“The Arithmetica… is deficient, sometimes pardonably, sometimes without excuse, in generalization. The book of Porismata, to which Diophantus sometimes refers, seems on the other hand to have been entirely devoted to the discussion of general properties of numbers. It is three times expressly quoted in the Arithmetica… Of all these propositions he says… 'we find it in the Porisms'; but he cites also a great many similar propositions without expressly referring to the Porisms. These latter citations fall into two classes, the first of which contains mere identities, such as the algebraical equivalents of the theorems in Euclid II…. The other class contains general propositions concerning the resolution of numbers into the sum of two, three or four squares…. It will be seen that all these propositions are of the general form which ought to have been but is not adopted in the Arithmetica. We are therefore led to the conclusion that the Porismata, like the pamphlet on Polygonal Numbers, was a synthetic and not an analytic treatise. It is open, however, to anyone to maintain the contrary, since no proof of any porism is now extant.”

p, 125
A Short History of Greek Mathematics (1884)

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 Arithmetica… is deficient, sometimes pardonably, sometimes without excuse, in generalization. The book of Porismata…" by James Gow (scholar)?

James Gow (scholar)22

scholar 1854–1923

Related quotes

“The most probable view is that adopted by Nesselmann, that the works which we know under the three titles formed part of one arithmetical work, which was, according to the author's own words, to consist of thirteen Books. The proportion of the lost parts to the whole is probably less than it might be supposed to be. The Porisms form the part the loss of which is most to be regretted, for from the references to them it is clear that they contained propositions in the Theory of Numbers most wonderful for the time.”

Thomas Little Heath (1861–1940) British civil servant and academic

Source: Diophantos of Alexandria: A Study in the History of Greek Algebra (1885), Ch. II, p.37

“Sometimes… Diophantus solves a problem wholly or in part by synthesis…. Although… Diophantus does not treat his problems generally and is usually content with finding any particular numbers which happen to satisfy the conditions of his problems,… he does occasionally attempt such general solutions as were possible to him. But these solutions are not often exhaustive because he had no symbol for a general coefficient.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

“My memoirs "On the Mechanical Theory of Heat" are of different kinds. Some are devoted to the development of the general theory and to the application thereof to those properties of bodies which are usually treated of in the doctrine of heat. Others have reference to the application of the mechanical theory of heat to electricity. …Other memoirs… have reference to the conceptions I have formed of the molecular motions which we call heat. These conceptions, however, have no necessary connexion with the general theory, the latter being based solely on certain principles which may be accepted without adopting any particular view as to the nature of molecular motions. I have therefore kept the consideration of molecular motions quite distinct from the exposition of the general theory.”

Rudolf Clausius (1822–1888) German mathematical physicist

Preface (August, 1864)
The Mechanical Theory of Heat (1867)

“…if you have so many lawyers, they have to find business, which sometimes they have to create. Sometimes nonsensical lawsuits are generated by lawyers. In this country (the United States everybody sues everybody.”

Akio Morita (1921–1999) Japanese businessman

Source: Made in Japan (1986), p. 174.

“Discussions without end have been devoted to the subject of peace, and the efforts to obtain a general and lasting peace have been frequent through many years of world history.”

George Marshall (1880–1959) US military leader, Army Chief of Staff

Essentials to Peace (1953)
Context: Discussions without end have been devoted to the subject of peace, and the efforts to obtain a general and lasting peace have been frequent through many years of world history. There has been success temporarily, but all have broken down, and with the most tragic consequences since 1914. What I would like to do is point our attention to some directions in which efforts to attain peace seem promising of success.