The first possibility results in a closed interval of tangent points in the f-plane, the end points of which fall into category ( B ) or ( C ).

A quadratic Bézier curve is the path traced by the function B ( t ), given points P < sub > 0 </ sub >, P < sub > 1 </ sub >, and P < sub > 2 </ sub >,

Writing B < sub > P < sub > i </ sub >, P < sub > j </ sub >, P < sub > k </ sub ></ sub >( t ) for the quadratic Bézier curve defined by points P < sub > i </ sub >, P < sub > j </ sub >, and P < sub > k </ sub >, the cubic Bézier curve can be defined as a linear combination of two quadratic Bézier curves:

B. Rives points out in his introduction to Tacitus's Germania ( book ) and moreover that the name Boiorix can work in Proto-Germanic as well as Celtic.

If the difference in vapor pressure between the two components A and B is large ( generally expressed as the difference in boiling points ), the mixture in the beginning of the distillation is highly enriched in component A, and when component A has distilled off, the boiling liquid is enriched in component B.

Mark three points A, B, C on the ruler.

The ruler is replaced by a rod with a pencil holder ( point C ) at one end, and two adjustable side pins ( points A and B ) that slide into two perpendicular slots cut into a metal plate.

Other figures, such as lines, triangles, or circles, are named by listing a sufficient number of points to pick them out unambiguously from the relevant figure, e. g., triangle ABC would typically be a triangle with vertices at points A, B, and C.

Thales ' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle.

These E and B fields are also in phase, with both reaching maxima and minima at the same points in space ( see illustrations ).

He and others used this information to achieve a significant and now well-accepted decipherment of Linear B, although many points remain to be clarified.

A positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to both the instantaneous velocity vector v and the B field according to the right-hand rule ( in detail, if the thumb of the right hand points along v and the index finger along B, then the middle finger points along F ).

The more common one occurs when the north-south component B < SUB > z </ SUB > of the interplanetary magnetic field ( IMF ) is appreciable and points southward.

If a and b are distances from the fulcrum to points A and B and if force F < sub > A </ sub > applied to A is the input force and F < sub > B </ sub > exerted at B is the output, the ratio of the velocities of points A and B is given by a / b, so the ratio of the output force to the input force, or mechanical advantage, is given by

Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers ( a, b ) to the Cartesian coordinates of every point in the set.

* In the plane ( d = 2 ), if there are b vertices on the convex hull, then any triangulation of the points has at most 2n − 2 − b triangles, plus one exterior face ( see Euler characteristic ).

* In a Cartesian coordinate system, gcd ( a, b ) can be interpreted as the number of points with integral coordinates on the straight line joining the points ( 0, 0 ) and ( a, b ), excluding ( 0, 0 ).

The lines connecting three points correspond to the group operation: a, b, and c on one line means a + b = c, a + c = b, and b + c = a.

The open interval ( a, b ) has the same measure, since the difference between the two sets consists only of the end points a and b and has measure zero.

For a b, the interval is the set of points x satisfying a x and x b, also written a x b. It contains at least the points a and b. One may choose to extend the definition to all pairs ( a, b ).

Now let us imagine a wing of B-52's, on alert near their `` positive control ( or fail-safe ) points '', the spots on the map, many miles from Soviet territory, beyond which they are forbidden to fly without specific orders to proceed to their targets.

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.

In Figure 2, the points in the network are designated by a letter accompanied by a number.

As Critic Walter Kerr points out: `` Adaptations, so long as they are good, still qualify as creative ''.

The Kansas City and the Topeka KCs are arranging that Juniors who win at their shows will be qualified to win points for Westminster.

Such locks are nearly always used where the switch points `` face '' oncoming traffic.

The lock insures that the points are thrown all the way with no chance that a wheel flange will snag on a partly thrown point.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

First, for any value of T for which all values of f{t} are ordinary points the number of values of f{t} must be odd.

The remaining ( incomplete ) components all have an even number of ordinary points at any argument, and are defined only on a proper sub-interval of Aj.

We must now show that on some component of the graph there exist two points for which the corresponding diagonal points in the C-plane are on opposite sides of C.

These are defined by a simple involutorial transformation of the points in which a general line meets a nonsingular quadric surface bearing a curve of symbol Af.

A general line L meets Q in two points, Af and Af, through each of which passes a unique generator of the regulus, Af, whose lines are simple secants of Aj.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

The invariant lines are the lines of the congruence of secants of **zg, since each of these meets Q in two points which are invariant.

Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.

If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.

With respect to this view, two points are worth making.

Less ambitious freeway plans may be more successful -- especially when the roadways and interchanges are raised, allowing for cross access at many points and providing parking areas below the ramp.

The brief notes introducing each work offer salient historical or technical points, and many listeners are probably grateful for being intelligently taken by the hand through an often difficult maze.

The Rockies have many `` Aspencades '', which are organized tours of the aspen areas with frequent stops at vantage points for viewing the golden panoramas.