“While then for a long time everyone was at a loss, Hippocrates of Chios was the first to observe that, if between two straight lines of which the greater is double of the less it were discovered how to find two mean proportionals in continued proportion, the cube would be doubled; and thus he turned the difficulty in the original problem into another difficulty no less than the former. Afterwards, they say, some Delians attempting, in accordance with an oracle, to double one of the altars fell into the same difficulty. And they sent and begged the geometers who were with Plato in the Academy to find for them the required solution. And while they set themselves energetically to work and sought to find two means between two given straight lines, Archytas of Tarentum is said to have discovered them by means of half-cylinders, and Eudoxus by means of the so-called curved lines. It is, however, characteristic of them all that they indeed gave demonstrations, but were unable to make the actual construction or to reach the point of practical application, except to a small extent Menaechmus and that with difficulty.”
Apollonius of Perga (1896)
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Thomas Little Heath 46
British civil servant and academic 1861–1940Related quotes
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid
Homily at the morning Mass at the Casa Santa Marta (23 February 2017), as quoted in "Pope: Don't put off conversion, give up a double life" at Vatican Radio (23 February 2017) http://en.radiovaticana.va/news/2017/02/23/pope_dont_put_off_conversion,_give_up_a_double_life/1294470; also quoted in "Did Pope Francis Say It Was Better to Be an Atheist Than a Bad Catholic? at snopes.com (28 February) http://www.snopes.com/pope-francis-bad-catholics/
2010s, 2017
Context: What is scandal? Scandal is saying one thing and doing another; it is a double life, a double life. A totally double life: "I am very Catholic, I always go to Mass, I belong to this association and that one; but my life is not Christian, I don’t pay my workers a just wage, I exploit people, I am dirty in my business, I launder money …" A double life. And so many Christians are like this, and these people scandalize others. How many times have we heard — all of us, around the neighborhood and elsewhere — "but to be a Catholic like that, it’s better to be an atheist." It is that, scandal. You destroy. You beat down. And this happens every day, it’s enough to see the news on TV, or to read the papers. In the papers there are so many scandals, and there is also the great publicity of the scandals. And with the scandals there is destruction.
p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
“On a double-log plot, my grandmother fits on a straight line.”
as quoted in Herbert Kroemer's Autobiography http://nobelprize.org/nobel_prizes/physics/laureates/2000/kroemer-autobio.html, The Nobel Prize in Physics 2000.
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)
“But, they need a goal or two double quick.”
2010s, 2014 FIFA World Cup, Brazil v. Germany (2014)