Quotes about axis

A collection of quotes on the topic of axis, earth, time, timing.

Quotes about axis

“The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple”

Archimedes book The Method of Mechanical Theorems

of the portion adjacent to the base
Proposition presumed from previous work.
The Method of Mechanical Theorems

“Any segment of a right-angled conoid (i. e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment”

Archimedes book The Method of Mechanical Theorems

Proprosition 4.
The Method of Mechanical Theorems

Time

“If we suppose the distance of the fixed stars from the sun to be so great that the diameter of the earth's orbit viewed from them would not subtend a sensible angle, or which amounts to the same, that their annual parallax is quite insensible; it will then follow that a line drawn from the earth in any part of its orbit to a fixed star, will always, as to sense, make the same angle with the plane of the ecliptic, and the place of the star, as seen from the earth, would be the same as seen from the sun placed in the focus of the ellipsis described by the earth in its annual revolution, which place may therefore be called its true or real place.
But if we further suppose that the velocity of the earth in its orbit bears any sensible proportion to the velocity with which light is propagated, it will thence follow that the fixed stars (though removed too far off to be subject to a parallax on account of distance) will nevertheless be liable to an aberration, or a kind of parallax, on account of the relative velocity between light and the earth in its annual motion.
For if we conceive, as before, the true place of any star to be that in which it would appear viewed from the sun, the visible place to a spectator moving along with the earth, will be always different from its true, the star perpetually appearing out of its true place more or less, according as the velocity of the earth in its orbit is greater or less; so that when the earth is in its perihelion, the star will appear farthest distant from its true place, and nearest to it when the earth is in its aphelion; and the apparent distance in the former case will be to that in the latter in the reciprocal proportion of the distances of the earth in its perihelion and its aphelion. When the earth is in any other part of its orbit, its velocity being always in the reciprocal proportion of the perpendicular let fall from the sun to the tangent of the ellipse at that point where the earth is, or in the direct proportion of the perpendicular let fall upon the same tangent from the other focus, it thence follows that the apparent distance of a star from its true place, will be always as the perpendicular let fall from the upper focus upon the tangent of the ellipse. And hence it will be found likewise, that (supposing a plane passing through the star parallel to the earth's orbit) the locus or visible place of the star on that plane will always be in the circumference of a circle, its true place being in that diameter of it which is parallel to the shorter axis of the earth's orbit, in a point that divides that diameter into two parts, bearing the same proportion to each other, as the greatest and least distances of the earth from the sun.”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

Star, Sense, Light, Distant

“We, as the winners [of WW1 & WW2], created a common country [Yugoslavia] with our enemies [Croats & Muslims], who were on the defeated side [Central Powers & Axis Powers].”

Ratko Mladić (1943) Commander of the Bosnian Serb military

From interview with PTC Б1, 1992
Interviews (1993 – 1995)

Country

“The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.”

Archimedes book The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

Way

“Your rights reach down where all owners meet, in Hell's
Pointed exclusive conclave, at earth’s centre
(Your spun farm's root still on that axis dwells);
And up, through galaxies, a growing sector.”

William Empson (1906–1984) English literary critic and poet

"Legal Fiction", line 9; cited from John Haffenden (ed.) The Complete Poems (London: Allen Lane, 2000) p. 37.
The Complete Poems

Hell

“In war, theory is all right so far as general principles are concerned; but in reducing general principles to practice there will always be danger. Theory and practice are the axis about which the sphere of accomplishment revolves.”

Napoleon I of France (1769–1821) French general, First Consul and later Emperor of the French

Napoleon : In His Own Words (1916)

War

“Use of better planetary parameters, the innovations in astronomical methods, and the concise style of exposition of Aryabhatiya makes it an excellent text book on Astronomy. As opposed to the geostationary theory, Aryahabata held the view that the earth rotates on its axis. His estimate of the period of the sidereal rotation of earth was 23 hours 56 min, and 4.1 s is close to the actual value.”

Aryabhata (476–550) Indian mathematician-astronomer

In, p. 254.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

Books, Making love

“I never did learn how to live in the moment, but I did learn that moments could be wasted and the world would continue to spin on its axis.”

Eloisa James (1962) American academic

Source: Paris in Love

World, Learning

“The silence grew deeper, so deep that if you listened carefully you might very well catch the sound of the earth revolving on its axis.”

Haruki Murakami book Kafka on the Shore

Source: Kafka on the Shore

Silence

“Between shame and shamelessness lies the axis upon which we turn; meteorological conditions at both these poles are of the most extreme, ferocious type. Shamelessness, shame: the roots of violence.”

Salman Rushdie Shame

Source: Shame

“A book is not an isolated being: it is a relationship, an axis of innumerable relationships”

Jorge Luis Borges book Ficciones

"Note on (toward) Bernard Shaw" ["Nota sobre (hacia) Bernard Shaw"] (1951)
Other Inquisitions (1952)
Source: Ficciones
Context: A book is more than a verbal structure or series of verbal structures; it is the dialogue it establishes with its reader and the intonation it imposes upon his voice and the changing and durable images it leaves in his memory. A book is not an isolated being: it is a relationship, an axis of innumerable relationships.

Books

“Literature is not exhaustible, for the sufficient and simple reason that a single book is not. A book is not an isolated entity: it is a narration, an axis of innumerable narrations. One literature differs from another, either before or after it, not so much because of the text as for the manner in which it is read.”

Jorge Luis Borges book Other Inquisitions

"Note on (toward) Bernard Shaw"
Variant translation: A book is not an autonomous entity: it is a relation, an axis of innumerable relations. One literature differs from another, be it earlier or later, not because of the texts but because of the way they are read: if I could read any page from the present time — this one, for instance — as it will be read in the year 2000, I would know what the literature of the year 2000 would be like.
Other Inquisitions (1952)

Books, Literature, Reading

“Drink your tea slowly and reverently, as if it is the axis on which the whole earth revolves”

Thich Nhat Hanh (1926) Religious leader and peace activist

The Miracle of Mindfulness (1999)
Context: Drink your tea slowly and reverently, as if it is the axis on which the whole earth revolves—slowly, evenly, without rushing toward the future. Live the actual moment. Only this actual moment is life.

Drink, Tea

“I imagine Johnny Mathis hates Bin Laden as much as I do, but could Johnny agree Bin Laden had a better speechwriter than Bush? "Axis of Evil"? Come on. "A swimmer in the ocean does not fear the rain" is much more powerful propaganda. Poetic, even.”

John Waters (1946) American filmmaker, actor, comedian and writer

Source: Role Models

Hate, Fear, Imagination, Evil

“It was strange how your world could shift on its axis and everything you trusted could invert itself in what seemed like no time at all.”

Cassandra Clare The City of Lost Souls

Source: City of Lost Souls

World, Time

“It was a kiss to level mountains and shake stars from the sky. It was a kiss to make angels faint and demons weep… a passionate, demanding, soul-searing kiss that nearly knocked the earth off its axis.”

Lisa Kleypas (1964) American writer

Source: Tempt Me at Twilight

Angels, Soul, Mountain, Star

“The true axis of evil in America is the brilliance of our marketing combined with the stupidity of our people.”

Bill Maher (1956) American stand-up comedian

People, Stupidity, Evil

“Felicity and I watch the dancers moving as one. They spin about like the earth on it's axis, enduring the dark, waiting for the sun.”

Libba Bray book The Sweet Far Thing

Source: The Sweet Far Thing

Waiting, Sun

“When I asked Bhutto what he thought of Assad, he described the Syrian leader as “The Levanter.” Knowing that, like himself, I was a keen reader of thrillers, the Pakistani Prime Minister knew that I would get the message. However, it was only months later when, having read Eric Ambler’s 1972 novel The Levanter that I understood Bhutto’s one-word pen portrayal of Hafez Al-Assad. In The Levanter the hero, or anti-hero if you prefer, is a British businessman who, having lived in Syria for years, has almost “gone native” and become a man of uncertain identity. He is a bit of this and a bit of that, and a bit of everything else, in a region that is a mosaic of minorities. He doesn’t believe in anything and is loyal to no one. He could be your friend in the morning but betray you in the evening. He has only two goals in life: to survive and to make money… Today, Bashar Al-Assad is playing the role of the son of the Levanter, offering his services to any would-be buyer through interviews with whoever passes through the corner of Damascus where he is hiding. At first glance, the Levanter may appear attractive to those engaged in sordid games. In the end, however, the Levanter must betray his existing paymaster in order to begin serving a new one. Four years ago, Bashar switched to the Tehran-Moscow axis and is now trying to switch back to the Tel-Aviv-Washington one that he and his father served for decades. However, if the story has one lesson to teach, it is that the Levanter is always the source of the problem, rather than part of the solution. ISIS is there because almost half a century of repression by the Assads produced the conditions for its emergence. What is needed is a policy based on the truth of the situation in which both Assad and ISIS are parts of the same problem.”

Amir Taheri (1942) Iranian journalist

Opinion: Like Father, Like Son http://www.aawsat.net/2015/02/article55341622/opinion-like-father-like-son, Ashraq Al-Awsat (February 20, 2015).

Life, Money, Truth, Game

“We all know that sun rises in the east and sets in the west, and earth spins on its axis from west to east. But on that day my jet plan was at 60 degree latitude near Greenland and the plane exceeded the speed of rotation of the earth on its axis so the sun was found moving from west towards east.”

Jayant Narlikar (1938) Indian physicist

His scientific explanation with regard to the position of sun closer to the west horizon, and the sun was going up, which he had noticed.
When Prof Jayant Narlikar saw the sun rise in the west

Sun, Speed

“She understood too much. She understood that she had reached her destiny point, that time and the circumstances of her life had conspired to bring her to this place. For one ecstatic moment she was the axis on which the stars revolved.”

Robert Charles Wilson book Bios

Source: Bios (1999), Chapter 15 (p. 140)

Life, Star, Time

“Elementarism has been born partly in reaction to an over-dogmatic and often narrow-minded application of NeoPlasticism [a critic on his former artist-companion Piet Mondrian, partly as its consequence but ultimately from what is primarily a radical correction of Neo-plastic ideas. Elementarism rejects the demands of pure statics which led to sterility and to the laming of creative potentialities. Instead of denying Time and Space, Elementarism acknowledge these elements to be the most elementary means for creating a new plastic expression... In contrast to the Neo-plastic [= De Stijl] manner of expression, which is restricted to two dimensions [the plane], Elementarism acknowledges a form of plastic expression in four dimensions, the realm of space-time. In opposition to the orthogonal style of plastic expression, which is 'homogeneous' with natural construction, Elementarism postulates a 'heterogeneous' contrasting, unstable manner of plastic expression based upon planes oblique in relation to the static, perpendicular axis of gravitation”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Quote of van Doesburg, in van 'Painting and plastic art': Elementarism – fragment of a manifesto' Paris, December 1926 – April 1927; in De Stijl, Theo van Doesburg – series XIII, 78, 1926–27, pp. 82–87
1926 – 1931

Idea, Nature, Time

“Purposeful life needs an axis or hinge to which it is firmly fixed and yet around which it can freely revolve. As I see it, this axis or hinge has been, in my own case, strongly enough, not the love of science, not even the love of Nature but a certain abstract idealism or belief in the value of the human spirit and the virtue of human endeavour and achievement. The nearest point to which I can trace this source of idealism in my recollection of reading Edwin Arnold's great book, The Light of Asia. I remember being powerfully moved by the story of Siddhartah's great renunciation, of his search for truth and of his final enlightenment.”

C. V. Raman (1888–1970) Indian physicist

From Chandrasekhara Venkata Raman:A Legend of Modern India's Science, 22 November 2013, Official Government of India's website Vigyan Prasar http://www.vigyanprasar.gov.in/scientists/cvraman/raman1.htm,

Love, Life, Truth, Books

“There is much that is lacking in the political education of American troops, for which army policy cannot be criticized in view of the similar apathy on the home front. Late in the struggle the army became aware of this weakness among our soldiers. The Information and Education Division was then organized to repair this gap in the psychological preparation for combat. Some progress in the face of considerable resistance has been made by this service, but at the time of writing the men still have only a dim comprehension of the meaning of the fascist political state and its menace to our liberal democratic government. The war is generally regarded as a struggle between national states for economic empires. The men are not fully convinced that our country was actually threatened, or, if so, only remotely, or because of the machinations of large financial interests. In such passive attitudes lie the seeds of disillusion, which could prove very dangerous in the postwar period. Certainly they stand in startling contrast with the strong political and national convictions of our Axis enemies, which can inspire their troops, when the occasion demands, with a fanatical and religious fervor. Fortunately, strong intellectual motivation has not proved to be of the first importance to good morale in combat. The danger of this lack seems to be less to the prospect of military success than to success in the peace and to stability in the postwar period.”

Roy R. Grinker, Sr. (1900–1993) American psychiatrist and neurologist

Source: Men Under Stress, 1945, p. 38-39 cited in: The Clare Spark Blog (2009) Strategic Regression in “the greatest generation” http://clarespark.com/2009/12/09/strategic-regression-in-the-greatest-generation/ December 9, 2009

Men, War, Lie, Education

“The Executive order that was issued on February 19, 1942, was for the sole purpose of prosecuting the war with the Axis Powers, and ceased to be effective with the end of those hostilities. Because there was no formal statement of its termination, however, there is concern among many Japanese-Americans that there may yet be some life in that obsolete document. I think it appropriate, in this our Bicentennial Year, to remove all doubts on that matter, and to make clear our commitment in the future.”

Gerald Ford (1913–2006) American politician, 38th President of the United States (in office from 1974 to 1977)

1970s, Proclamation 4417 (1976)

Life, Hostility, War, Thinking

“When the utter absurdity of the Mosaic account of creation became apparent to all thoughtful men, the church changed the reading of the Bible. Then it was pretended that the “days” of creation were vast periods of time. When it was shown to be utterly impossible that the sun revolved around the earth, then the account given by Joshua of the sun standing still for the space of a whole day, was changed into a figure of speech. It was said that Joshua merely conformed to the mode of speech common in his day; and that when he said the sun stood still, he merely intended to convey the idea that the earth ceased turning upon its axis. Is there a sensible man in the world who believes this wretched piece of ignorance?”

Robert G. Ingersoll (1833–1899) Union United States Army officer

My Reviewers Reviewed (lecture from June 27, 1877, San Francisco, CA)

Men, World, Idea, Change

“The notion of the "axis of evil" has an interesting provenance. In early drafts of the President's speech the "axis of evil" was the "axis of hatred", "axis" having been settled on for its associations with the enemy in the second world war. The "axis of hatred" at this point consisted of only two countries, Iran and Iraq. whereas of course the original axis consisted of three (Germany, Italy, Japan). It was additionally noticed that Iran and Iraq, while not both Arab, were both Muslim. So they brought in North Korea.
We may notice, in this embarras of the inapposite, that the Axis was an alliance, whereas Iran and Iraq are blood-bespattered enemies, and the zombie nation of North Korea is, in truth, so mortally ashamed of itself that it can hardly bear to show its face.”

Martin Amis (1949) Welsh novelist

"The Palace of the End" (2003)

War, Truth, World, Evil

“I don't know if men will ever journey again, as we journeyed, to that intersection of latitude and longitude where a shell hangs forever — forever and yet not forever, in space and out of space — on the axis stretching through time from beginning to end.
From the dawn of the nebulae to the twilight of absolute entropy, when the framework of the cosmos has broken down into chaos, still that axis will stretch from dawn to dusk, from beginning to end. For as this world spins on an axis through space, so the sphere of time spins on its own axis.”

Henry Kuttner (1915–1958) American author

Source: The Time Axis (1949), Ch. 1 : Encounter In Rio

Men, World, Time

“My observation of the flight of buzzards leads me to believe that they regain their lateral balance when partly overturned by a gust of wind, by a torsion of the tips of the wings. If the rear edge of the right wing tip is twisted upward and the left downward the bird becomes an animated windmill and instantly begins to turn, a line from its head to its tail being the axis. It thus regains its level even if thrown on its beam’s end, so to speak, as I have frequently seen them. I think the bird also in general retains its lateral equilibrium, partly by presenting its two wings at different angles to the wind, and partly by drawing in one wing, thus reducing its area. I incline to the belief that the first is the more important and usual method….
My business requires that my experimental work be confined to the months between September and January and I would be particularly thankful for advice as to a suitable locality where I could depend on winds of about 15 miles per hour without rain or too inclement weather. I am certain that such localities are rare.”

Wilbur Wright (1867–1912) American aviation pioneer

Letter to Octave Chanute (13 May 1900)

Business, Bird, Thinking, Animals

“the axis of the universe
—love”

E.E. Cummings (1894–1962) American poet

73
73 poems (1963)

Love, Universe

“We, therefore, having directed our inquiry toward a cause that is manifest, sensible, and comprehended by all men, do know that the earth rotates on its own poles, proved by many magnetical demonstrations to exist. For not in virtue only of its stability and its fixed permanent position does the earth posses poles and verticity; it might have had another direction, as eastward or westward, or toward any other quarter. By the wonderful wisdom of the Creator, therefore, forces were implanted in the earth, forces primarily animate, to the end the globe might, with steadfastness, take direction, and that the poles might be opposite, so that on them, as at the extremities of an axis, the movement of diurnal rotation might be performed.”

William Gilbert (astronomer) book De Magnete

As quoted in Gilbert, William. 2013 ed. De Magnete https://books.google.com.mx/books?id=QsLDAgAAQBAJ&printsec=frontcover#v=onepage&q&f=false. Courier Corporation, pp. 328-329. <br class="br">De Magnete (1600)

Wisdom, Men, Animals

“The Rumsfeld-Cheney axis has self-destructed right in front of our eyes, along with the once-proud Perle-Wolfowitz bund that is turning to wax. They somehow managed to blow it all, like a gang of kids on a looting spree, between January and July, or even less. It is genuinely incredible. The U. S. Treasury is empty, we are losing that stupid, fraudulent chickencrap War in Iraq, and every country in the world except a handful of Corrupt Brits despises us. We are losers, and that is the one unforgiveable sin in America.”

Hunter S. Thompson (1937–2005) American journalist and author

2000s, Welcome to the Big Darkness (2003)

War, Stupidity, World, Country

“My mother was a Chinese trapeze artist in pre-war Paris
Smuggling bombs for the underground.
And she met my father at a fete in Aix-en-Provence;
He was disguised as a Russian cadet in the employ of the Axis.”

Colin Meloy (1974) American musician

My Mother was a Chinese Trapeze Artist (5 Songs - 2001)
Lyrics

War

“Life is immense, comprehensive and dynamic. It includes spirit and matter and idealism and pragmatism and rotates round the axis of the noble and the ignoble. Life strives for higher ends. It is a mission, a service, and finally worship.”

Zakir Hussain (politician) (1897–1969) 3rd President of India

Source: Uniqueness of Zakir Husain and His Contributions (1997), p. 22.

Life

“If in two ellipses having a common major axis we take two such arcs that their chords are equal, and that also the sums of the radii vectores, drawn respectively from the foci to the extremities of these arcs, are equal to each other, then the sectors formed in each ellipse by the arc and the two radii vectores are to each other as the square roots of the parameters of the ellipses.”

Johann Heinrich Lambert (1728–1777) German mathematician, physicist and astronomer

Sect. 4, Lemma 26, Insigniores orbitae cometarum proprietates (1761) [Notable properties of comets' orbits] translated by Florian Cajori, A History of Mathematics https://books.google.com/books?id=kqQPAAAAYAAJ (1906) p. 259, from the German of Michel Chasles, Geschichte der Geometrie, haupsächlich mit Bezug auf die neuern Methoden https://books.google.com/books?id=NgYHAAAAcAAJ (1839) p. 183.

“Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

“Proposition 13. The straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the moon move is less than double of the diameter of the moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the sun, but has to it a ratio greater than that which 22 has to 225. But it has to the straight line drawn from the centre of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10125.”

Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

Sun, Parting

“The sword is the axis of the world and grandeur cannot be divided.”

Charles de Gaulle (1890–1970) eighteenth President of the French Republic

L'épée est l'axe du monde et la grandeur ne se divise pas.
in Vers l’armée de métier.
Writings

World

“To rotate on its own axis is not the one movement for the human soul. There is also its wheeling round the Sun of an inexhaustible illumination.”

Sri Aurobindo (1872–1950) Indian nationalist, freedom fighter, philosopher, yogi, guru and poet

Thoughts and Glimpses (1916-17)

Soul, Sun

“When General Osborne came to see me just after the victory, he asked me what I thought should be done to educate the Germans. I said there is only one thing to be done and that is to teach them disobedience, as long as they are obedient so long sooner or later they will be ordered about by a bad man and there will be trouble. Teach them disobedience, I said, make every German child know that it is its duty at least once a day to do its good deed and not believe something its father or its teacher tells them, confuse their minds, get their minds confused and perhaps then they will be disobedient and the world will be at peace. The obedient peoples go to war, disobedient people like peace, that is the reason that Italy did not really become a good Axis, the people were not obedient enough, the Japs and the Germans are the only really obedient people on earth and see what happens, teach them disobedience, confuse their minds, teach them disobedience, and the world can be peaceful. General Osborne shook his head sadly, you'll never make the heads of an army understand that.”

Gertrude Stein (1874–1946) American art collector and experimental writer of novels, poetry and plays

Off we all went to see Germany. In: LIFE Magazine, Vol. 19, No. 6, August 6, 1945, S.56, ISSN 0024-3019. google books https://books.google.at/books?id=0EkEAAAAMBAJ&pg=PA54&lpg=PA54&dq=%22gertrude+stein%22+%22off+we+all+went%22&source=bl&ots=xOi2_KGtgA&sig=rCjhy5aEb48I1LiWrDQNNVtw37c&hl=de&sa=X&ved=2ahUKEwij1sqZr7_cAhUFdcAKHQQhB_sQ6AEwAHoECAAQAQ#v=onepage&q=%22gertrude%20stein%22%20%22off%20we%20all%20went%22&f=false

War, People, World, Education

“If one looks back at the short period of time of the Badoglio government, one must remember that the Italian longing and need for peace was no secret to the German command. Since the German retreat at el Alamein in November 1942 and the collapse of the Italian Army on the eastern front, the Italians had repeatedly stated their weariness of battle and had made certain suggestions. In steadily increasing numbers, measures were being taken by the German military command out of fear for the Axis loyalty of Italy. As the course of events showed, the view on betrayal dominated all other German reflections, nourished by the fall of Mussolini and his style of leadership.”

Walter Warlimont (1894–1976) German general

Quoted in "Forgotten Battles: Italy's War of Liberation, 1943-1945" - Page 50 - by Charles T. O'Reilly - History - 2001

Secret, Fear, Peace, Betrayal

“If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of "purpose" must necessarily be associated with some anthropomorphic deity.”

Arthur Koestler (1905–1983) Hungarian-British author and journalist

Epilogue
The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959)

Imagination, Reality, Time, Past

“Mercury on its axis turns like the Moon:
One side has lasting day, the other night;
One side in everlasting fire doth swoon;
While th'other hides forever from the light.”

Giovanni Schiaparelli (1835–1910) Italian astronomer and science historian

Originally in Latin; translated by Agnes Mary Clerke (1842–1907)
Quoted in Sky and Telescope, March 2011, p. 33

Light, Night

“We usually speak of the Jewish-Christian civilization — perhaps, the time has come, especially with regard to the Middle East conflict, to talk about the Jewish-Muslim civilization as an axis opposed to Christianity.”

Slavoj Žižek (1949) Slovene philosopher

"A Glance into the Archives of Islam" http://www.lacan.com/zizarchives.htm, Lacan dot com (2006)

Time

“The axis of the earth sticks out visibly through the center of each and every town or city.”

Oliver Wendell Holmes (1809–1894) Poet, essayist, physician

The Autocrat of the Breakfast Table (1858)

“Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius.
Such an ellipse will be formed in our present case…”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

Star, Nature, Appearance

“Another school opposed this dream with its summons to military adventure in Anatolia, and took its blueprint from a Western reading of classical antiquity. While conceding the demographic break with the ancient Greek world, the westernized intelligentsia claimed a continuing spiritual affinity between modem Western, secular ideals and those of classical Athens. Locating the modern Greeks through their cultural heritage of classical antiquity along an cast—west axis that stretched from Paris and London to Athens and Constantinople, the ‘Hellenic’ map differed profoundly from the ‘Byzantine’ one; for the Latter had a north—south axis from Moscow to Constantinople and Egypt, which aligned a re-nascent Byzantine Greece with Orthodox Russia as the protector of Eastern Christianity. There was a similar contrast in ethnic moralities. While the Byzantine conception of Greek revival envisaged a renewal of the Orthodox Christian virtues and ecclesiastical controls, the secular Hellenic vision advocated a ‘return’ to the qualities of rational enquiry, self-control and reflective choice which seemed to sum up the ethical message of ancient Greece.”

Anthony D. Smith (1939–2016) British academic

Source: The Ethnic Origins of Nations (1987), p. 203.

World, School, Dreams, Reading

“It is time for students of the evolutionary process, especially those who have been misquoted and used by the creationists, to state clearly that evolution is a fact, not theory, and that what is at issue within biology are questions of details of the process and the relative importance of different mechanisms of evolution. It is a fact that the earth, with liquid water, is more than 3.6 billion years old. It is a fact that cellular life has been around for at least half of that period and that organized multicellular life is at least 800 million years old. It is a fact that major life forms now on earth were not at all represented in the past. There were no birds or mammals 250 million years ago. It is a fact that major life forms of the past are no longer living. There used to be dinosaurs and Pithecanthropus, and there are none now. It is a fact that all living forms come from previous living forms. Therefore, all present forms of life arose from ancestral forms that were different. Birds arose from nonbirds and humans from nonhumans. No person who pretends to any understanding of the natural world can deny these facts any more than she or he can deny that the earth is round, rotates on its axis, and revolves around the sun. The controversies about evolution lie in the realm of the relative importance of various forces in molding evolution.”

Richard C. Lewontin (1929) American evolutionary biologist

" Evolution/Creation Debate: A Time for Truth http://bioscience.oxfordjournals.org/content/31/8/local/ed-board.pdf", BioScience volume 31 (1981), p. 559; Reprinted in J. Peter Zetterberg, editor, Evolution versus Creationism, Oryx Press, Phoenix, Arizona, 1983.

Life, Lie, World, Understanding

“I want to impose on everyone that the bad times are over, they are finished! Our mandate from the Prime Minister is to destroy the Axis forces in North Africa…It can be done, and it will be done!”

Bernard Montgomery, 1st Viscount Montgomery of Alamein (1887–1976) British Army officer, Commander of Allied forces at the Battle of El Alamein

Said to his troops in North Africa, promising the swift defeat of Rommel[citation needed]

Time

“If the intensity of the material world is plotted along the horizontal axis, and the response of the human mind is on the vertical, the relation between the two is represented by the logarithmic curve. Could this rule provide a clue to the relationship between the objective measure of information, and our subjective perception of it?”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 10, Counting Digits, The ubiquitous logarithm, p. 85

World

“I fear the future I wish for my children is at risk, so I'm taking action. Please join me. Our greatest risk is not terrorism, and it's not Iraq or the "Axis of Evil". Our greatest risk is a lack of leadership, a lack of honesty and a complete lack of consciousness. Unfortunately our current government cannot see the big picture. They think too small. They suffer from the “what's in it for me?” syndrome. The simple truth is that the current administration has squandered incredible opportunities to bring the world together, to promote peace in regions that have only known war, to encourage health in places that are ravaged with disease, to make us more secure by living up to our principles at home and abroad. The simple truth is that the policies of our current administration do not reflect what is great about America.”

Madonna (1958) American singer, songwriter, and actress

From Madonna's open letter about the War in Iraq & the Bush administration http://www.foxnews.com/story/0,2933,107771,00.html

War, Children, Health, Truth

“In short, the regime ruling Iran is the axis of Islamic fundamentalism in terms of ideology, policies, money, weapons, and logistical support.”

Maryam Rajavi (1953) Iranian politician

Remark made on 29 April, 2015, in a testimony to The House Foreign Affairs Committee, Subcommittee on Terrorism, Non-Proliferation and Trade http://docs.house.gov/meetings/FA/FA18/20150429/103392/HHRG-114-FA18-Wstate-RajaviM-20150429.pdf.

Money, Support

“Arthropods and vertebrates share some broad features of general organization - elongated, bilaterally symmetrical bodies, with sensory organs up front, excretory structures in the back, and some form of segmentation along the major axis. But the geometry of major internal organs could hardly be more different… Arthropods concentrate their nervous system on their ventral (belly) side as two major cords running along the bottom surface of the animal. The mouth also opens on the ventral side, with the esophagus passing between the two nerve cords, and the stomach and remainder of the digestive tube running along the body above the nerve cords. In vertebrates, and with maximal contrast, the central nervous system runs along the dorsal (top) surface as a single tube culminating in a bulbous brain at the front end. The entire digestive system then runs along the body axis below the nerve cord.”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

"Brotherhood by Inversion", p. 321
Leonardo's Mountain of Clams and the Diet of Worms (1998)

Animals

“We can hardly suppose a possibility of the production of a globular form without a consequent revolution of the nebulous matter, which in the end may settle in a regular rotation about some fixed axis.”

William Herschel (1738–1822) German-born British astronomer, technical expert, and composer

p, 125
Astronomical Observations relating to the Construction of the Heavens... (1811)

“Having now retrieved a little more of leasure, both for Delineation and Description, for a further elucidation of what I have said, I shall make it my third Attempt, to explain;
First, A Helioscope to look upon the body of the Sun, without any offence to the Observers eye.
Secondly, A way of shortening reflective and refractive Telescopes.
Thirdly, A way of using a Glass of any length, without moving the Tube.
Fourthly, An Instrument for taking the Diameters of the Sun, Moon and Planets, or for taking any other Distances, to five or ten Degrees, to the certainty of a Second. …
Fifthly, An Instrument for describing all manner of Dials, by the tangent projection.
Sixthly, The uses thereof;
1. For adjusting the Hand of a Clock, so as to make it move in the shadow of a Dial, whose style is parallel to the Axis: Or,
2. In the Azimuth of any Celestial Body, that is, in the shadow of the upright, or any other way inclining Style, upon any plain.
3. For making a Hand move according to the true æquation of Time.
4. For making all manner of Elliptical Dials, in Mr. Foster's way, &c.
5. For communicating a circular motion in a Curve Line, without any shaking: And for divers other excellent purposes.”

Robert Hooke (1635–1703) English natural philosopher, architect and polymath

A Description of Helioscopes, and Some Other Instruments https://books.google.com/books?id=KQtPAAAAcAAJ (1676)

Way, Communication, Time, Sun

“After examining the doctrinal manifestations of this single-axis framework, I will discuss how it contributes to the marginalization of Black women in feminist theory and in antiracist politics. I argue that Black women are sometimes excluded from feminist theory and antiracist policy discourse because both are predicated on a discrete set of experiences that often does not accurately reflect the interaction of race and gender. These problems of exclusion cannot be solved simply by including Black women within an already established analytical structure. Because the intersectional experience is greater than the sum of racism and sexism, any analysis that does not take intersectionality into account cannot sufficiently address the particular manner in which Black women are subordinated. Thus, for feminist theory and antiracist policy discourse to embrace the experiences and concerns of Black women, the entire framework that has been used as a basis for translating “women’s experience” or “the Black experience” into concrete policy demands must be rethought and recast.”

Kimberlé Williams Crenshaw book Demarginalizing the Intersection of Race and Sex

Demarginalizing the Intersection of Race and Sex (1989)

Women, Problem

“The United States is evil. There's this axis of evil. What about the allies of evil – the United States, England, Japan, Australia? These are the evildoers.”

Bobby Fischer (1943–2008) American chess prodigy, chess player, and chess writer

Press conference in Iceland, March 25 2005 http://www.bobby-fischer.net/Fischer_clips_hair_but_not_views.htm <br class="br">2000s

Evil

“The Allies had the resources, industry, and logistics of an entire planet. The Axis, on the other hand, had to depend on what scant assets they could scrape up within their borders. This time we were the Axis.”

Max Brooks book World War Z

World War Z

Time, Dependency

“Love is the axis and breath of my life. The art I produce is a byproduct, an excrescence of love, the song I sing, the joy which must explode, the overabundance — that is all!”

Anaïs Nin (1903–1977) writer of novels, short stories, and erotica

Oct. 21, 1934
Diary entries (1914 - 1974)

Love, Life, Art, Singing

“For common purposes we may without sensible error suppose the earth's motion equable and neglect the corrections, and then the rule for the parallax of right ascension will be this:
Sine lat. : rad. : : cotang. A : cotang. C, or rad : sine lat. : : tang. A : tang. C; then long. star \mp C = long. of λ.
Cosine C : cosine A : : semi transverse axis : z.
And cosine decl. cosine (ʘ - λ) :: z : x = parallax of right ascension.”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

Error, Star

“If time is an illusion, then all movement and change are also illusions. So the only thing that gives us the illusion of movement and change and events and time is the fact that our consciousness is moving through this mass along the time axis. If you imagine it as a strip of celluloid, each of those individual cells is motionless. If they each represent a moment, they’re unchanging. They’re not going anywhere, but as the projector beam of our consciousness passes across them, it provides the illusion of movement, and narrative and cause and effect and circumstances.”

Alan Moore (1953) English writer primarily known for his work in comic books

The Believer interview (2013)

Imagination, Change, Time

“I've been playing the CNN Drinking Game, have you ever played that? Where you do a shot every time George Bush says the word "evil"? Oh, I'm a wreck! You gotta do a double shot every time he says "evildoers". Chug the bottle for "axis of evil."”

Doug Stanhope (1967) American stand-up comedian, actor, and author

Are you a president or an exorcist?!
Word of Mouth (2002)

Game, Drink, Evil, Time

“Grief is a sphere in that it can be turned a quarter turn or turned a millionth, it can be spun on any axis and by any degree and still its aspect is the same.”

Antonella Gambotto-Burke book The Pure Weight of the Heart

Source: The Pure Weight of the Heart (1998), P. 28.

“Honesty is the axis on which leadership spins.”

Mike Pence (1959) 48th Vice President of the United States

Remarks at Reagan Library https://www.c-span.org/video/?414899-1/mike-pence-delivers-remarks-reagan-library, C-SPAN.org (September 8, 2016) <br class="br">Trump/Pence 2016 Presidential Campaign

“For peace and brotherhood at the axis of a democratic republic, I am ready to serve the Turkish State, and I believe that for this end I must remain alive.”

Abdullah Öcalan (1949) Founder of the PKK

As quoted in Turkish Press Review (1 June 1999) http://www.byegm.gov.tr/YAYINLARIMIZ/CHR/ING99/06/99X06X01.HTM#%200.

Peace

“The centre of gravity of any cylinder is the point of bisection of the axis.”

Archimedes book The Method of Mechanical Theorems

Proposition presumed from previous work.
The Method of Mechanical Theorems

“When the year was completed, I began to examine and compare my observations, and having pretty well satisfied myself as to the general laws of the phenomena, I then endeavored to find out the cause of them. I was already convinced that the apparent motion of the stars was not owing to the nutation of the earth's axis. The next thing that offered itself was an alteration in the direction of the plumb-line with which the instrument was constantly rectified; but this upon trial proved insufficient. Then I considered what refraction might do, but here also nothing satisfactory occurred. At length I conjectured that all the phenomena hitherto mentioned, proceeded from the progressive motion of light and the earth's annual motion in its orbit. For I perceived that, if light was propagated in time, the apparent place of a fixed object would not be the same when the eye is at rest, as when it is moving in any other direction than that of the line passing through the eye and the object; and that, when the eye is moving in different directions, the apparent place of the object would be different.”

James Bradley (1693–1762) English astronomer; Astronomer Royal

As quoted by W. S. Eichelberger, "The Distances of the Heavenly Bodies," http://www.jstor.org/stable/1639343 Science New Series, Vol. 43, No. 1110 (Apr. 7, 1916), pp. 475-483.

Law, Star, Light, Time

“Where does your responsibility begin here? Wiping away the nebula from your sight, you struggle to find where you really are. You're trying to find the direction of the flow, struggling to hold on to the axis of time. But you can't locate the borderline separating dream and reality. Or even the boundary between what's real and what's possible. All you're sure of is that you're in a delicate position. Delicate-and dangerous. You're pulled along, a part of it, unable to pin down the principles of prophecy, or of logic. Like when a river overflows, washing over a town, all road signs have sunk beneath the waves. And all you can see are the anonymous roofs of the sunken houses.”

Haruki Murakami book Kafka on the Shore

Source: Kafka on the Shore (2002), Chapter 29, A Boy Named Crow

Dreams, Reality, Time, Parting

“But some years after, a letter, which he received from Dr. Hooke, put him on inquiring what was the real figure, in which a body let fall from any high place descends, taking the motion of the earth round its axis into consideration. Such a body, having the same motion, which by the revolution of the earth the place has whence it falls, is to be considered as projected forward and at the same time drawn down to the centre of the earth. This gave occasion to his resuming his former thoughts concerning the moon, and Picard in France having lately measured the earth, by using his measures the moon appeared to be kept in her orbit purely by the power of gravity; and consequently, that this power decreases, as you recede from the centre of the earth, in the manner our author had formerly conjectured. Upon this principle he found the line described by a falling body to be an ellipsis, the centie of the earth being one focus. And the primary planets moving in such orbits round the sun, he had the satisfaction to see, that this inquiry, which he had undertaken merely out of curiosity, could be applied to the greatest purposes. Hereupon he composed near a dozen propositions, relating to the motion of the primary planets about the sun. Several years after this, some discourse he had with Dr. Halley, who at Cambridge made him a visit, engaged Sir Isaac Newton to resume again the consideration of this subject; and gave occasion to his writing the treatise, which he published under the title of Mathematical Principles of Natural Philosophy. This treatise, full of such a variety of profound inventions, was composed by him, from scarce any other materials than the few propositions before mentioned, in the space of a year and a half.”

Henry Pemberton (1694–1771) British doctor

Republished in: Stephen Peter Rigaud (1838) Historical Essay on the First Publication of Sir Newton's Principia http://books.google.com/books?id=uvMGAAAAcAAJ&pg=RA1-PA49. p. 519 <br class="br">Preface to View of Newton's Philosophy, (1728)

Appearance, Time, Sun

“We analyzed the first stage of our construction, confined to two-dimensional space, and found it to be as durable and resistant as the earth itself. We build in this space just as we would on the ground, and therefore must take as our point of departure the concepts of gravity and force of attraction, as the foundation of everything built on the land. In PROUN the reciprocity of the effects of gravity [Newton, 'for every action an equal and opposite reaction'] manifests itself in a new capacity. We see that on the surface (plane) of the picture, the PROUN ceases to exist as such and becomes a building surveyed from every direction — considered from above or examined from below. The result of this turns out to be the destruction of the single axis that leads to the horizon.”

El Lissitsky (1890–1941) Soviet artist, designer, photographer, teacher, typographer and architect

1915 - 1925, Theses on the 'PROUN': from painting to architecture' (1920)

Departure

“It's a rule worth having in mind. Income almost always flows along the same axis as power but in the opposite direction.”

John Kenneth Galbraith (1908–2006) American economist and diplomat

Source: The Age of Uncertainty (1977), Chapter 1, p. 13

“Beware! By Allah the son of Abu Quhafah (Abu Bakr) dressed himself with it (the caliphate) and he certainly knew that my position in relation to it was the same as the position of the axis in relation to the hand-mill. The flood water flows down from me and the bird cannot fly upto me. I put a curtain against the caliphate and kept myself detached from it.
Then I began to think whether I should assault or endure calmly the blinding darkness of tribulations wherein the grown up are made feeble and the young grow old and the true believer acts under strain till he meets Allah (on his death). I found that endurance thereon was wiser. So I adopted patience although there was pricking in the eye and suffocation (of mortification) in the throat. I watched the plundering of my inheritance till the first one went his way but handed over the Caliphate to Ibn al-Khattab after himself.
(Then he quoted al-A`sha's verse):
My days are now passed on the camel's back (in difficulty) while there were days (of ease) when I enjoyed the company of Jabir's brother Hayyan.
It is strange that during his lifetime he wished to be released from the caliphate but he confirmed it for the other one after his death. No doubt these two shared its udders strictly among themselves. This one put the Caliphate in a tough enclosure where the utterance was haughty and the touch was rough. Mistakes were in plenty and so also the excuses therefore. One in contact with it was like the rider of an unruly camel. If he pulled up its rein the very nostril would be slit, but if he let it loose he would be thrown. Consequently, by Allah people got involved in recklessness, wickedness, unsteadiness and deviation.
Nevertheless, I remained patient despite length of period and stiffness of trial, till when he went his way (of death) he put the matter (of Caliphate) in a group and regarded me to be one of them. But good Heavens! what had I to do with this "consultation"? Where was any doubt about me with regard to the first of them that I was now considered akin to these ones? But I remained low when they were low and flew high when they flew high. One of them turned against me because of his hatred and the other got inclined the other way due to his in-law relationship and this thing and that thing, till the third man of these people stood up with heaving breasts between his dung and fodder. With him his children of his grand-father, (Umayyah) also stood up swallowing up Allah's wealth like a camel devouring the foliage of spring, till his rope broke down, his actions finished him and his gluttony brought him down prostrate.
At that moment, nothing took me by surprise, but the crowd of people rushing to me. It advanced towards me from every side like the mane of the hyena so much so that Hasan and Husayn were getting crushed and both the ends of my shoulder garment were torn. They collected around me like the herd of sheep and goats. When I took up the reins of government one party broke away and another turned disobedient while the rest began acting wrongfully as if they had not heard the word of Allah saying:
That abode in the hereafter, We assign it for those who intend not to exult themselves in the earth, nor (to make) mischief (therein); and the end is (best) for the pious ones. (Qur'an, 28:83)
Yes, by Allah, they had heard it and understood it but the world appeared glittering in their eyes and its embellishments seduced them. Behold, by Him who split the grain (to grow) and created living beings, if people had not come to me and supporters had not exhausted the argument and if there had been no pledge of Allah with the learned to the effect that they should not acquiesce in the gluttony of the oppressor and the hunger of the oppressed I would have cast the rope of Caliphate on its own shoulders, and would have given the last one the same treatment as to the first one. Then you would have seen that in my view this world of yours is no better than the sneezing of a goat.”

Ali book Nahj al-Balagha

Known as the Sermon of ash-Shiqshiqiyyah (roar of the camel), It is said that when Amir al-mu'minin reached here in his sermon a man of Iraq stood up and handed him over a writing. Amir al-mu'minin began looking at it, when Ibn `Abbas said, "O' Amir al-mu'minin, I wish you resumed your Sermon from where you broke it." Thereupon he replied, "O' Ibn `Abbas it was like the foam of a Camel which gushed out but subsided." Ibn `Abbas says that he never grieved over any utterance as he did over this one because Amir al-mu'minin could not finish it as he wished to.
Nahj al-Balagha

Death, Hunger, Children, People

“We are taught all this [the motion of the earth on its axis and around the sun] by the order of succession, in which those phenomena (various planetary happenings) follow each other, and by the harmony of the world, if we will only, as the saying goes, look at the matter with both eyes.”

Nicolaus Copernicus book De revolutionibus orbium coelestium

Book 1, Ch. 9 as quoted by Edwin Arthur Burtt in The Metaphysical Foundations of Modern Physical Science (1925)
De revolutionibus orbium coelestium (1543)

World, Success, Sun

“The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections…There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being… L. …the Greeks named these curves and many others… loci… Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve…”

Tobias Dantzig (1884–1956) American mathematician

Number: The Language of Science (1930)

Lying, Problem

“The day after Pearl Harbor our Navy's position in the Pacific was extremely grave. The bulk of our major ships had been put out of commission for a year; only our small Asiatic Fleet under Admiral Hart in the Philippines and portions of the Pacific Fleet that had been absent from Pearl Harbor on the day of the attack were in fighting condition in the Pacific. Even Hawaii might be attacked and overrun at any moment. And in the Atlantic the Axis submarines were destroying a tremendous tonnage of our shipping within sight of our very shores. Then, even at the lowest of the war tide, the decision was made, and correctly: first fight for time, especially in the Pacific- and then assemble the might to conquer first Italy and then Germany, and then inevitably Japan must succumb.”

Ernest King (1878–1956) United States Navy admiral, Chief of Naval Operations

From King's Foreword in Battle Stations! Your Navy In Action (1946) by Admirals of the U.S. Navy, p. 10

War, Decision, Time, Fight

“The discovery of Hippocrates amounted to the discovery of the fact that from the relation
(1)\frac{a}{x} = \frac{x}{y} = \frac{y}{b}it follows that(\frac{a}{x})^3 = [\frac{a}{x} \cdot \frac{x}{y} \cdot \frac{y}{b} =] \frac{a}{b}and if a = 2b, [then (\frac{a}{x})^3 = 2, and]a^3 = 2x^3.The equations (1) are equivalent [by reducing to common denominators or cross multiplication] to the three equations
(2)x^2 = ay, y^2 = bx, xy = ab[or equivalently…y = \frac{x^2}{a}, x = \frac{y^2}{b}, y = \frac{ab}{x} ]Doubling the Cube
the 2 solutions of Menaechmusand the solutions of Menaechmus described by Eutocius amount to the determination of a point as the intersection of the curves represented in a rectangular system of Cartesian coordinates by any two of the equations (2).
Let AO, BO be straight lines placed so as to form a right angle at O, and of length a, b respectively. Produce BO to x and AO to y.
The first solution now consists in drawing a parabola, with vertex O and axis Ox, such that its parameter is equal to BO or b, and a hyperbola with Ox, Oy as asymptotes such that the rectangle under the distances of any point on the curve from Ox, Oy respectively is equal to the rectangle under AO, BO i. e. to ab. If P be the point of intersection of the parabola and hyperbola, and PN, PM be drawn perpendicular to Ox, Oy, i. e. if PN, PM be denoted by y, x, the coordinates of the point P, we shall have

\begin{cases}y^2 = b. ON = b. PM = bx\\ and\\ xy = PM. PN = ab\end{cases}whence\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.
In the second solution of Menaechmus we are to draw the parabola described in the first solution and also the parabola whose vertex is O, axis Oy and parameter equal to a.”

Thomas Little Heath (1861–1940) British civil servant and academic

The point P where the two parabolas intersect is given by<center><math>\begin{cases}y^2 = bx\\x^2 = ay\end{cases}</math></center>whence, as before,<center><math>\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.</math></center>
Apollonius of Perga (1896)

Drawing

“Turtles, he adds, and such large ammonites as are found in Portland, seem to have been the productions of the seas of hotter countries, and it is necessary to suppose that England once lay under the sea within the torrid zone! To explain this and similar phenomena, he indulges in a variety of speculations concerning changes in the position of the axis of the earth's rotation, a shifting of the earth's center of gravity, 'analogous to the revolutions of the magnetic pole,' &c. None of these conjectures, however, are proposed dogmatically, but rather in the hope of promoting fresh inquiries and experiments.”

Charles Lyell book Principles of Geology

Chpt.3, p. 37
Principles of Geology (1832), Vol. 1
Context: Respecting the extinction of species, Hooke was aware that the fossil ammonites, nautili, and many other shells and fossil skeletons found in England, were of different species from any then known; but he doubted whether the species had become extinct, observing that the knowledge of naturalists of all the marine species, especially those inhabiting the deep sea, was very deficient. In some parts of his writings, however, he leans to the opinion that species had been lost; and in speculating on this subject, he even suggests that there might be some connection between the disappearance of certain kinds of animals and plants, and the changes wrought by earthquakes in former ages. Some species, he observes with great sagacity, are peculiar to certain places, and not to be found elsewhere. If, then, such a place had been swallowed up, it is not improbable but that those animate beings may have been destroyed with it; and this may be true both of aerial and aquatic animals: for those animated bodies, whether vegetables or animals, which were naturally nourished or refreshed by the air, would be destroyed by the water, &c.; Turtles, he adds, and such large ammonites as are found in Portland, seem to have been the productions of the seas of hotter countries, and it is necessary to suppose that England once lay under the sea within the torrid zone! To explain this and similar phenomena, he indulges in a variety of speculations concerning changes in the position of the axis of the earth's rotation, a shifting of the earth's center of gravity, 'analogous to the revolutions of the magnetic pole,' &c.; None of these conjectures, however, are proposed dogmatically, but rather in the hope of promoting fresh inquiries and experiments.

Hope, Change, Sea, Country

“States like these, and their terrorist allies, constitute an axis of evil, arming to threaten the peace of the world.”

George W. Bush (1946) 43rd President of the United States

Bush referring to Iraq, Iran, and North Korea as an "Axis of Evil" in his State of the Union Address (January 29, 2002)
2000s, 2002, State of the Union address (January 2002)
Context: States like these, and their terrorist allies, constitute an axis of evil, arming to threaten the peace of the world. By seeking weapons of mass destruction, these regimes pose a grave and growing danger. They could provide these arms to terrorists, giving them the means to match their hatred. They could attack our allies or attempt to blackmail the United States. In any of these cases, the price of indifference would be catastrophic.

World, Peace, Evil

“Those who treat "axis of evil" remark and the bombing of Libya as watershed traumas in the North Korean psyche are really lampooning their own narrative, because if a regime has spent 50 or 60 years defying, humiliating and threatening a trigger-happy superpower like the United States, and the greatest shocks it has been dealt in return have been a rude line in a speech and an attack on a completely different country, its safety clearly does not depend on developing a new kind of weapon.”

Brian Reynolds Myers (1963) American professor of international studies

Its conventional artillery must have been protecting it very well indeed.
2010s, Interview with the Reuters War College (April 2017)

Evil, Dependency, Country, Happiness

“That's the problem with the Drudge-Rush-Fox axis-of-evil news bubble. Nothing gets into these people's heads. They only listen to what they want to hear. They listen to what confirms what they believe.”

Bill Maher (1956) American stand-up comedian

Larry King Live interview (2010)
Context: That's the problem with the Drudge-Rush-Fox axis-of-evil news bubble. Nothing gets into these people's heads. They only listen to what they want to hear. They listen to what confirms what they believe. And what they believe is what they got from these people to begin with.
You know, when Glenn Beck had his big rally on the mall, he said something like — he at one point said, "Today, I was holding George Washington's inaugural in my hand." No — you can't do that — it's in Plexiglas. You can't — it's 200 years old. You can't give that to people to pass around and smudge up with their grimy fingers. But it didn't matter, because it never matters to these people because nothing they say is ever fact-checked. The governor of Arizona talks about how illegals — you saw this on the news — were beheading people in Arizona. When the press asked her about it, because it was patently untrue, she just ran away. Sarah Palin never talks to the press because they might ask her a question that she doesn't have a pat answer for. They know they don't have to deal with reality, because they don't have to go to what used to be the mainstream press.

People, Problem, Evil

“I do not leave any verses, dogmas, nor any moulded standard principles as moral heritage. My moral heritage is science and reason. What I have done and intended to do for the Turkish nation lies in that. Anyone willing to appropriate my ideas for themselves after me will be my moral inheritors provided they would approve the guidance of science and reason on this axis.”

Mustafa Kemal Atatürk (1881–1938) Turkish army officer, revolutionary, and the first President of Turkey

As quoted in Kemalist Devrim ve İdeolojisi (1980) by İsmet Giritli, İstanbul Üniversitesi Yayınları, p. 13

Idea, Science

“War criminals are not confined to the Axis powers alone. Roosevelt and Churchill are no less war criminals than Hitler and Mussolini.”

Mahatma Gandhi (1869–1948) pre-eminent leader of Indian nationalism during British-ruled India

Mahatma Gandhi. Interview given to Ralph Coniston, ‘before April 25, 1945’, reproduced in Collected Works, vol. 79, p. 423. Quoted from Elst, Koenraad (2018). Why I killed the Mahatma: Uncovering Godse's defence. New Delhi : Rupa, 2018.
1940s

War

“We really need to understand that the North Koreans are not as traumatized by things like the "Axis of Evil" remark or things like this Vinson flotilla as some people in the Pyongyang-watching community seem to think.”

Brian Reynolds Myers (1963) American professor of international studies

2010s, Interview with the Reuters War College (April 2017)

Understanding, People, Communication, Thinking