A Quote by Carl Friedrich Gauss

Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density. — © Carl Friedrich Gauss
Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.
So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, Herapath, Joule, Kronig, Clausius, &c., have shewn that the relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure.
The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence that numerical data may be introduced into discussions of the general curvature of space.
A common way to compute density is, of course, to take the ratio of an object's mass to its volume. But other types of densities exist, such as the resistance of somebody's brain to the imparting of common sense.
Just as the system of the sun, planets and comets is put in motion by the forces of gravity, and its parts persist in their motions, so the smaller systems of bodies also seem to be set in motion by other forces and their particles to be variously moved in relation to each other and, especially, by the electric force.
The waves travel with the velocity of light and slightly squeeze and stretch space transverse to the direction of their motion. The first waves we measured came from the collision of two black holes each about 30 times the mass of our sun.
After the planet becomes theirs, many millions of years will have to pass before a beetle particularly loved by God, at the end of its calculations will find written on a sheet of paper in letters of fire that energy is equal to the mass multiplied by the square of the velocity of light. The new kings of the world will live tranquilly for a long time, confining themselves to devouring each other and being parasites among each other on a cottage industry scale.
In bodies moved, the motion is received, increased, diminished, or lost, according to the relations of the quantity of matter and velocity; each diversity is uniformity, each change is constancy.
What's great in theater is that you can sustain the arc of a character for a full three hours, whereas in film or TV, you have to create that arc in little pieces, and usually out of sequence.
It comes up over and over and over again that a ten times increase in the weight-oriented density of batteries or the volume metric, the space-oriented density of batteries, would enable so many other moonshots that that's one that just constantly comes up over and over again, and we will start that moonshot if we can find a great idea.
All motion is curved and all curvature is spiral.
Morality—like velocity—is relative. The determination of it depends on what the objects around you are doing. All one can do is measure one's position in relation to them; never can one measure one's velocity or morality in terms of absolutes.
Motion is always a relative thing. I move in relation to something else. Any particle in this universe can change in relation to any other particle; but take the whole universe as one, and in relation to what can it move? There is nothing besides it. So this infinite Unit is unchangeable, immovable, absolute, and this is the Real Man.
In a gas, motion has the upper hand; the atoms are moving so fast that they have no time to enter into any sort of combination with each other: occasionally, atom must meet atom and, so to speak, each hold out vain hands to the other, but the pace is too great and, in a moment, they are far away from each other again.
A true community consists of individuals - not mere species members, not couples - respecting each others individuality and privacy while at the same time interacting with each other mentally and emotionally - free spirits in free relation to each other - and co-operating with each other to achieve common ends. Traditionalists say the basic unit of "society" is the family; "hippies" say the tribe; noone says the individual.
The Gulf of Mexico is a very big ocean. The amount of volume of oil and dispersant we are putting into it is tiny in relation to the total water volume.
On average, the Chinese, Koreans, and Japanese are more similar to each other and are different from Australians, Israelis and the Swedes, who in turn are similar to each other and are different from Nigerians, Kenyans, and Jamaicans.
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