# „There are two general Methods made use of in the Mathematicks, viz. Synthesis and Analysis, which we shall explain, after having acquainted the Reader, that the Method we make use of to resolve a Mathematical Problem, is called Zetetick; and that that Method which determines when, and by what way, and how many different ways a Problem may be resolved, is called Poristick. But in treating of Methods, we will first premise, that in general, a Method is the Art of disposing a Train of Arguments or Consequences in a right Order, either to discover the Truth of a Theorem, which we would find out, or to demonstrate it to others, when found.“

Quelle: A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702, p. 26

Übernommen aus Wikiquote. Letzte Aktualisierung 4. Juni 2020. Geschichte
##### Jacques Ozanam
französischer Mathematiker 1640 - 1718

## Ähnliche Zitate

### „I thought fit to… explain in detail in the same book the peculiarity of a certain method, by which it will be possible… to investigate some of the problems in mathematics by means of mechanics. This procedure is… no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards… But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.“

—  Archimedes, buch The Method of Mechanical Theorems

The Method of Mechanical Theorems

### „We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

"The Regressive Method of Discovering the Premises of Mathematics" (1907), in Essays in Analysis (1973), pp. 273–274
1900s

### „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, buch The Method of Mechanical Theorems

The Method of Mechanical Theorems

### „It would be better, I think, for the man who really seeks the truth not to ask what the poets say; rather, he should first learn the method of finding the scientific premises that I discussed in the second book; then he should train and exercise himself in this method; and when his training is sufficiently advanced, then, as he approaches each particular problem, he should enquire into the premise needed for proving it, which premise he should take from simple sense-perception, which from experience, whether drawn from life or from the arts, which from the truths clearly apprehended by the mind, in order to draw out from them the desired conclusion.“

—  Galén Roman physician, surgeon and philosopher 129 - 216

Galen, On the Doctrines of Hippocrates and Plato,: PHP III 8.35.1-11 translation: De Lacy, Phillip (1978- 1984) Galen, On the Doctrines of Hippocrates and Plato, Berlin. p. 233; cited in: Christopher Jon Elliott. "Galen, Rome and the Second Sophistic." p. 147-8.

### „The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.“

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

Discussion to ‘Statistics in agricultural research’ by J.Wishart, Journal of the Royal Statistical Society, Supplement, 1, 26-61, 1934.
1930s

### „Either one or the other [ analysis or synthesis ] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.“

—  André-Marie Ampère French physicist and mathematician 1775 - 1836

André-Marie Ampè, in André-Marie Ampère: Enlightenment and Electrodynamics http://books.google.co.in/books?id=QWZKQWB-sbQC&pg=PA159, Cambridge University Press, 1996, p. 159

### „The order of authority derives from God, as the Apostle says [ in Romans 13:1-7]. For this reason, the duty of obedience is, for the Christian, a consequence of this derivation of authority from God, and ceases when that ceases. But, as we have already said, authority may fail to derive from God for two reasons: either because of the way in which authority has been obtained, or in consequence of the use which is made of it. There are two ways in which the first may occur. Either because of a defect in the person, if he is unworthy; or because of some defect in the way itself by which power was acquired, if, for example, through violence, or simony or some other illegal method.“

—  Thomas Aquinas Italian Dominican scholastic philosopher of the Roman Catholic Church 1225 - 1274

in Aquinas: Selected Political Writings (Basil Blackwell: 1974), p. 183
Commentary on the Sentences of Peter Lombard

### „The method of viewing things which proceeds in accordance with the principle of sufficient reason is the rational method, and it alone is valid and of use in practical life and in science. The method which looks away from the content of this principle is the method of genius, which is only valid and of use in art.“

—  Arthur Schopenhauer, buch Die Welt als Wille und Vorstellung

Die dem Satz vom Grunde nachgehende ist die vernünftige Betrachtungsart, welche im praktischen Leben, wie in der Wissenschaft, allein gilt und hilft: die vom Inhalt jenes Satzes wegsehende ist die geniale Betrachtungsart, welche in der Kunst allein gilt und hilft.
Die Welt als Wille und Vorstellung, Zweiter Band, Ergänzungen zum dritten Buch, para. 36 (1859)
The World as Will and Representation (1819; 1844; 1859)

### „If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems.“

—  David Hilbert, Mathematische Probleme

Mathematical Problems (1900)

### „The entire method consists in the order and arrangement of the things to which the mind’s eye must turn so that we can discover some truth.“

—  René Descartes, buch Rules for the Direction of the Mind

Rules for the Direction of the Mind: X.379
As quoted in [Clarke, Desmond M., 2006, Descartes : a Biography, Cambridge Press, 67, ISBN 978-0-521-82301-2]

### „The vast array of methods and techniques which comprise Buddhism, particularly the Tibetan tradition, are all to help us come to know simply what we are, buddha, awake and aware. Time and time again, we are told that we are buddha, that the buddha qualities are present now, but that we just don’t know it. The problem, for many of us, is that this knowing is not a form of knowing that we are used to. We need tools and methods to dismantle the emotional blocks, the habitual patterns, the worries, concerns, expectations, and hopes that keep us from trusting and knowing what we are.“

—  Ken McLeod Canadian lama 1948

Buddha Nature http://www.unfetteredmind.org/buddha-nature. Unfettered Mind http://www.unfetteredmind.org. (Topic: Practice)

### „Because of experimental science we know a very large number of things about the natural world of which our predecessors were ignorant. In the great books we can observe the birth of science, applaud the development of the experimental technique, and celebrate the triumphs it has won. But we can also note the limitations of the method and mourn the errors that its misapplication has caused. We can distinguish the outlines of those great persistent problems that the method … may never solve and find the clues to their solutions offered by other methods and other disciplines.“

—  Robert Maynard Hutchins philosopher and university president 1899 - 1977

Great Books: The Foundation of a Liberal Education (1954)

### „Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? …If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.“

—  Henri Poincaré, buch Wissenschaft und Hypothese

Quelle: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Kontext: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

### „The right method in any particular case must be largely determined by the nature of the problem.“

—  Arnold Toynbee British economic historian 1852 - 1883

Quelle: Lectures on The Industrial Revolution in England (1884), p. 29

### „Only an unashamed dogmatist would dare to assert that the issue has finally been resolved now, in favor of the view that, outside logic or mathematics, the method of modern science is the only method to employ in seeking knowledge. The dogmatist who made this assertion would have to be more than ashamed. He would have to blind himself to the fact that his own assertion was not established by the experimental method, nor made as an indisputable conclusion of mathematical reasoning or of purely logical analysis.“

—  Robert Maynard Hutchins philosopher and university president 1899 - 1977

Great Books: The Foundation of a Liberal Education (1954)

### „I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.“

—  Hermann Grassmann German polymath, linguist and mathematician 1809 - 1877

Ausdehnungslehre (1844)

### „Object-oriented analysis is a method of analysis that examines requirements from the perspective of the classes and objects found in the vocabulary of the problem domain.“

—  Grady Booch American software engineer 1955

Quelle: Object-oriented design: With Applications, (1991), p. 37

### „If our farmers now used the wasteful methods that served for their great grand-fathers they would not merely fail in the present, but would work a grave wrong to the American citizens of the future. In the same way we must apply new political methods to meet the new political needs, or else we shall stiffer, and our children also.“

—  Theodore Roosevelt American politician, 26th president of the United States 1858 - 1919

1910s, The Progressives, Past and Present (1910)

### „The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.“

—  Paul Carus American philosopher 1852 - 1919

Science, Vol. 18 (1903), p. 106, as reported in Memorabilia Mathematica; or, The Philomath's Quotation-Book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), by Robert Edouard Moritz, p. 352

### „I am SO tired of this trope. It may indeed be the case that we can’t justify a priori via philosophical lucubrations that we arrive at the truth about nature only by using the methods of science. My answer to that is increasingly becoming, “So bloody what?” The use of science is justified because it works, not because we can justify it philosophically. If we are interested in finding out what causes malaria, no amount of appeal to a deity, philosophical rumination, listening to music, reading novels, or waiting for a revelation will answer that question. We have to use scientific methods, which, of course, is how causes of disease are found.“

—  Jerry Coyne American biologist 1949

" A belated reply from Francis Spufford, who defends his faith http://whyevolutionistrue.wordpress.com/2012/10/02/a-belated-reply-from-francis-spufford-who-defends-his-faith/" October 2, 2012