“The student of the Differential Calculus may… be brought to think it possible that the terms and ideas which that science requires may exist in his own mind in the same rude form as that of a straight line in the conceptions of a beginner in geometry. …he must be prepared to stop his course until he can form exact notions, acquire precise ideas, both of resemblance between those things which have appeared most distinct, and of distinction between those which have appeared most alike. To do this… formal definitions would be useless; for he cannot be supposed to have one single notion in that precise form which would make it worth while to attach it to a word. One reason of the great difficulty which is found in treatises on this subject… the tacit assumption that nothing is necessary previously to actually embodying the terms and rules of the science, as if mere statement of definitions could give instantaneous power of using terms rightly. We shall here attempt… a wider degree of verbal explanation than is usual with the view of enabling the student to come to the definitions in some state of previous preparation.”

— Augustus De Morgan

The Differential and Integral Calculus (1836)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The student of the Differential Calculus may… be brought to think it possible that the terms and ideas which that scien…" by Augustus De Morgan?

Augustus De Morgan 41

British mathematician, philosopher and university teacher (… 1806–1871

Related quotes

“The knowledge of God, the formation of ideas, the mastery of desire and passion, the distinction between that which is to be chosen and that which is to be rejected, all these man owes to his form…”

Maimónides book The Guide for the Perplexed

Source: Guide for the Perplexed (c. 1190), Part III, Ch.8

“A master in the art of living draws no sharp distinction between his work and his play; his labor and his leisure; his mind and his body; his education and his recreation. He hardly knows which is which. He simply pursues his vision of excellence through whatever he is doing, and leaves others to determine whether he is working or playing. To himself, he always appears to be doing both.”

L. P. Jacks (1860–1955) British educator, philosopher, and Unitarian minister

Misattributed to Chateaubriand on the internet and even some recently published books, this statement actually originated with L. P. Jacks in Education through Recreation (1932)
Misattributed

“Like those statues which must be made larger than "nature" in order that, viewed from below, or from a distance, they may appear to be of the "natural" size, certain truths must be "strained" in order that the public may form a just idea of them.”

Joseph Roux (1834–1905) French poet

Part 4, XCIX
Meditations of a Parish Priest (1866)

“The activity of observing establishes a distinction in a space that remains unmarked, the space from which the observer executes the distinction. The observer must employ a distinction in order to generate the difference between unmarked and marked space, and between himself and what he indicates. The whole point of this distinction (its intention) is to mark something as distinct from something else. At the same time, the observer — in drawing a distinction - makes himself visable to others. He betrays his presence - even if a further distinction is required to distinguish him.”

Niklas Luhmann (1927–1998) German sociologist, administration expert, and social systems theorist

Source: Art As a Social System (2000), p. 54 as cited in: Pamela M. Lee (2004) Chronophobia: On Time in the Art of the 1960's. p. 66.

“Without much preliminary exposition and without feeling himself to be out of touch with his contemporaries, Darwin set to work to explain species in terms of the process out of which they have arisen, rather than out of the prime cause to which the distinction between them may he due.”

Thorstein Veblen book The Theory of Business Enterprise

Source: The Theory of Business Enterprise, 1904, p. 369

“It is essentially to the very idea and concept of organization that we there must be a process, formal in character, through which the supreme co-ordinating authority operates throughout the whole structure of the organized body. This process is not an abstraction; it is a tangible reality observable in every organization. It appears in a form so distinct and characteristic that it practically names itself, — hence the term Scalar Process.”

James D. Mooney (1884–1957) American businessman

Source: Onward Industry!, 1931, p. 31

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“In the field of non-Euclidean geometry, Riemann… began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length.
…he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom… In brief, there are no parallel lines. This … had been tried… in conjunction with the infiniteness of the straight line and had led to contradictions. However… Riemann found that he could construct another consistent non-Euclidean geometry.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 454

“In discussing the distinction between minor inventions, whose cumulative impact is decisive in productivity growth, and major technological breakthroughs, it may be useful to draw an analogy between the history of technology and the modem theory of evolution ( … ) Some biologists distinguish between micromutations, which are small changes in an existing species and which gradually alter its features, and macromutations, which creates new species. The distinction between the two could provide a useful analogy for our purposes. I define micro inventions as the small, incremental steps that improve, adapt an extremeline existing techniques already in use, reducing costs, improving form and function, increasing durability, and reducing energy and raw material requirements. Macroinventions, on the other hand, are those inventions in which a radical new idea, without clear precedent, emerges more or less ab nihilo. In terms of sheer numbers, micro inventions are far more frequent and account for most gains in productivity. Macroinventions, however, are equally crucial in technological history.”

Joel Mokyr (1946) Israeli American economic historian

Source: The lever of riches: Technological creativity and economic progress, 1992, p. 12-13 as cited in: Pol, Eduardo, and Peter Carroll. "Innovation heterogeneity and schumpeterian growth models." (2004): 1.

“Between levity and cheerfulness there is a wide distinction; and the mind which is most open to levity is frequently a stranger to cheerfulness.”

Hugh Blair (1718–1800) British philosopher

Reported in The Saturday Magazine‎ (September 28, 1833), p. 118 https://books.google.com/books?id=jh_nAAAAMAAJ&pg=118.

Help us to complete the source, original and additional information

Augustus De Morgan 41

Related quotes

Related topics