usually more convenient for the traveller coming from the direction of Milan.

Whereas SOOs establish high-level outcomes and objectives for performance and PWSs emphasize outcomes, desired results and objectives at a more detailed and measurable level, SOWs provide explicit statements of work direction for the contractor or offeror to follow.

`` Whereas, a Bridge over Merrimack River, from the Land of Hon'ble Jonathan Greenleaf, Esquire, in Newbery, to Deer Island, and from said Island to Salisbury, would be of very extensive utility, by affording a safe Conveyance to Carriages, Teams and Travellers at all seasons of the year, and at all Times of Tide.

Whereas the United States enjoys a long season that generally runs from March to November, other areas often have much shorter seasons.

Whereas philosophers merely had views about things, he taught the Noble Eightfold Path which liberates from suffering.

The British Statute of Anne ( 1710 ) further alluded to individual rights of the artist, beginning: " Whereas Printers, Booksellers, and other Persons, have of late frequently taken the Liberty of Printing ... Books, and other Writings, without the Consent of the Authors ... to their very great Detriment, and too often to the Ruin of them and their Families :" A right to benefit financially from the work is articulated, and court rulings and legislation have recognized a right to control the work, such as ensuring that the integrity of it is preserved.

Whereas the philosophical approach to consciousness focuses on its fundamental nature and its contents, the medical approach focuses on the amount of consciousness a person has: in medicine, consciousness is assessed as a " level " ranging from coma and brain death at the low end, to full alertness and purposeful responsiveness at the high end.

Whereas transition metals sometimes attract most of the attention in the study of catalysis, small organic molecules without metals can also exhibit catalytic properties, as is apparent from the fact that many enzymes lack transition metals.

Whereas Sergei Eisenstein viewed his montage of attractions as a propaganda tool through which the film-viewing masses could be subjected to “ emotional and psychological influence ” and therefore able to perceive “ the ideological aspect ” of the films they were being shown, Vertov believed the Kino-Eye would influence the actual evolution of man, “ from a bumbling citizen through the poetry of the machine to the perfect electric man .”

Whereas various types of Infantry weapons were acquired from Belgium.

Indeed, these Four Freedoms were explicitly incorporated into the preamble to the Universal Declaration of Human Rights which reads, " Whereas disregard and contempt for human rights have resulted in barbarous acts which have outraged the conscience of mankind, and the advent of a world in which human beings shall enjoy freedom of speech and belief and freedom from fear and want has been proclaimed the highest aspiration of the common people ,...."

Whereas elements of the disclosure may be available from third parties, only that provided by the franchisor can be depended upon.

Whereas Infocom's games had benefited significantly from the portability offered by running on top of a virtual machine, this strategy did not prove to be a significant advantage for Cornerstone ; in fact, the virtual machine significantly slowed the database's execution speed.

Whereas the other Central Asian republics have sometimes complained of Russian interference, Kyrgyzstan has more often wished for more attention and support from Moscow than it has been able to obtain.

Whereas previously it was hazardous to guess if there would be a storm or little activity, the predictions of Asher and McNaught timed bursts in activity down to ten minutes by narrowing down the clouds of particles to individual streams from each passage of the comet, and their trajectories amended by subsequent passage near planets.

Whereas MVC comes from the previous decade ( by work at Xerox PARC in the late 1970s and early 1980s ) and is based on observations of applications that ran on a single graphical workstation ; MVC was applied to distributed applications later in its history ( see Model 2 ).

Whereas the origin of the name norn is uncertain, it may derive from a word meaning " to twine " and which would refer to their twining the thread of fate.

Whereas Nisrani is of direct Semitic origin, it is very likely that Nazzarenu was adopted via the Italian Nazzareno ( from Latin, Nazarenus, meaning Nazarene.

Whereas previously the OUP had thought London too far from Oxford, after 1925 Craigie worked on the dictionary in Chicago, where he was a professor.

Whereas, mobile phone and Internet penetration in the household market ended up being one of the highest in the world with more than 50 percent of the revenue coming from these two industries.

Whereas the council of citizens served as an ordinary assembly, representing the people of FRY, the council of republics was made equally by representatives from the federation's constituent republics, to ensure federal equality.

Whereas the sociology of religion broadly differs from theology in assuming indifference to the supernatural, theorists tend to acknowledge socio-cultural reification of religious practice.

Whereas the k-opt methods remove a fixed number ( k ) of edges from the original tour, the variable-opt methods do not fix the size of the edge set to remove.

Whereas English judges won their independence from the Crown in the Act of Settlement 1701, American colonial judges still served at the pleasure of the King.

Whereas Quake maps are compiled from a variety of different components, Unreal maps are inherently editable on the fly.

Whereas the vocoder analyzes speech, transforms it into electronically transmitted information, and recreates it, The Voder ( from Voice Operating Demonstrator ) generates synthesized speech by means of a console with fifteen touch-sensitive keys and a pedal, basically consisting of the " second half " of the vocoder, but with manual filter controls, needing a highly trained operator.