On the Sphere and the Cylinder, Book I
On the Sphere and the Cylinder, Book I
... same side of the straight. It is only this family which is being discussed in the following Definition 2 (a similar family, this time for planes, is singled out in Definition 3, and is discussed in ... observations on his linguistic habits and assumptions. general comments Definitions 1–4 Following Archimedes, we start with Definition 1. Imagine a “curved line,” and the straight line joining its ... astronomer: the main indications are Apollonius’ Conics, introduction to Book IV, Diocles’ On Burning Mirrors, introduction, and Catullus’ poem 66.) Archimedes shows less admiration towards Dositheus....
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Eutocius’ Commentary to On the Sphere and the Cylinder I
... that “there are in a plane some curved lines, which are either all on the same side as the straight lines joining their limits or have nothing on the other side.” 3 The assertion will be clear if ... those which are composed of straight lines, and it is among these that lines concave in the same direction are identified, it is possible to take, on some line, concave in the same direction, two ... points, so that the line joined to them will fall on neither side of the line, but will coincide with the line itself. Therefore he says that he calls “concave in the same direction, a line in...
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On the Sphere and the Cylinder, Book II
... answering the three sine qua non conditions of Greek mathematical communication – written, proved, drawn. What is the relation between the idea in the mind of the mathematician and the idea in actual ... operation of “imagination:” the border between the conceptual and spatial The construction furnishes us with a new handle on the operation of imagi- nation: “(b) and let a cone be imagined, having, ... +E:E (and so the “dividedly” operation bites). That is, a spatial de- composition enters inside a proportion. With this implicit reinterpretation and the verbal manipulation of the “dividedly,” we...
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Cambridge.University.Press.The.Works.of.Archimedes.Volume.1.The.Two.Books.On.the.Sphere.and.the.Cylinder.Translation.and.Commentary.May.2004.pdf
... 10Translation and Commentary 2 9On the Sphere and the Cylinder, Book I 3 1On the Sphere and the Cylinder, Book II 185Eutocius’ Commentary to On the Sphere andthe Cylinder I 243Eutocius’ Commentary to On ... the NationalLibrary in Paris, the Marcian Library in Venice, the Laurentian Libraryin Florence and the Vatican Library in Rome. The librarians at theseinstitutions were all very kind and patient ... fledgedtranslation of his works into English. It is also the first publication ofa major ancient Greek mathematician to include a critical edition ofthe diagrams, and the first translation into English of...
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Eutocius’ Commentary to On the Sphere and the Cylinder II
... reciprocal to the heights; 13 (3) and the task is then made. And if it is not the base being given, but the axis, then, obtaining Y by the same principle, the things mentioned in the proposition will ... magnitude, as a position: it is the line on which Z is situated, K is erected, etc. Hence the strange description, “Given in position, limited at .” 101 Z begins as a position at (d) and becomes ... generalizability. Rather, the hypothetical nature of the construction is stressed. Further, the main idea of the construction is to fix a machine on a diagram. So the impression is as hero 275...
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the book report on the power and the glory by graham greene
... working on the Church by administering the sacraments,listening confessions and saying masses. A young lieutenant of police, and ardent revolutionist and an anti-clerical, asked his chief to let himsearch ... policeofficers in Texas; the other was that of the priest. No one noticed the irony, including the young lieutenant, who was more interested inarresting the priest. When the officer received ... villagestreets, and across impassible mountain ranges, half-believing that I would glimpse a dim figure stumbling in the rain on his way to the border.There is no greater tribute possible to your creation...
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The student and the book
... his familiarity with Sinbad the Sailor 1 and Jack and the Beanstalk; new London editions of these two works appeared the year the Allan family came to England. 3 So did new editions of The History ... of his narrative; 10 Poe and the printed word yet in dignity, in strength, in harmony and in purity, he is surpassed by Robertson, who in his History of Scotland, his ®rst and, in our opinion, ... express his literary ambitions by writing poetry and critiquing the work of established writers. Might Poe's literary The student and the book 11 aspirations have allowed him to consider a...
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United Nations Convention on the Law of the Sea and the polar marine environment
... the protection and preservation of the marine environment’ in its exclusive economic zone is confirmed in the basic provisions on the rights, jurisdiction and duties of the coastal state in the ... this provision is the possibility of differentiating between developed and developing states in relation to the interpretation and application of some provisions of the Convention, as well as in ... provisions. The Convention contains only basic, general principles on the protection of the marine environ- ment. Provisions dealing with particular sources of pollution, with the protection of...
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