“He… gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam.”

Source: History of Mathematics (1925) Vol.2, p.464

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 "He… gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam." by David Eugene Smith?

David Eugene Smith33

American mathematician 1860–1944

Related quotes

“have enumerated, in a compendious and systematical form, the principal facts which have been discovered with respect to galvanic electricity; and I have fortunately been able to profit by Mr. Davy's most important experiments, which have lately been communicated to the Royal Society, and which have already given to this branch of science a much greater perfection, and a far greater extent, than it before possessed.”

Thomas Young (scientist) (1773–1829) English polymath

Preface
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

“Cardan's originality in the matter seems to have been shown chiefly in four respects. First, he reduced the general equation to the type x^3 + bx = c; second, in a letter written August 4, 1539, he discussed the question of the irreducible case; third, he had the idea of the number of roots to be expected in the cubic; and, fourth, he made a beginning in the theory of symmetric functions. …With respect to the irreducible case… we have the cube root of a complex number, thus reaching an expression that is irreducible even though all three values of x turn out to be real. With respect to the number of roots to be expected in the cubic… before this time only two roots were ever found, negative roots being rejected. As to the question of symmetric functions, he stated that the sum of the roots is minus the coefficient of x2</sup”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, pp.461-464

“He had waked her; he had given her what she lacked, and what few men could have given her: the sense of peril, which is the root of love.”

Ursula K. Le Guin (1929–2018) American writer

Ile Forest (p. 29)
Short fiction, Orsinian Tales (1976)

“We cannot always choose the vocation to which we believe we are called. Our social relations, to some extent, have already begun to form before we are in a position to determine them.”

Karl Marx (1818–1883) German philosopher, economist, sociologist, journalist and revolutionary socialist

Writings of the Young Marx on Philosophy and Society, L. Easton, trans. (1967), p. 37
Reflections of a Youth on Choosing an Occupation (1835)

“Everyone with any experience of life is aware of the extent to which the characters of people he has known have been given their particular forms by the sufferings through which they have passed. But it is not simply what has happened to them that has defined them; their responses to what has happened to them have been of even greater importance, and these responses have been shaped by their interpretations of what they suffered.”

H. Richard Niebuhr (1894–1962) American theologian

Source: The Responsible Self: An Essay in Christian Moral Philosophy (1963), pp. 60-61

“All of this is so insignificant. In the grand scale of things, there have been so many before who have been in this position. I'm just another one. Life is so short. It's like we're already gone, really, in retrospect.”

Heath Ledger (1979–2008) Australian actor

On fame and celebrity, as quoted in the New York Daily News, June 26, 2000.

“Pāṇini had before him a list of irregularly formed words, which survives, in a somewhat modified form, as the Uṇādi Sūtra. There are also two appendixes to which Pāṇini refers: one is the Dhātupāṭha, "List of Verbal Roots," containing some 2000 roots, of which only about 800 have been found in Sanskrit literature, and from which about fifty Vedic verbs are omitted; the second is the Gaṇapāṭha, or "List of Word-Groups," to which certain rules apply. These gaṇas were metrically arranged in the Gaṇaratna-mahodadhi, composed by Vardhamāna in 1140 A. D.”

Pāṇini ancient Sanskrit grammarian

Appendix A History of Sanskrit Literature

“Thus, while the refugee serfs only wished to be free to develop and assert those conditions of existence which were already there, and hence, in the end, only arrived at free labour, the proletarians, if they are to assert themselves as individuals, will have to abolish the very condition of their existence hitherto (which has, moreover, been that of all society up to the present), namely, labour. Thus they find themselves directly opposed to the form in which, hitherto, the individuals, of which society consists, have given themselves collective expression, that is, the State. In order, therefore, to assert themselves as individuals, they must overthrow the State.”

Karl Marx book The German Ideology

"Communism. The Production of the Form of Intercourse Itself",
The Marx-Engels Reader
The German Ideology (1845/46)

“As for negative numbers… most mathematicians of the sixteenth and seventeenth centuries did not accept them… In the fifteenth century Nicolas Chuquet and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. …Descartes accepted them, in part. …he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 252.

“The position of England, gentlemen, is a peculiar position in the world. England has inherited from bygone ages more, perhaps, of what was most august and venerable in those ages than any other European country, and at the same time that her traditions of the past are so rich and fruitful that all our minds and all our characters have both within our knowledge and beyond our knowledge been largely moulded by them. … geographically she stands with Europe on one side of her and America on the other, so she stands between those feudal institutions in which European society was formed, and which have given her hierarchy of class, and on the other side those principles of equality forming the basis of society in America.”

William Ewart Gladstone (1809–1898) British Liberal politician and prime minister of the United Kingdom

Speech to the Liverpool Liberal Association (6 April 1866), quoted in The Times (7 April 1866), p. 9.
1860s

“He… gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam.”

Help us to complete the source, original and additional information

David Eugene Smith33

Related quotes

Related topics