# „Hippocrates... is said to have proved the theorem that circles are to one another as the squares on their diameters, and it is difficult to see how he could have done this except by some form, or anticipation, of the method [of exhaustion].“

—  Thomas Little Heath, p, 125
##### Thomas Little Heath45
British civil servant and academic 1861 - 1940

### „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 British civil servant and academic 1861 - 1940
p, 125

### „A circle looks at a square and sees a badly made circle.“

—  Jeff VanderMeer, Authority

### „If you have formed a circle to go into,Go into it yourself and see how you would do.“

—  William Blake English Romantic poet and artist 1757 - 1827
To God

### „The method of exhaustion was not discovered all at once; we find traces of gropings after such a method before it was actually evolved. It was perhaps Antiphon. the sophist, of Athens, a contemporary of Socrates, who took the first step. He inscribed a square (or, according to another account, a triangle) in a circle, then bisected the arcs subtended by the sides, and so inscribed a polygon of double the number of sides; he then repeated the process, and maintained that, by continuing it, we should at last arrive at a polygon with sides so small as to make the polygon coincident with the circle. Thought this was formally incorrect, it nevertheless contained the germ of the method of exhaustion.“

—  Thomas Little Heath British civil servant and academic 1861 - 1940
p, 125

### „No one ever squared the circle with so much genius, or, excepting his principal object, with so much success.“

—  Jean-Étienne Montucla French mathematician 1725 - 1799
Attributed to Montucla in Augustus De Morgan, A Budget of Paradoxes, (London, 1872), p. 96; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book, (1914) p. 366 About Gregory St. Vincent, described by De Morgan as "the greatest of circle-squarers, and his investigations led him into many truths: he found the property of the arc of the hyperbola which led to Napier's logarithms being called hyperbolic."

### „The point is that philosophy is seen to have come full circle, and to have exhausted itself.“

—  David Wood British philosopher, born 1946 1946
Chapter 5, Nietzsche's Styles, p. 95

### „How can a man be said to have a country where he has no right to a square inch of soil...“

—  Henry George American economist 1839 - 1897
Ch. 2 : Political Dangers

### „I agreed the situation was sticky. Indeed, offhand it was difficult to see how it could have been more glutinous.“

—  P.G. Wodehouse English author 1881 - 1975

### „I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.“

—  Archimedes Greek mathematician, physicist, engineer, inventor, and astronomer -287 - -212 a.C.

### „History can predict nothing except that great changes in human relationships will never come about in the form in which they have been anticipated.“

—  Johan Huizinga Dutch historian 1872 - 1945
De historie kan niets voorspellen, behalve één ding: dat geen groote wending in de menschelijke verhoudingen ooit uitkomt in den vorm, waarin vroeger levenden zich haar hebben kunnen verbeeld. Ch. 20.

### „In the name of Hippocrates, doctors have invented the most exquisite form of torture ever known to man: survival.“

—  Luis Buñuel film director 1900 - 1983

### „One physicist writes a study on microphysics, but another writes a book on the importance of Lenin’s and Engels’ works for the development of physics; one mathematician proves theorems, another publishes demagoguery on ingenious mathematical ideas of classical Marxists.“

—  Aleksandr Zinovyev Russian writer 1922 - 2006

### „Eudoxes... not only based the method [of exhaustion] on rigorous demonstration... but he actually applied the method to find the volumes (1) of any pyramid, (2) of the cone, proving (1) that any pyramid is one third part of the prism which has the same base and equal height, and (2) that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them (which no doubt means, not that he gave no sort of proof, but that he was not able to establish the propositions by the rigorous methods of Eudoxes. Archimedes adds that we must give no small share of the credit for these theorems to Democritus... another testimony to the marvellous powers, in mathematics as well as in other subjects, of the great man who, in the words of Aristotle, "seems to have thought of everything".... Democritus wrote on irrationals; he is also said to have discussed the question of two parallel sections of a cone (which were evidently supposed to be indefinitely close together), asking whether we are to regard them as equal or unequal... Democritus was already close on the track of infinitesimals.“

—  Thomas Little Heath British civil servant and academic 1861 - 1940

### „Only when the habit of one's consciousness to see in paintings bits of nature, Madonna's and shameless nudes.... has disappeared, shall we see a pure painting composition. I have transformed myself into the nullity of forms and pulled myself out of the circle of things, out of the circle-horizon in which the artist and forms of nature are locked.“

—  Kazimir Malevich Russian and Soviet artist of polish descent 1879 - 1935
as quoted in: Marc Chagall, – a Biography, Sidney Alexander, Cassell, London, 1978, p. 178

### „It can be... difficult to to learn how the world truly is, to see it in its true shape and form... most human beings never do. Most could not bear it.“

—  Cassandra Clare, Clockwork Angel

### „I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof“

—  Pierre de Fermat French mathematician and lawyer 1601 - 1665
Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square. Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)