# „The theory of perspective was taught in painting schools from the sixteenth century onward according to principles laid down by the masters... However, their treatises on perspective had on the whole been precept, rule, and ad hoc procedure; they lacked a solid mathematical basis. In the period from 1500 to 1600 artists and subsequently mathematicians put the subject on a satisfactory deductive basis, and it passed from quasi-empirical art to a true science. Definitive works on perspective were written much later by eighteenth-century mathematicians Brook Taylor and J. H. Lambert.“

## Citações relacionadas

### „Germans have a rather healthy respect for the arts and artists, [could] not be more different from the British perspective.“

— Anish Kapoor British contemporary artist of Indian birth 1954

### „The whole Renaissance tradition is antipathic to me. The hard-and-fast rules of perspective which it succeeded in imposing on art were a ghastly mistake which it has taken four centuries to redress; Cézanne and after him Picasso and myself can take a lot of credit for this.... scientific perspective forces the objects in a picture to disappear away from the beholder instead of bringing them within his reach as painting should.“

— Georges Braque French painter and sculptor 1882 - 1963

### „Mathematics is written for mathematicians“

— Nicolaus Copernicus Renaissance mathematician, Polish astronomer, physician 1473 - 1543

Context: If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash. For it is not unknown that Lactantius, the writer celebrated in other ways but very little in mathematics, spoke somewhat childishly of the shape of the earth when he derided those who declared the earth had the shape of a ball. So it ought not to surprise students if such should laugh at us also. Mathematics is written for mathematicians to whom these our labors, if I am not mistaken, will appear to contribute something even to the ecclesiastical state the headship of which your Holiness now occupies. (Author's preface to de revolutionibus) http://la.wikisource.org/wiki/Pagina:Nicolai_Copernici_torinensis_De_revolutionibus_orbium_coelestium.djvu/8
Translation as quoted in The Gradual Acceptance of the Copernican Theory of the Universe (1917) by Dorothy Stimson, p. 115

### „Mathematics is written for mathematicians, to whom these my labours“

— Nicolaus Copernicus Renaissance mathematician, Polish astronomer, physician 1473 - 1543

Context: Nor do I doubt that skilled and scholarly mathematicians will agree with me if, what philosophy requires from the beginning, they will examine and judge, not casually but deeply, what I have gathered together in this book to prove these things.... Mathematics is written for mathematicians, to whom these my labours, if I am not mistaken, will appear to contribute something.... What... I may have achieved in this, I leave to the decision of your Holiness especially, and to all other learned mathematicians.... If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash.
Preface Letter to Pope Paul III as quoted by Edwin Arthur Burtt in The Metaphysical Foundations of Modern Physical Science (1925)

### „It was, however, from Spain, and not from Arabia, that a knowledge of eastern mathematics first came into western Europe. The Moors had established their rules in Spain in 747, and by the tenth or eleven century had attained a high degree of civilisation.“

— W. W. Rouse Ball English mathematician 1850 - 1925

W. W. Rouse Ball, A Short Account of the History of Mathematics (1888), Courier Dover, 1960, p. 164

### „I had this sense that ideas about democracy, theories of democracy which I had learned about of course from graduate school on, from Aristotle and Plato onward, that they were inadequate. I don’t want to diminish them; I have always retained a great respect for classical and medieval and eighteenth-century theory, but meanwhile a whole new kind of political system emerged to which the term democracy became attached, and for which democracy remained an ideal, even though classical democracy as an ideal was so far removed from reality. The gap between that ideal and the actual political institutions that had developed, particularly from about the sixteenth, seventeenth century on, was just enormous. And what we didn’t have enough of, had very little of, was an adequate description of what the actual institutions of so-called democracy, modern democracy, representative democracy, were.“

— Robert A. Dahl American political scientist 1915 - 2014

### „Many of the greatest masters of the mathematical sciences were first attracted to mathematical inquiry by problems relating to numbers, and no one can glance at the periodicals of the present day which contain questions for solution without noticing how singular a charm such problems still continue to exert. The interest in numbers seems implanted in the human mind, and it is a pity that it should not have freer scope in this country. The methods of the theory of numbers 271 are peculiar to itself, and are not readily acquired by a student whose mind has for years been familiarized with the very different treatment which is appropriate to the theory of continuous magnitude; it is therefore extremely desirable that some portion of the theory should be included in the ordinary course of mathematical instruction at our University. From the moment that Gauss, in his wonderful treatise of 1801, laid down the true lines of the theory, it entered upon a new day, and no one is likely to be able to do useful work in any part of the subject who is unacquainted with the principles and conceptions with which he endowed it.“

— James Whitbread Lee Glaisher English mathematician and astronomer 1848 - 1928

p. 467 : On the theory of numbers

### „During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical.“

— Augustus De Morgan British mathematician, philosopher and university teacher (1806-1871) 1806 - 1871

Introductory p.2

### „These rules will enable you to have a free and sound judgment; since good judgment is born of clear understanding, and a clear understanding comes of reasons derived from sound rules, and sound rules are the issue of sound experience — the common mother of all the sciences and arts. Hence, bearing in mind the precepts of my rules, you will be able, merely by your amended judgment, to criticise and recognise every thing that is out of proportion in a work, whether in the perspective or in the figures or any thing else.“

— Leonardo Da Vinci Italian Renaissance polymath 1452 - 1519

### „Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.“

— Auguste Comte French philosopher 1798 - 1857

Bk. 1, chap. 1; as cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), p. 224

### „At the present time it is of course quite customary for physicists to trespass on chemical ground, for mathematicians to do excellent work in physics, and for physicists to develop new mathematical procedures... Trespassing is one of the most successful techniques in science.“

— Wolfgang Köhler German-American psychologist and phenomenologist 1887 - 1967

p. 116

### „Schools currently excel in encouraging children to express opinions, but are deficient in encouraging children to say, for example, “Oh, that’s different from my perspective – tell me more.”“

— Warren Farrell author, spokesperson, expert witness, political candidate 1943

p. 36.

### „For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.“

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

Preface p. v

### „Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.“

— George Frederick James Temple British mathematician 1901 - 1992