Now the only way in which all curves of the image family of Af can pass through a fixed point is to have a generator of Af which is not a secant but a tangent of **zg, for then any point on such a generator will be transformed into the point of tangency.

Fermat always started with an algebraic equation and then described the geometric curve which satisfied it, while Descartes starts with geometric curves and produces their equations as one of several properties of the curves.

The chromatographic separation behavior was then unknown for the element 97, but was anticipated by analogy with terbium ( see elution curves ).

The Vajrayana system states that the central channel ( avadhūtī ) begins at the point of the third eye, curves up to the crown of the head, and then goes straight down to the lower body.

And, reflecting the then lack of international standards, sizes varied and not all were built as ovals-for example, the oldest velodrome in the UK, at Preston Park, Brighton ( 1877 ), is 579m long and features four straights linked by banked curves, while the 536m Portsmouth velodrome has a single straight linked by one long curve.

Often a vector field is drawn by curves ( field lines ) following the " flow "; the magnitude of the vector field is then the line density, and the flux through a surface is the number of lines.

In modern candles, the wick is constructed so that it curves over as it burns ( see picture on the right ), so that the end of the wick gets oxygen and is then consumed by fire — a self-trimming wick.

From a geometric standpoint, if we consider f ( x, θ ) as a function of two variables then the family of probability distributions can be viewed as a family of curves parallel to the x-axis, while the family of likelihood functions are the orthogonal curves parallel to the θ-axis.

If two goods are perfect substitutes then the indifference curves will have a constant slope since the consumer would be willing to switch between at a fixed ratio.

If two goods are perfect complements then the indifference curves will be L-shaped.

He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves ( 1696 ) and isoperimetry ( 1700, 1701 ).

Route 18 then interchanges with County Route 622 ( River Road ), Campus Road ( Rutgers ' Busch Campus and stadium ), Metlars Lane ( Rutgers ' Livingston Campus and Louis Brown Athletic Center ), where the route curves to the west before ending near Buckingham Drive.

He reasoned that if the animals were showing insight, then their time to escape would suddenly drop to a negligible period, which would also be shown in the learning curve as an abrupt drop ; while animals using a more ordinary method of trial and error would show gradual curves.

The river then flows generally east and a little north with some large curves for 15 miles ( 24 kilometers ) to the city of Williamsport, followed by the borough of Montoursville ( both on the north bank ) as well as the boroughs of Duboistown and South Williamsport ( on the south bank ).

It is multiplexed with US 301 and 441 until it reaches Florida SR 492 ( Northwest 10th Street ), then makes a sharp turn onto NW 10th Street then curves northwest through Williston, Perry, Tallahassee, and beyond.

The path travels east from Kipton and then curves northeast, going through Oberlin and continuing on to Elyria.

To make this graph paper, one places a grid of parallels and meridians on the hemisphere, and then stereographically projects these curves to the disk.

Y are both real or complex irreducible curves, X has degree m and Y has degree n then the number of intersection points does not exceed mn.

If P is a common point of two plane algebraic curves X and Y that is a non-singular point of both of them and, moreover, the tangent lines to X and Y at P are distinct then the intersection multiplicity is one.

If the curves X and Y have a common tangent at P then the multiplicity is at least two.

The use of Edwards curves needs fewer modular multiplications and less time then the use of Montgomery curves or Weierstrass curves ( other used methods ).

As a concentration gradient develops from the diffusion of the chemoattractant into the gel, various cell populations requiring different stimulation levels to migrate can then be visualized over time using microphotography as they tunnel upward through the gel against gravity along the gradient.

The gas then flows up through the base through a small hole at the bottom of the barrel and is directed upward.

If we postulate that coral reefs were eroded down to the glacial sea level, then coral reefs have grown 120m upward since the end of the recent glacial.

The upward arc motion is stopped, and then the attacking foot is lowered so as to strike the target from above.

For example, if one finds a neuron with preference for upward motion, and then we use an electrode to stimulate it, the monkey becomes more likely to report ' upward ' motion.

Players advance the football, a spherical leather ball, up the field with a combination of carrying, bouncing, kicking, hand-passing, and soloing ( dropping the ball and then toe-kicking the ball upward into the hands ).

After another instrument indicated that all turret systems were still operational, the loader would gently push the 152mm fixed round into the breech and watch the breech block slowly rotate upward, then forward into the breech, then again, wait for the lights.

The new spring shoots are sometimes called " candles "; they are covered in brown or whitish bud scales and point upward at first, then later turn green and spread outward.

If, on the contrary, the upper air is cooler than predicted by the adiabatic lapse rate, then when the air parcel rises to its new height it will have a higher temperature and a lower density than its surroundings, and will continue to accelerate upward.

This flame provides sufficient heat to keep the candle burning via a self-sustaining chain of events: the heat of the flame melts the top of the mass of solid fuel, the liquefied fuel then moves upward through the wick via capillary action, and the liquefied fuel is then vaporized to burn within the candle's flame.

He becomes an extremely well behaved ACCURSED WANDERER, then dies, and in POST-HUMOUS FANTASY sequences-though he is too wise really to question the fact of death, and too calmly confident to have doubts about his continuing upward mobility-he learns greater wisdom.

As a general rule, lower altitudes tend to have higher temperatures where the sun heats the ground and that heat is then radiated upward, but as the air begins to rise it is trapped by ( 1 ) the surrounding elevation and ( 2 ) the weight of the air ( essentially the atmospheric pressure ) above it.

The convention is that a sawtooth wave ramps upward and then sharply drops.

The male lowers its head, charges, and then slashes upward with its tusks.

Contact lenses are typically inserted into the eye by placing them on the index finger with the concave side upward and then using the index finger to place the lens on the eye.

If we define the exobase as the height at which upward traveling molecules experience one collision on average, then at this position the mean free path of a molecule is equal to one pressure scale height.

A post-WWII building boom then pushed the population upward to 353 in 1960.

If, on top of that, the asker also doesn't know that they should search its expansion before asking someone, then once again, there may be legitimate resentment in his subordinates that they must " manage upward " to such a mollycoddling degree, because the very GIYF principle itself has been shifting into the area of " general knowledge that is lacked only by incompetents.

His mustache drooped gracefully beyond the corners of his mouth and then turned upward at the ends.

A slow upward drift then occurs toward the field-cooled magnetization.

When an action potential is triggered, the membrane potential abruptly shoots upward, often reaching as high as + 100 mV, then equally abruptly shoots back downward, often ending below the resting level, where it remains for some period of time.

If a deeper aquifer has a lower permeable unit that confines the upward flow, then the water level in a well screened in this aquifer may rise to a level that is greater or less than the elevation of the actual water table.