Doubling Quotes - page 2
These men [medical doctors] plan ways of doubling their incomes and come to the public with the plea that they are sincerely interested in the health and welfare of our children and that they put over their income-increasing programs for the health of our babies and for the welfare of the school children. They are as cold-blooded as any class of criminals on the whole earth. Indeed, I know of no other class of criminals who live by crippling, maiming and killing babies and children.
Herbert M. Shelton
By the time of Hippocrates of Chios the scope of Greek geometry was no longer even limited to the Elements; certain special problems were also attacked which were beyond the power of the geometry of the straight line and circle, and which were destined to play a great part in determining the direction taken by Greek geometry in its highest flights. The main problems in question were three: (1) the doubling of the cube, (2) the trisection of any angle, (3) the squaring of the circle; and from the time of Hippocrates onwards the investigation of these problems proceeded pari passu with the completion of the body of the Elements.
Thomas Little Heath
Hippocrates also attacked the problem of doubling the cube. ...Hippocrates did not, indeed, solve the problem, but he succeeded in reducing it to another, namely, the problem of finding two mean proportionals in continued proportion between two given straight lines, i. e. finding x, y such that a:x=x:y=y:b, where a, b are the two given straight lines. It is easy to see that, if a:x=x:y=y:b, then b/a = (x/a)3, and, as a particular case, if b=2a, x3=2a3, so that the side of the cube which is double of the cube of side a is found.
Thomas Little Heath
There is perhaps no question that occupies, comparatively, a larger space in the history of Greek geometry than the problem of the Doubling of the Cube. The tradition concerning its origin is given in a letter from Eratosthenes of Cyrene to King Ptolemy Euergetes quoted by Eutocius...
"Eratosthenes to King Ptolemy greeting.
"There is a story that one of the old tragedians represented Minos as wishing to erect a tomb for Glaucus and as saying, when he heard that it was a hundred feet every way,Too small thy plan to bound a royal tomb.
Let it be double; yet of its fair form
Fail not, but haste to double every side.But he was clearly in error; for when the aides are doubled, the area becomes four times as great, and the solid content eight times as great. Geometers also continued to investigate the question in what manner one might double a given solid while it remained in the same form.
Thomas Little Heath
Take the case of a famous problem which plays a great part in the history of Greek geometry, the doubling of the cube, or its equivalent, the finding of two mean proportionals in continued proportion between two given straight lines. ...if all the recorded solutions are collected together, it is much easier to see the relations, amounting in some cases to substantial identity, between them, and to get a comprehensive view of the history of the problem. I have therefore dealt with this problem in a separate section of the chapter devoted to 'Special Problems,' and I have followed the same course with the other famous problems of squaring the circle and trisecting any angle.
Thomas Little Heath
I went to art school... but I worked at the Museum of Modern Art. I worked in fundraising at the information membership desk. I ended up, over a period of time, doubling the amount of membership revenue that came in through people entering the museum, so people would ask me to come and work for them.
Jeff Koons
The speed and density of computation have been doubling every three years (at the beginning of the twentieth century) to one year (at the end of the twentieth century), regardless of the type of hardware used. ...Despite many decades of progress since the first calculating equipment was used in the 1890 census, it was not until the mid-1960s that this phenomenon was even noticed.
Ray Kurzweil
It is as though the space between us were time: an irrevocable quality. It is as though time, no longer running straight before us in a diminishing line, now runs parallel between us like a looping string, the distance being the doubling accretion of the thread an not the interval between.
William Faulkner
