1. Citáty
  2. Autoři
  3. Augustus De Morgan

Augustus De Morgan citáty
strana 2

Augustus De Morgan byl britský matematik, který představil formální verze zákonů v klasické výrokové logice.

De Morganův zápis byl ovlivněn algebrarickou logikou vymyšlenou Georgem Boolem, který se později přihlásil o část zásluh na těchto logických zákonech. Ačkoliv byla podobná pozorování zapsána již Aristotelem a byly známy už ve starém Řecku a ve středověku, De Morgan jim dodal klasickou formu a zavedl tím matematickou řeč do matematické logiky. De Morganovy zákony jsou lehce dokazatelné a mohou se jevit triviálními. Nicméně, tyto zákony jsou užitečné pro důkazy platnosti závěrů a pro deduktivní úlohy. Wikipedia  

✵ 27. červen 1806 – 18. březen 1871
Augustus De Morgan foto
Augustus De Morgan: 41 citátů0 lajků

Augustus De Morgan: Citáty anglicky

“The moving power of mathematical invention is not reasoning, but imagination.”

Help us translate this quote

Augustus De Morgan

Quoted in Robert Perceval Graves, The Life of Sir William Rowan Hamilton, Vol. 3 (1889), p. 219.

“I am far from saying that this Treatise will be easy; the subject is a difficult one, as all know who have tried it.”

Help us translate this quote

Augustus De Morgan

Advertisement, p.4
The Differential and Integral Calculus (1836)

“The work now before the reader is the most extensive which our language contains on the subject.”

Help us translate this quote

Augustus De Morgan

Preface, p. iii
The Differential and Integral Calculus (1836)

“The absolute requisites for the study of this work… are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.
…A. De Morgan. London July 1, 1836”

Help us translate this quote

Augustus De Morgan

The Differential and Integral Calculus (1836)

“Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise.”

Help us translate this quote

Augustus De Morgan

Zdroj: On the Study and Difficulties of Mathematics (1831), Ch. I.

“Aspiring to lead others, they have never given themselves the fair chance of being first led by other others into something better than they can start for themselves; and that they should first do this is what both those classes of others have a fair right to expect. New knowledge… must come by contemplation of old knowledge… mechanical contrivance sometimes, not very often, escapes this rule.”

Help us translate this quote

Augustus De Morgan

Introductory p.5
A Budget of Paradoxes (1872)

“I did not hear what you said, but I absolutely disagree with you.”

Help us translate this quote

Augustus De Morgan

Attributed to Augustus De Morgan in: August Stern (1994). The Quantum Brain: Theory and Implications. North-Holland/Elsevier. p. 7

“A great many individuals ever since the rise of the mathematical method, have, each for himself, attacked its direct and indirect consequences. …I shall call each of these persons a paradoxer, and his system a paradox.”

Help us translate this quote

Augustus De Morgan

I use the word in the old sense: ...something which is apart from general opinion, either in subject-matter, method, or conclusion. ...Thus in the sixteenth century many spoke of the earth's motion as the paradox of Copernicus, who held the ingenuity of that theory in very high esteem, and some, I think, who even inclined towards it. In the seventeenth century, the depravation of meaning took place... Phillips says paradox is "a thing which seemeth strange"—here is the old meaning...—"and absurd, and is contrary to common opinion," which is an addition due to his own time.
A Budget of Paradoxes (1872)

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit.”

Help us translate this quote

Augustus De Morgan

It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.
The Differential and Integral Calculus (1836)

“Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction.”

Help us translate this quote

Augustus De Morgan

This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could.
The Differential and Integral Calculus (1836)

“I have throughout introduced the Integral Calculus in connexion with the Differential Calculus. …Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction?”

Help us translate this quote

Augustus De Morgan

The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold...
The Differential and Integral Calculus (1836)