Parabolic Sentence Examples
Here Jesus' teaching contains no parables and but three allegories, the Synoptists present it as parabolic through and through.
It consists of two parabolic branches tending in opposite directions.
The above formulae apply only to a parabolic trapezette.
For parabolic or bowstring girders, when r =8, the limiting span is 1280 ft.
The epithets hyperbolic and parabolic are of course derived from the conic hyperbola and parabola respectively.Advertisement
He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes.
In Short's first telescopes the specula were of glass, as suggested by Gregory, but he afterwards used metallic specula only, and succeeded in giving to them true parabolic and elliptic figures.
The reflecting surface is first ground to a spherical form, the parabolic figure being given in the final process by regulating the size of the pitch squares and the stroke of the polishing machine.
The result might of course have been inferred from the theory of the parabolic funicular in 2.
This applies to an elliptic or hyperbolic orbit; the case of the parabolic orbit may be examired separately or treated as a limiting case.Advertisement
Even when the resolution is regularized by the action of external vibrations of suitable frequency, as in the beautiful experiments of Savart and Plateau, the drops must still come into contact before they reach the summit of their parabolic path.
Names may also be used for the different forms of infinite branches, but we have first to consider the distinction of hyperbolic and parabolic. The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other.
Next, if the line S2 touch at b the arc aa so that the two portions ab, ba lie on the same side of the line Sl, then projecting the figure as before, the tangent at b, that is, the line S2 itself, is projected to infinity; the arc ab is projected into a parabolic leg, and at the same time the arc ba is projected into a parabolic leg, having at infinity the same direction as the other leg, but so that the two legs may or may not belong to the same branch.
And we thus see that the two parabolic legs represent a contact of the line infinity with the curve, - the point of contact being of course the point at infinity determined by the common direction of the two legs.
The two legs of a parabolic branch may converge to ultimate parallelism, as in the conic parabola, or diverge to ultimate parallelism, as in the semi-cubical parabola y 2 = x 3, and the branch is said to be convergent, or divergent, accordingly; or they may tend to parallelism in opposite senses, as in the cubical parabola y = x 3 .Advertisement
He, moreover, threw out the suggestion (in his Cometographia, 1668) that comets move round the sun in orbits of a parabolic form.
The values of d 2 E/dt 2 agree as well as can be expected, considering the difference of the ranges of temperature and the great variety in the methods of observation adopted; they are calculated assuming the parabolic formula, which is certainly in many cases inadequate.
In this particular case the parabolic formula appears to be undoubtedly inadequate.
It consists in half of a short focused parabolic mirror, which concentrates all the light coming from the one side on to the object.
In 1937 another radio engineer, Grote Reber, began work with a parabolic reflector antenna 9.7 m in diameter.Advertisement
Tan Lei (Warwick) Orbits correspondence in parabolic implosion.
The LMT consists of a 3 m diameter parabolic dish that holds four gallons of liquid mercury.
Had the elevation of the parabolic mirror been a few yards higher, none could have lived to tell the tale.
The design is an ISCC involving the operation of a parabolic trough solar plant and a combined-cycle gas turbine using naphtha.
Companies such as Solar Millenium AG, headquartered in Erlangen, Germany, now market solar chimney power plants, along with parabolic troughs.Advertisement
This remark applies to the finding of the area of a parabolic segment (mechanical solution) and of a spiral, the surface and volume of a sphere and of a segment thereof, and the volume of any segments of the solids of revolution of the second degree.
The second book in ten propositions is devoted to the finding the centres of gravity (I) of a parabolic segment, (2) of the area included between any two parallel chords and the portions of the curve intercepted by them.
To illustrate the method, suppose that we use the chordal area C1, and that the trapezette is in fact parabolic. The difference between C 1 and the true area is made up of a series of areas bounded by chords and arcs; this difference becoming less as we subdivide the figure into a greater number of strips.
Ingalls, U.S.A., for approximating to a high angle trajectory in a single arc, which assumes that the mean density of the air may be taken as the density at two-thirds of the estimated height of the vertex; the rule is founded on the fact that in an unresisted parabolic trajectory the average height of the shot is two-thirds the height of the vertex, as illustrated in a jet of water, or in a stream of bullets from a Maxim gun.
The length of a parabolic arc can be obtained by the methods of the infinitesimal calculus; the curve is directly quadrable, the area of any portion between two ordinates being two thirds of the circumscribing parallelogram.
Their reward was a session in a weightless environment aboard a parabolic flight which is normally used to train astronauts.
Shaped or parabolic skis were first made by Elan and featured a deeper sidecut and shorter length.
Elliptic orbits, and a parabolic orbit considered as the special case when the eccentricity of the ellipse is 1, are almost the only ones the astronomer has to consider, and our attention will therefore be confined to them in the present article.
In a letter, Del movimento della cometa apparsa it mese di decembre 1664, published in 1665 under the pseudonym Pier Maria Mutoli, he was the first to suggest the idea of a parabolic path; and another of his astronomical works was Theorica mediceorum planetarum ex causis physicis deducta (Florence, 1666), in which he considered the influence of attraction on the satellites of Jupiter.
These doctrinal interpretations introduce the economy of blinding the Jews into the parabolic teaching; the declaration as to the redemptive character of the Passion into the sayings; the sacramental, institutional words into the account of the Last Supper, originally, a solemnly simple Messianic meal; and the formal night-trial before Caiaphas into the original Passion-story with its informal, morning decision by Caiaphas, and its one solemn condemnation of Jesus, by Pilate.
The great variety in the apparent motions of meteors proves that they are not directed from the plane of the ecliptic; hence their orbits are not like the orbits of planets and short-period comets, which are little inclined, but like the orbits of parabolic comets, which often have great inclinations.
A trapezette of this kind will be called a parabolic trapezette.
It follows that, by taking two ordinates in a certain position with regard to the bounding ordinates, the area of any parabolic trapezette whose top passes through their extremities can be expressed in terms of these ordinates and of the breadth of the trapezette.
In the case of the parabolic trapezette, for instance, xu is of degree 3 in x, and therefore the first moment is lh(xouo+4xlui-+x2u2).
Then we can take the strips in pairs, and treat each pair as a parabolic trapezette.
Scott (Comptes rendus, 1861, 53, p. 108) any sound whatever may be made to record its trace on the paper by means of a large parabolic cavity resembling a speaking-trumpet, which is freely open at the wider extremity, but is closed at the other end by a thin stretched membrane.
Let the length of half the parabolic chain be called s, then 4.
It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.
In this case it is found that the body falls relatively to the ship as if the latter were at rest, and alights at the foot of the mast, having consequently pursued a parabolic path relatively to the earth.
If the dimensions of the bar are suitably chosen, the distribution of temperature is always very nearly parabolic, so that it is not necessary to determine the value of the critical current C 2 = hpllaRo very accurately, as the correction for external loss is a small percentage in any case.
If two roots are imaginary the equation is y 2 =(x 2 +a 2) (x - b) and the curve resembles the parabolic branch, as in the preceding case.
Another corollary is that in the case of a body moving in a parabolic orbit the velocity at any moment is that which would be acquired by the body in falling from an infinite distance to the place it occupies at the moment.
The candle holder with the parabolic reflector casts a golden light upwards or pools it along the length of a wall.