It is picked out from numbers progressing in continuous proportion. Of continuous progressions, an arithmetical is one which proceeds by equal intervals; a geometrical one which advances by unequal and proportionally increasing or decreasing intervals. Arithmetical progressions: 1, 2, 3, 4, 5, 6, 7, &c.; or 2, 4, 6, 8, 10, 12, 14, 16, &c, Geometrical progressions: 1, 2, 4, 8, 16, 32, 64, &c.; or 243, 81, 27, 9, 3, 1.
John NapierRelated topics
equal increasing numbers proceeds proportion unequalRelated quotes
No mockery in this world ever sounds to me so hollow as that of being told to cultivate happiness. What does such advice mean? Happiness is not a potato, to be planted in mould, and tilled with manure. Happiness is a glory shining far down upon us out of Heaven. She is a divine dew which the soul, on certain of its summer mornings, feels dropping upon it from the amaranth bloom and golden fruitage of Paradise.
Charlotte Brontë
Unable to create a meaningful life for itself, the personality takes its own revenge from the lower depths comes a regressive form of spontaneity raw animality forms a counterpoise to the meaningless stimuli and the vicarious life to which the ordinary man is conditioned. Getting spiritual nourishment from this chaos of events, sensations, and devious interpretations is the equivalent of trying to pick through a garbage pile for food.
Lewis Mumford
When, in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth the separate and equal station to which the laws of nature and of nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
Thomas Jefferson
It cannot be too frequently emphasized that the behavior of any animal must depend upon on the nature of the stimulus which it meets, its anatomic and physiologic capacities, and its background of previous experience. Unless it has been conditioned by previous experience, an animal should respond identically to identical stimuli, whether they emanate from some part of its own body, from another individual of the same sex, or from an individual of the opposite sex.
Alfred Kinsey
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
Benoît Mandelbrot
