“I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident… that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded…”

— Galileo Galilei

Author, Day Four, On the Motion of Projectiles, Stillman Drake translation (1974) p. 268
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

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Galileo Galilei 70

Italian mathematician, physicist, philosopher and astronomer 1564–1642

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“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.

“Proposition I. Theorem I: When a projectile is carried in motion compounded from equable horizontal and from naturally accelerated downward [motions], it describes a semiparabolic line in its movement.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Author, Day Four, Stillman Drake translation (1974) p. 269
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

“It seems to me proper to adorn the Author's thought here with its conformity to a conception of Plato's regarding the determination of the various speeds of equable motion in the celestial motions of revolution. …he said that God, after having created the movable celestial bodies, in order to assign to them those speeds with which they must be moved perpetually in equable circular motion, made them depart from rest and move through determinate spaces in that natural straight motion in which we sensibly see our moveables to be moved from the state of rest, successively accelerating. And he added that these having been made to gain that degree [of speed] which it pleased God that they should maintain forever, He turned their straight motion into circulation, the only kind [of motion] that is suitable to be conserved equably, turning always without retreat from or approach toward any pre-established goal desired by them. The conception is truly worthy of Plato, and it is to be more esteemed to the extent that its foundations, of which Plato remained silent, but which were discovered by our Author in removing their poetical mask or semblance, show it the guise of a true story.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

I. Bernard Cohen's thesis: Galileo believed only circular (not straight line) motion may be conserved (perpetual), see The New Birth of Physics (1960).
Sagredo, Day Four, Stillman Drake translation (1974) pp.283-284
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

“You could leave this Plane yourself, if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see.”

Edwin Abbott Abbott book Flatland

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 17. How the Sphere, Having in Vain Tried Words, Resorted to Deeds
Context: I groaned with horror, doubting whether I was not out of my senses; but the Stranger continued: "Surely you must now see that my explanation, and no other, suits the phenomena. What you call Solid things are really superficial; what you call Space is really nothing but a great Plane. I am in Space, and look down upon the insides of the things of which you only see the outsides. You could leave this Plane yourself, if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see.

“…the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i. e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. …such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“When I draw horizontals
you see this big plane and you have certain feelings like
you're expanding over the plane
Anything can be painted without representation”

Agnes Martin (1912–2004) American artist

1970's, The Untroubled Mind', 1971

“[T]he principal part in the human body, namely, the heart, is in constant motion, and is the source of every motion noticed in the body; it rules over the other members, and communicates to them through its own pulsations the force required for their functions. The outermost sphere by its motion rules in a similar way over all other parts of the universe, and supplies all things with their special properties. Every motion in the universe has thus its origin in the motion of that sphere; and the soul of every animated being derives its origin from the soul of that same sphere.”

Maimónides book The Guide for the Perplexed

Source: Guide for the Perplexed (c. 1190), Part I, p. 296 (1881) Tr. Friedlander

“.. modern destruction begins where architectural structure is opened up and set into motion by colour relationships. The colour-planes, however, are always in orthogonal relationship.”

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

Quote in Van Doesburg's article: 'Aantekeningen bij Bijlage 12 (Notes), De Zaag en de goudvischkom van P.Alma', by Theo van Doesburg; in art-magazine 'De Stijl' 1 8, June 1918, p. 93
1912 – 1919

“The plane is the mainstay of all graphic representation. It is so familiar that its properties seem self-evident, but the most familiar things are often the most poorly understood. The plane is homogeneous and has two dimensions. The visual consequences of these properties must be fully explored.”

Jacques Bertin (1918–2010) French geographer and cartographer

Source: Semiology of graphics (1967/83), p. 44

“I put piss stains on private planes cuz its my jet nigga”

Lil Wayne (1982) American rapper, singer, record executive and businessman

Source: Tha Block Is Hot (1999)

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Galileo Galilei 70

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