Parabola Quotes

It is a curve each of them feels, unmistakably. It is the parabola. They must have guessed, once or twice - guessed and refused to believe - that everything, always, collectively, had been moving toward that purified shape latent in the sky, that shape of no surprise, no second chance, no return. Yet they do move forever under it, reserved for its own black-and-white bad news certainly as if it were the rainbow, and they its children.... (Thomas Pynchon)

Human history, like all great movements, was cyclical, and returned to the point of beginning. the idea of indefinite progress in a right line was a chimera of the imagination, with no analogue in nature. The parabola of a comet was perhaps a better illustration of the career of humanity. Tending upward and sunward from the aphelion of barbarism, the race attained the perihelion of civilization only to plunge downward once more to its nether goal in the regions of chaos.

Edward Bellamy

As an artist, you don't think about the parabola or the arc you're describing or where you're going to ultimately end up, you're just kind of crawling around, seeing what's out there.

Michael Nesmith

Along a parabola life like a rocket flies, Mainly in darkness, now and then on a rainbow.

Andrey Voznesensky

First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right angled cone (i.e., a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...

Archimedes

The Ellipse is the most simple of the Conic Sections, most known, and nearest of Kin to a Circle, and easiest describ'd by the Hand in plano. Though many prefer the Parabola before it, for the Simplicity of the Æquation by which it is express'd. But by this Reason the Parabola ought to be preferr'd before the Circle it self, which it never is. Therefore the reasoning from the Simplicity of the Æquation will not hold. The modern Geometers are too fond of the Speculation of Æquations.

Isaac Newton

Menæchmus, a pupil of Eudoxus, and a contemporary of Plato, found the two mean proportionals by means of conic sections, in two ways, (α) by the intersection of two parabolas, the equations of which in Cartesian co-ordinates would be x2=ay, y2=bx, and (β) by the intersection of a parabola and a rectangular hyperbola, the corresponding equations being x2=ay, and xy=ab respectively. It would appear that it was in the effort to solve this problem that Menæchmus discovered the conic sections, which are called, in an epigram by Eratosthenes, "the triads of Menæchmus."

Thomas Little Heath

It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts.

Galileo Galilei

It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

Galileo Galilei

It is not known so generally that Kepler was... a geometrician and algebraist of considerable power, and that he, Desargues, and perhaps Galileo, may be considered as forming a connecting link between the mathematicians of the renaissance and those of modern times. Kepler's work in geometry consists rather in certain general principles enunciated, and illustrated by a few cases, than in any systematic exposition of the subject. In a short chapter on conics inserted in his Paralipomena, published in 1604, he lays down what has been called the principle of continuity, and gives as an example the statement that a parabola is at once the limiting case of an ellipse and of a hyperbola; he illustrates the same doctrine by reference to the foci of conics (the word focus was introduced by him); and he also explains that parallel lines should be regarded as meeting at infinity. He introduced the use of the eccentric angle in discussing properties of the ellipse.

Johannes Kepler

Kepler's achievements in mathematics would alone have been sufficient to win for him enduring fame; he first enunciated clearly the principle of continuity in mathematics, treating the parabola as at once the limiting case of the ellipse and the hyperbola, and showing that parallel lines can be regarded as meeting at infinity; he introduced the word 'focus' into geometry; while in his Stereometria Dolorum, published 1615, he applied the conception to the solution of certain volumes and areas by the use of infinitesimals, thus preparing the way for Desargues, Cavalieri, Barrow, and the developed calculus of Newton and Leibniz. (Johannes Kepler)