# „The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.“

—  Isaac Newton, buch Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiæ Naturalis Principia Mathematica (1687)

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##### Isaac Newton53
englischer Naturforscher und Verwaltungsbeamter 1643 - 1727

## Ähnliche Zitate

### „The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name.“

—  Isaac Newton, buch Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiae Naturalis Principia Mathematica (1687)
Kontext: The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.

### „Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.“

—  Isaac Newton, buch Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiae Naturalis Principia Mathematica (1687)
Kontext: The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.

### „Useful Things, though Mechanical, are justly preferable to useless Speculations in Geometry“

—  Isaac Newton, buch Arithmetica Universalis

Arithmetica Universalis (1707), p.248

### „I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect... Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.“

—  Carl Friedrich Gauss German mathematician and physical scientist 1777 - 1855

As quoted in Solid Shape (1990) by Jan J. Koenderink

### „The expectations of life depend upon diligence the mechanic that would perfect his work must first sharpen his tools.“

—  Confucius Chinese teacher, editor, politician, and philosopher -551 - -479 v.Chr

Quelle: The Analects of Confucius:

### „More than any of his predecessors Plato appreciated the scientific possibilities of geometry... By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is… clear. …That Plato should hold the view… is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.“

—  David Eugene Smith American mathematician 1860 - 1944

Quelle: History of Mathematics (1923) Vol.1, p. 90

### „Newton… (after having remarked that geometry only requires two of the mechanical actions which it postulates, namely, to describe a straight line and a circle) says: geometry is proud of being able to achieve so much while taking so little from extraneous sources. One might say of metaphysics, on the other hand: it stands astonished, that with so much offered it by pure mathematics it can effect so little.“

—  Immanuel Kant, buch Metaphysische Anfangsgründe der Naturwissenschaft

In the meantime, this little is something which mathematics indispensably requires in its application to natural science, which, inasmuch as it must here necessarily borrow from metaphysics, need not be ashamed to allow itself to be seen in company with the latter.
Preface, Tr. Bax (1883) citing Isaac Newton's Principia
Metaphysical Foundations of Natural Science (1786)

### „The contrivances of nature surpass the contrivances of art, in the complexity, subtlety, and curiosity of the mechanism; and still more, if possible, do they go beyond them in number and variety; yet in a multitude of cases, are not less evidently mechanical, not less evidently contrivances, not less evidently accommodated to their end, or suited to their office than are the most perfect production of human ingenuity.“

—  William Paley Christian apologist, natural theologian, utilitarian 1743 - 1805

Natural Theology (1802)

### „Newton… (after having remarked that geometry only requires two of the mechanical actions which it postulates, namely, to describe a straight line and a circle) says: geometry is proud of being able to achieve so much while taking so little from extraneous sources. One might say of metaphysics, on the other hand: it stands astonished, that with so much offered it by pure mathematics it can effect so little. In the meantime, this little is something which mathematics indispensably requires in its application to natural science, which, inasmuch as it must here necessarily borrow from metaphysics, need not be ashamed to allow itself to be seen in company with the latter.“

—  Immanuel Kant German philosopher 1724 - 1804

Preface, Tr. Bax (1883) citing Isaac Newton's Principia
(1786)

### „We have already various treatises on Mechanics, but the plan of this one is entirely new. I intend to reduce the theory of this Science, and the art of solving problems relating to it, to general formulae, the simple development of which provides all the equations necessary for the solution of each problem. I hope that the manner in which I have tried to attain this object will leave nothing to be desired. No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain.“

—  Joseph Louis Lagrange, buch Mécanique analytique

Mécanique analytique (1788) as quoted by E. W. Hobson, Mathematics, from the points of view of the Mathematician and of the Physicist (1912) an address delivered to the Mathematical and Physical Society of University College London, p.13. https://books.google.com/books?id=H7Y_AQAAIAAJ&pg=PA13

### „Higgs mechanism should be renamed the “ABEGHHK'tH mechanism”“

—  Peter Higgs British physicist 1929

During the opening of one conference Peter Higgs attended to. The name is after all of the people (Philip Warren Anderson, Robert Brout, François Englert, Gerry Guralnik, Dick Hagen, Peter Higgs, Tom Kibble and Gerard 't Hooft) who discovered it, or rediscovered it.

### „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

### „For 12 years I have had the honor of teaching geometry and mechanics applied to the arts, in favor of the industrial class… on the most important questions to the well-being, education, and morality of the workers, to the progress of national industry, to the development of all means of prosperity that work can produce for the splendor and happiness of our country.“

—  Charles Dupin French mathematician 1784 - 1873

Charles Dupin (1831), Discours sur le Sort des Ouvriers [Discourse on the Condition of the Workers] Paris: Bachelier Librairie. p. 1. ; Translation Wren & Bedeian (2005, 73)

### „The mechanical engineer today is carrying forward, under the direction of science, the work that was begun by the mechanic who first learned to chip flint or make a fire; and it is he alone that can lead the mechanic of today to a better understanding of his problems, and the capitalist to a better appreciation of their solution.“

—  Henry Gantt American engineer 1861 - 1919

Quelle: Work, Wages, and Profits: Their Influence on the Cost of Living. 1910, p. 5.

### „Mechanics… was an axiomatic construction; and… its problem could be solved quantitatively by algebraic methods.“

—  Eduard Jan Dijksterhuis Dutch historian 1892 - 1965

Robert Jacobus Forbes and E. J. Dijksterhuis (1963) A History of Science and Technology, vol. I: Ancient Times to the Seventeenth Century, Baltimore.

### „The most efficient and practical interpretation of quantum mechanics is… no interpretation at all.“

—  F. J. Duarte Chilean-American physicist 1954

in [Quantum Optics for Engineers, CRC, New York, 2013, 978-1439888537, F. J. Duarte]

### „The so-called mysteries of quantum mechanics are in its philosophical interpretation, not in its mathematics.“

—  Victor J. Stenger American philosopher 1935 - 2014

In God and the Folly of Faith: The Incompatibility of Science and Religion (2012)

### „Literacy remains even now the base and model of all programs of industrial mechanization; but, at the same time, locks the minds and senses of its users in the mechanical and fragmentary matrix that is so necessary to the maintenance of mechanized society.“

—  Marshall McLuhan Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a communicatio… 1911 - 1980

1960s, Understanding Media (1964)

### „A lawyer without history or literature is a mechanic, a mere working mason; if he possesses some knowledge of these, he may venture to call himself an architect.“

—  Walter Scott Scottish historical novelist, playwright, and poet 1771 - 1832

Sir Walter Scott Collection Guy Mannering. Chap. xxxvii.
Bartlett's Familiar Quotations, 10th ed. (1919)

### „Made poetry a mere mechanic art.“

—  William Cowper (1731–1800) English poet and hymnodist 1731 - 1800

Quelle: Table Talk (1782), Line 654.