“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress. Diophantus also represents the outbreak of a movement which probably was not Greek in its origin, and which the Greek genius long resisted, but which was especially adapted to the tastes of the people who, after the extinction of Greek schools, received their heritage and kept their memory green. But no Indian or Arab ever studied Pappus or cared in the least for his style or his matter. When geometry came once more up to his level, the invention of analytical methods gave it a sudden push which sent it far beyond him and he was out of date at the very moment when he seemed to be taking a new lease of life.”

— James Gow (scholar)

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

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James Gow (scholar) 22

scholar 1854–1923

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“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress.”

Ptolemy (100–170) Greco-Egyptian writer and astronomer of Alexandria

James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884) p.308.

“With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.”

James Gow (scholar) (1854–1923) scholar

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

“Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions and determinations which are not in the problem. Of such "fudged" solutions, as a schoolboy would call them, two particular kinds are very frequent. Sometimes an unknown is assumed at a determinate value… Sometimes a new condition is introduced.”

James Gow (scholar) (1854–1923) scholar

A Short History of Greek Mathematics (1884)

“It would be inconvenient to interrupt the account of Menaechmus's solution of the problem of the two mean proportionals in order to consider the way in which he may have discovered the conic sections and their fundamental properties. It seems to me much better to give the complete story of the origin and development of the geometry of the conic sections in one place, and this has been done in the chapter on conic sections associated with the name of Apollonius of Perga. Similarly a chapter has been devoted to algebra (in connexion with Diophantus) and another to trigonometry”

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

under Hipparchus, Menelaus and Ptolemy
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.”

James Gow (scholar) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

“The cultural tradition of which the Greek language is the focal point has the longest unbroken history of any in Europe. The Greek state, however, was newly born out of the conflict of 1821-8 and was without precedent in the history of the Greeks. The newly defined nation therefore had, as a matter of urgency, to create its own past, that is, to select and endorse those elements of earlier Greek history which retrospectively could claim to have made the present existence and future aspirations of the nation inevitable. Since the state itself was in many ways the creation of European Romanticism, it was only natural that the means to hand for defining and justifying its existence should derive from the same source.”

Roy Porter (1946–2002) British historian

[Roderick Beaton, Mikuláš Teich & Roy Porter, Romanticism in national context, Cambridge University Press, Cambridge, UK, 1988, 99, 0-521-33913-8]

“The future belongs to the young. It is a young and new world which is now under process of development and it is the young who must create it. But it is also a world of truth, courage, justice, lofty aspiration and straightforward fulfilment which we seek to create. For the coward, for the self-seeker, for the talker who goes forward at the beginning and afterwards leaves his fellows in the lurch there is no place in the future of this movement. A brave, frank, clean-hearted, courageous and aspiring youth is the only foundation on which the future nation can be built….”

Sri Aurobindo (1872–1950) Indian nationalist, freedom fighter, philosopher, yogi, guru and poet

August 7, 1909
India's Rebirth

“Nationalism is always an effort in a direction opposite to that of the principle which creates nations. The former is exclusive in tendency, the latter inclusive.”

José Ortega Y Gasset book The Revolt of the Masses

Source: The Revolt of the Masses (1929), Chapter XIV: Who Rules The World?
Context: Nationalism is always an effort in a direction opposite to that of the principle which creates nations. The former is exclusive in tendency, the latter inclusive. In periods of consolidation, nationalism has a positive value, and is a lofty standard. But in Europe everything is more than consolidated, and nationalism is nothing but a mania, a pretext to escape from the necessity of inventing something new, some great enterprise.

“The only simplicity for which I would give a straw is that which is on the other side of the complex — not that which never has divined it.”

Oliver Wendell Holmes Jr. (1841–1935) United States Supreme Court justice

"Holmes-Pollock Letters : The Correspondence of Mr. Justice Holmes and Sir Frederick Pollock, 1874-1932" (2nd ed., 1961), p. 109.
Often quoted as "I wouldn't give a fig for the simplicity on this side of complexity; I would give my right arm for the simplicity on the far side of complexity" and attributed to Oliver Wendell Holmes, Sr..
1930s

“At last, here is a new man [ Millet ], who has the knowledge which I would like to have, and movement, color, expression, too, - here is a painter!”

Narcisse Virgilio Díaz (1807–1876) French painter

Quote of Diaz, 1844; as cited by fr:Alfred Sensier, in Jean-Francois Millet – Peasant and Painter, translated from the French original by Helena de Kay; publ. Macmillan and Co., London, 1881, p. 62
Diaz de la Peña gave this comment when he saw for the first time work of Millet: the painting 'The Riding Lessons' on the Paris' Salon of 1844
Quotes of Diaz

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James Gow (scholar) 22

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