In his curious tract on Stereometry, published in 1615, Kepler made some advances in the doctrine of infinitesimals. Prompted to the task by a dispute with the seller of some casks of wine, he studied the measurement of solids formed by the revolution of a curve round any line whatever. In solving some of the simplest of these problems, he conceived a circle to be formed of an infinite number of triangles having all their vertices in the centre, and their infinitely small bases in the circumference of the circle, and by thus rendering familiar the idea of quantities infinitely great and infinitely small, he gave an impulse to this branch of mathematics. The failure of Kepler, too, in solving some of the more difficult of the problems which he himself proposed roused the attention of geometers, and seems particularly to have attracted the notice of Cavaleri.
Johannes KeplerRelated topics
attention base branch centre circle circumference curve dispute doctrine failure familiar great having idea impulse infinite line mathematics measurement notice number rendering revolution round seller small solving stereometry study task thus tract vertex whatever wine kepler trianglesRelated quotes
For in spite of much greater public interest in all aspects of visual culture, including design and architecture, the challenge posed by contemporary art has not evaporated. We have only to recall the headlines for last year's Turner Prize. "Eminence without merit" (The Sunday Telegraph). "Tate trendies blow a raspberry" (Eastern Daily Press), and my favourite, "For 1,000 years art has been one of our great civilising forces. Today, pickled sheep and soiled bed threaten to make barbarians of us all" (The Daily Mail). Are these papers speaking the minds of their readers? I have no delusions. People may be attracted by the spectacle of new buildings, they may enjoy the social experience of visiting a museum, taking in the view, an espresso or glass of wine, purchasing a book or an artist designed t-shirt. Many are delighted to praise the museum, but remain deeply suspicious of the contents.
Nicholas Serota
There are two types of education: education for livelihood and education for life. When we study in college, it helps us to get a job so that we can earn a living. We can become a doctor, a scientist, an engineer or whatever we want. We may go on to attain wealth, possession and fame. All of this comes from education for livelihood. But this alone will never make our life full and complete. Education is not only to help us live a comfortable life of plenty. When our plans fall apart, when we face failure and loss, when we are knocked down, education should help us get back on our feet. Education should help us regain our mental equipoise, self-confidence and positive attitude, so that we can continue forward. This is why education for life is as important as education for livelihood. Education for life is spirituality.
Mata Amritanandamayi
Hippocrates himself is an example of the concurrent study of the two departments. On the one hand, he was the first of the Greeks who is known to have compiled a book of Elements. This book, we may be sure, contained in particular the most important propositions about the circle included in Euclid, Book III. But a much more important proposition is attributed to Hippocrates; he is said to have been the first to prove that circles are to one another as the squares on their diameters (= Eucl. XII., 2) with the deduction that similar segments of circles are to one another as the squares on their bases. These propositions were used by him in his tract on the squaring of lunes, which was intended to lead up to the squaring of the circle. The latter problem is one which must have exercised practical geometers from time immemorial. Anaxagoras for instance is said to have worked at the problem while in prison.
Thomas Little Heath
The idea that work is something apportioned out by men leaves people discontent with their portion and dubious about whether work is a good thing at all. ... The ancient injunction to labor fades when we regard our work as cut out for us by men, who, by present dogma, are no better than ourselves. That curious modern hypostatization "service” is often called in to substitute for the now incomprehensible doctrine of vocation. It tries to secure subordination by hypothesizing something larger than the self, which turns out, however, to be only a multitude of selfish selves. The familiar change from quality to quantity may again be noted; one serves not the higher part of the self (this entails hierarchy) ... but merely consumer demand. And who admires those at the top of a hierarchy of consumption? Man as a consuming animal is thus seen to be not enough.
Richard Weaver
As a graduate student at Yale, I studied the whole of Christian theology but focused my attention on the Darwinian controversies. I wanted to get to the root of the conflict between Darwinian evolution and Christian doctrine. In the course of my research I learned (to my surprise) that biblical chronology played almost no role in the 19th- century controversies, since most theologians had already accepted geological evidence for the age of the earth and re-interpreted the days in Genesis as long periods of time. Instead, the central issue was design. God created the cosmos with a plan in mind. This affirmation is among the most basic in all of Christianity (and other theistic religions as well, including Unificationism). And that plan included human beings as the final outcome of the creative process: we are created in the image of God.
Jonathan Wells
