
Nor can our Fansie imagine how there should be a Fourth Local Dimension beyond these Three.
Treatise of Algebra (1685)
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 19. How, Though the Sphere Showed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It
Context: p>Those who have thus appeared — no one knows whence — and have returned — no one knows whither — have they also contracted their sections and vanished somehow into that more Spacious Space, whither I now entreat you to conduct me?SPHERE (MOODILY). They have vanished, certainly — if they ever appeared. But most people say that these visions arose from the thought — you will not understand me — from the brain; from the perturbed angularity of the Seer.I. Say they so? Oh, believe them not. Or if it indeed be so, that this other Space is really Thoughtland, then take me to that blessed Region where I in Thought shall see the insides of all solid things. There, before my ravished eye, a Cube, moving in some altogether new direction, but strictly according to Analogy, so as to make every particle of his interior pass through a new kind of Space, with a wake of its own — shall create a still more perfect perfection than himself, with sixteen terminal Extra-solid angles, and Eight solid Cubes for his Perimeter. And once there, shall we stay our upward course? In that blessed region of Four Dimensions, shall we linger on the threshold of the Fifth, and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth —How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of my ecstatic aspirations. Perhaps I was to blame; but indeed I was intoxicated with the recent draughts of Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a velocity that precluded speech. Down! down! down! I was rapidly descending; and I knew that return to Flatland was my doom. One glimpse, one last and never-to-be-forgotten glimpse I had of that dull level wilderness — which was now to become my Universe again — spread out before my eye. Then a darkness. Then a final, all-consummating thunder-peal; and, when I came to myself, I was once more a common creeping Square, in my Study at home, listening to the Peace-Cry of my approaching Wife.</p
Nor can our Fansie imagine how there should be a Fourth Local Dimension beyond these Three.
Treatise of Algebra (1685)
“We shall strive for perfection. We shall not achieve it immediately — but we still shall strive.”
1940s, Fourth Inaugural Address (1945)
Context: We shall strive for perfection. We shall not achieve it immediately — but we still shall strive. We may make mistakes — but they must never be mistakes which result from faintness of heart or abandonment of moral principle.
Prem Nagar Ashram, India, 10 December 1971 - quoted on p256 of "Who is Guru Maharaj Ji?" published by Bantam, 1973
1970s
this harmonic proportion may be expressed as <math>\frac{12}{6}=\frac{12-8}{8-6}</math> or inversely.
Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 61.
Valence of Prince Berthold, in Act IV.
Colombe's Birthday (1844)
Context: p>He gathers earth's whole good into his arms;
Standing, as man now, stately, strong and wise,
Marching to fortune, not surprised by her.
One great aim, like a guiding-star, above—
Which tasks strength, wisdom, stateliness, to lift
His manhood to the height that takes the prize;
A prize not near — lest overlooking earth
He rashly spring to seize it — nor remote,
So that he rest upon his path content:
But day by day, while shimmering grows shine,
And the faint circlet prophesies the orb,
He sees so much as, just evolving these,
The stateliness, the wisdom and the strength,
To due completion, will suffice this life,
And lead him at his grandest to the grave.
After this star, out of a night he springs;
A beggar's cradle for the throne of thrones
He quits; so, mounting, feels each step he mounts,
Nor, as from each to each exultingly
He passes, overleaps one grade of joy.
This, for his own good: — with the world, each gift
Of God and man, — reality, tradition,
Fancy and fact — so well environ him,
That as a mystic panoply they serve —
Of force, untenanted, to awe mankind,
And work his purpose out with half the world,
While he, their master, dexterously slipt
From such encumbrance, is meantime employed
With his own prowess on the other half.
Thus shall he prosper, every day's success
Adding, to what is he, a solid strength —
An aery might to what encircles him,
Till at the last, so life's routine lends help,
That as the Emperor only breathes and moves,
His shadow shall be watched, his step or stalk
Become a comfort or a portent, how
He trails his ermine take significance, —
Till even his power shall cease to be most power,
And men shall dread his weakness more, nor dare
Peril their earth its bravest, first and best,
Its typified invincibility.Thus shall he go on, greatening, till he ends—
The man of men, the spirit of all flesh,
The fiery centre of an earthly world!</p
Preface to the Second and Revised Edition (1884)
Flatland: A Romance of Many Dimensions (1884)
Context: p>Suppose a person of the Fourth Dimension, condescending to visit you, were to say, 'Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you INFER a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes — we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said — 'One touch of Nature makes all worlds akin.' </p
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 19. How, Though the Sphere Showed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of It
Context: My Lord, your own wisdom has taught me to aspire to One even more great, more beautiful, and more closely approximate to Perfection than yourself. As you yourself, superior to all Flatland forms, combine many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme Existence, surpassing even the Solids of Spaceland. And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me — O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend — some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed.
The Principles of the Most Ancient and Modern Philosophy (1690)
A Model of Christian Charity, a sermon delivered onboard the Arbella (1630)