The beginning is the most important part of the work.
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375 BCE — 1,929
140 entries
In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.
Prime numbers are more than any assigned multitude of prime numbers.
The area of a circle is to the square on its diameter as 11 to 14.
The sum of zero and a negative number is negative; the sum of a positive number and zero is positive; the sum of zero and zero is zero.
A debt minus zero is a debt. A fortune minus zero is a fortune. Zero minus zero is zero.
Completion and balancing.
The product of two numbers of like signs is positive, and the product of two numbers of unlike signs is negative.
These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0, any number may be written.
I thought about the origin of all square numbers and discovered that they arise from the ordered sequence of odd numbers.
It is much safer to be feared than loved, when, of the two, either must be dispensed with.
It has been demonstrated that three equations suffice for the cube and things equal to number.
Analytic art appropriates to itself the glory of leaving no problem unsolved.
There is nothing either good or bad but thinking makes it so.
Seeing there is nothing that is so troublesome to mathematical practice... as the multiplications, divisions, square and cubical extractions of great numbers.
We are such stuff as dreams are made on, and our little life is rounded with a sleep.
It is absolutely necessary to conclude that the blood in the animal body is impelled in a circle, and is in a state of ceaseless motion.
Any problem in geometry can easily be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction.
If a hexagon be inscribed in a conic, the three points of intersection of pairs of opposite sides are collinear.
It is impossible to separate a cube into two cubes, a fourth power into two fourth powers, or in general any power higher than the second into two like powers.
The life of man, solitary, poor, nasty, brutish, and short.
The division of stakes must be proportional to what the players may legitimately expect from fortune.
If anyone should expect a or b, and has an equal chance of gaining either of them, his expectation is worth (a+b)/2.
The moments of quantities are as their fluxions.
The mind is its own place, and in itself can make a Heaven of Hell, a Hell of Heaven.
The heart has its reasons, which reason does not know.
If I have seen further it is by standing on the shoulders of Giants.
d(xy) = x dy + y dx.
The change of motion is proportional to the motive force impressed.
Reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions.
Where-ever law ends, tyranny begins, if the law be transgressed to another's harm.
For I am not yet satisfied about it for want of Experiments.
I learned to look more upon the bright side of my condition, and less upon the dark side.
I cannot but conclude the bulk of your natives to be the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth.
The logarithms of the terms of the binomial expansion form a curve approaching the form of a parabola.
f(x)
It is impossible to cross each of the seven bridges of Königsberg exactly once in a single walk.
Custom, then, is the great guide of human life.
e^(πi) = -1
A system of linear equations may be solved by ratios of determinants.
V - E + F = 2
Man is born free; and everywhere he is in chains.
Every positive integer is the sum of four squares.
It is the greatest happiness of the greatest number that is the measure of right and wrong.
It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner.
i = √-1
Sapere aude! Have courage to make use of your own understanding!
If men were angels, no government would be necessary.
I do not wish them to have power over men; but over themselves.
Congruent numbers are those which have the same remainder when divided by a given modulus.
The probability of an event is the ratio of the number of favorable cases to that of all possible cases, when nothing leads us to expect one case more than another.
It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.
Remember, that I am thy creature; I ought to be thy Adam; but I am rather the fallen angel, whom thou drivest from joy for no misdeed.
Beware; for I am fearless, and therefore powerful.
Poets are the unacknowledged legislators of the world.
When the values successively attributed to the same variable approach indefinitely a fixed value... this fixed value is called the limit.
An arbitrary function can be represented by a trigonometric series under suitable conditions.
A volume integral can be transformed into a surface integral through the relation now called Green's theorem.
The Gaussian curvature of a surface is invariant under local isometry.
A consistent geometry can be developed in which Euclid's parallel postulate does not hold.
Running water and volcanic action are two antagonistic forces; the one labouring continually to reduce the whole of the land to the level of the sea, the other to restore and maintain the inequalities of the crust.
A geometry independent of Euclid's parallel postulate is possible.
Please, sir, I want some more.
Whoso would be a man must be a nonconformist.
A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.
Whoso would be a man, must be a nonconformist.
Mankind was my business. The common welfare was my business; charity, mercy, forbearance, and benevolence, were, all, my business.
i² = j² = k² = ijk = -1
You have seen how a man was made a slave; you shall see how a slave was made a man.
I am no bird; and no net ensnares me: I am a free human being with an independent will; which I now exert to leave you.
I am no bird; and no net ensnares me: I am a free human being with an independent will.
Whatever our souls are made of, his and mine are the same.
That government is best which governs least;
Happy are you, Hester, that wear the scarlet letter openly upon your bosom! Mine burns in secret!
Queequeg was a native of Rokovoko, an island far away to the West and South. It is not down in any map; true places never are.
Call me Ishmael.
To be a philosopher is not merely to have subtle thoughts, nor even to found a school, but so to love wisdom as to live according to its dictates.
The mass of men lead lives of quiet desperation. What is called resignation is confirmed desperation.
It is never too late to give up our prejudices.
In the fields of observation chance favors only the prepared mind.
The mass of men lead lives of quiet desperation.
If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
The laws we have to examine are the laws of one of the most important of our mental faculties.
Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)
I too am not a bit tamed, I too am untranslatable, I sound my barbaric yawp over the roofs of the world.
I celebrate myself, and sing myself.
It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way—in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.
These facts seemed to me to throw some light on the origin of species—that mystery of mysteries, as it has been called by one of our greatest philosophers.
Over himself, over his own body and mind, the individual is sovereign.
There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
It was the best of times, it was the worst of times.
The only freedom which deserves the name, is that of pursuing our own good in our own way.
From so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
Bear in mind then, that Brag is a good dog, but Holdfast is a better.
There is no better, there is no more open door by which you can enter into the study of natural philosophy, than by considering the physical phenomena of a candle.
Take nothing on its looks; take everything on evidence. There's no better rule.
Neither historically nor experimentally, do we at present know anything whatsoever about the origin of living forms.
Our experience is certainly most extensive.
Begin at the beginning, the King said gravely, and go on till you come to the end; then stop.
Curiouser and curiouser!
No one is useless in this world who lightens the burden of it for any one else.
Man still bears in his bodily frame the indelible stamp of his lowly origin.
The set of real algebraic numbers is countable, while the set of real numbers is not.
I must stand quite alone, if I am to understand myself and everything about me.
The strongest man in the world is he who stands most alone.
Upward, not Northward.
All right, then, I'll go to hell.
Man is not truly one, but truly two.
Real knowledge in science means personal acquaintance with the facts, be they few or many.
If natural causation is competent to account for the not-living part of our globe, why should it not account for the living part?
Power tends to corrupt and absolute power corrupts absolutely.
For my part, I hold to the former opinion. Looking Backward was written in the belief that the Golden Age lies before us and not behind us, and is not far away.
If a man knows the wherefore of his existence, then the manner of it can take care of itself.
The only way to get rid of a temptation is to yield to it. Resist it, and your soul grows sick with longing for the things it has forbidden to itself.
Nowadays people know the price of everything and the value of nothing.
There is only one thing in the world worse than being talked about, and that is not being talked about.
All art is quite useless.
Hope is the thing with feathers that perches in the soul.
No, we are all in the gutter, but some of us are looking at the stars.
There is nothing more deceptive than an obvious fact.
We are all in the gutter, but some of us are looking at the stars.
Mere book learning in physical science is a sham and a delusion.
The truth is rarely pure and never simple.
He had been to touch the great death, and found that, after all, it was but the great death. He was a man.
We are kept keen on the grindstone of pain and necessity.
For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.
Listen to them—the children of the night. What music they make!
Our errors are surely not such awfully solemn things.
No one would have believed in the last years of the nineteenth century that this world was being watched keenly and closely by intelligences greater than man’s and yet as mortal as his own.
The horror! The horror!
The problem of the twentieth century is the problem of the color-line.
One ever feels his twoness,—an American, a Negro; two souls, two thoughts, two unreconciled strivings.
Tomorrow is always fresh, with no mistakes in it yet.
To die will be an awfully big adventure.
I have measured out my life with coffee spoons.
Two roads diverged in a yellow wood, and sorry I could not travel both.
p(n) ~ 1/(4n√3) · exp(π√(2n/3))
April is the cruellest month, breeding lilacs out of the dead land, mixing memory and desire.
Nothing gold can stay.
The world breaks every one and afterward many are strong at the broken places.
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