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Page "General position" ¶ 13
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For and points
For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.
For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.
For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.
For all these points he relies exclusively on Berle and Means's study of 1932, The Modern Corporation And Private Property.
: For a detailed presentation of the various points of view around the definition of " algorithm " see Algorithm characterizations.
For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.
For example, using Cartesian coordinates on the plane, the distance between two points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >) is defined by the formula
For two geometric objects P and Q represented by the relations P ( x, y ) and Q ( x, y ) the intersection is the collection of all points ( x, y ) which are in both relations.
For example, Barrett points out that the Pastoral Epistles are concerned that ministers of the generation of Timothy and Titus should pass on the doctrine they had received to the third generation.
For example, the graph contains the points ( 1, 1 ), ( 2, 0. 5 ), ( 5, 0. 2 ), ( 10, 0. 1 ), ... As the values of x become larger and larger, say 100, 1000, 10, 000 ..., putting them far to the right of the illustration, the corresponding values of y,. 01,. 001,. 0001, ..., become infinitesimal relative to the scale shown.
For purposes of scoring and reference, each player is identified by one of the points of the compass and thus North and South play against East and West.
For example, if the player rolls a 6 and a 3 ( notated as " 6-3 "), that player must move one checker six points forward, and another or the same checker three points forward.
For example, the real line equipped with the discrete topology is closed and bounded but not compact, as the collection of all singleton points of the space is an open cover which admits no finite subcover.
For example, the file to which the link < tt >/ bin / ls </ tt > points in a typical Unix-like system probably has a defined size that seldom changed.
For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 4.
For a function of one variable, f, the set of all points ( x, y ) where y
For example, philosophy professor Robert Carroll points to Dianetics ' lack of empirical evidence:
For a set of scattered points in the plane, the diameter of the points is the same as the diameter of their convex hull.
For many cases, the boiling points of the components in the mixture will be sufficiently close that Raoult's law must be taken into consideration.
For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.
For the current loop, the magnetic dipole moment points through the loop ( according to the right hand grip rule ), with a magnitude equal to the current in the loop times the area of the loop.
For a set of points on the same line there is no Delaunay triangulation ( the notion of triangulation is degenerate for this case ).

For and plane
For if it did, the plane of L and l' would contain two generators of Af, which is impossible.
For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.
For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.
`` For three days now a German reconnaissance plane has been over the city taking pictures.
For an object swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope.
For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.
For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.
For example, there are two fundamental operations on the plane.
For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation
For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz-plane ( z is the vertical axis ).
For example an F < sub > 2 </ sub > fold, with an S < sub > 2 </ sub > axial plane foliation would be the result of a D < sub > 2 </ sub > deformation.
For example, the sphere and torus are orientable, while the real projective plane is not ( because deleting a point or disk from the real projective plane produces the Möbius strip ).
For example, in the first Tomb Raider game manual, Lara Croft is said to have survived a plane crash in the Himalayas at the age of twenty one, and was later disowned by her parents, who are still living.
For example, if the given manifold is a 2-sphere, one can picture the tangent space at a point as the plane which touches the sphere at that point and is perpendicular to the sphere's radius through the point.
For N cities randomly distributed on a plane, the algorithm on average yields a path 25 % longer than the shortest possible path.
For example, during the development of the SR-71 Blackbird spy plane, Lockheed engineers at the " Skunk Works " under Clarence " Kelly " Johnson used unobtainium as a dysphemism for titanium.
For example, estimates of position on a plane may have less certainty in one direction than another.
For the plane wave ( left ), the wave-like probability distribution ψ the particle is likely to be found anywhere, due to the periodicity of the wave.

For and on
`` For Christ's sake, don't waste your powder on one of 'em ''!!
For although I had crossed a corner of the hall on my way to the toilet I still could not tell for sure how far to the rear the darkness extended.
For less than a dozen miles from the unplowed land of the dead man lived another settler who had ignored the warnings that his existence might be foreclosed on -- a blatant and defiant rustler named Fred Powell.
For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.
For last-ditch emergencies SAC has alternate command posts on KC-135 jet tankers.
For these centers, too, are on the gold circuit.
For the beatnik, like the hipster, is in opposition to a society that is based on the repression of the sex instinct.
For over a hundred years Southerners have felt that the North was picking on them.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
The second specific comment was the report of Eisenhower's Commission on National Goals, titled Goals For Americans.
For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.
For the figure of Vincent Berger Malraux has obviously drawn on his studies of T. E. Lawrence ( though Berger fights on the side of the Turks instead of against them ), and like both Lawrence and Malraux himself he is a fervent admirer of Nietzsche.
For every person on Taiwan, there are sixty in Mainland China.
Small Business Administration, What It Is, What It Does, SBA Services For Community Economic Development, and various other useful publications on currently important management, technical production, and marketing topics are available, on request, from Small Business Administration, Washington 25, D.C..
For many years a state tax on cities and towns was paid by the several municipalities to the state from the proceeds of the general property tax.
and overhead projector transparency sets on the subjects of Military Sanitation: First Aid For Soldiers ; ;
In May 1960, the Armed Forces Institute of Pathology began a series of articles on the `` Medical Museum '', and in June, the Institute started contributing a regular monthly `` Case For Diagnosis ''.
For each State ( except Puerto Rico, Guam, the Virgin Islands, and, prior to 1962, Alaska and Hawaii ) determine average per capita income based on the last three years.
For readjustment to the U.S., volunteers should be given some separation allowance at the end of their overseas service, based on the length of time served.
For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.
For change is dependent on the possibilities that individual men glimpse for the future.

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