First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right angled cone (i.e., a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]... (Archimedes)

First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right angled cone (i.e., a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...

Archimedes

Related topics

base book end equal height known mechanics parabola right segment set theorem triangle means

Related quotes

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. View quote
Benoît Mandelbrot
Is not a patron, my lord, one who looks with unconcern on a man struggling for life in the water, and when he has reached ground encumbers him with help The notice which you have been pleased to take care of my labors, had it been early, had been kind but it has been delayed till I am indifferent, and cannot enjoy it till I am solitary, and cannot impart it till I am known, and do not want it. View quote
Samuel Johnson
Philosophy is written in this grand book, which stands continually open before our eyes (I say the 'Universe'), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth. View quote
Galileo Galilei
I can imagine no greater disservice to the country than to establish a system of censorship that would deny to the people of a free republic like our own their indisputable right to criticise their own public officials. While exercising the great powers of the office I hold, I would regret in a crisis like the one through which we are now passing to lose the benefit of patriotic and intelligent criticism. View quote
Woodrow Wilson
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. View quote
Thomas Jefferson