Eutocius’ Commentary to On the Sphere and the Cylinder I
Eutocius’ Commentary to On the Sphere and the Cylinder I
... arithmetical treatise of Nicomachus. To write commen- taries on Platonist/Aristotelian treatises, with excursions into elementary mathematics, was the standard among Neo-platonists. Eutocius, evidently ... mathematical significance: Eutocius has a¯tinev where Archimedes has a¬; the toi in Archimedes becomes £ in Eutocius; the word order in the phrase the straight lines joining their limits” differs ... differs slightly between the two versions. Point 1 shows that Eutocius is willing to change the original text while incorporating it into his own discursive prose. This is no direct quotation. Point...
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Eutocius’ Commentary to On the Sphere and the Cylinder II
... of signaling 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 ... common). 38 Elements III.36. 39 Elements III.36. 40 Elements VI.16. 41 And then apply Elements VI.2 in addition to VI.16, to get Step 11. 278 eutocius’ commentary to sc ii in Hero’s construction, ... 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...
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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
... 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 Eutocius’ancient ... conventions 53 Preliminary notes: Archimedes’ works 10Translation and Commentary 2 9On the Sphere and the Cylinder, Book I 3 1On the Sphere and the Cylinder, Book II 18 5Eutocius’ Commentary to On ... Archimedes kept in several libraries: the NationalLibrary in Paris, the Marcian Library in Venice, the Laurentian Libraryin Florence and the Vatican Library in Rome. The librarians at theseinstitutions...
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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 ... magnitudes and a circle, it is possible to inscribe a polygon inside the circle and to circumscribe another, so that the side i. 3 47 of the circumscribed polygon has to the side of the inscribed ... Definition 1 demands that the line be consistent in its non- straightness relative to its start and end points only, Definition 2 demands that the line be consistent in its non-straightness relative...
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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 ... second was: given a cone or a cylinder, to find a sphere equal to the cone or to the cylinder. 188 on the sphere and the cylinder ii Let a cone or a cylinder be given, A, (a) and let the sphere ... participating in the geometrical configuration. Imagination is a spatial, not a conceptual act. The purely conceptual cone M need not be imagined – it is beyond the pale of imagination, it exists not in...
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United Nations Convention on the Law of the Sea and the polar marine environment
... although the activity endangering the marine environment is not navigation. In Part XI of the Convention (entitled The Area’) special consideration is given to the protection of the marine environment ... derived from 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, ... jurisdiction of the coastal state in respect of the protection and preservation of the marine environment’ in its exclusive economic zone is confirmed in the basic provisions on the rights, jurisdiction...
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Tài liệu The Insider’s Guide to PR: Chapter 4 A PR LIFE – THE LADDER, THE PAY AND THE LIFESTYLE doc
... is related to the senior execrole in that it is a transition to the next level. Senior managers will begin to take on the responsibility for directing accounts in a mentored environment as theyprogress ... Director: the responsibility of the account director is to manage the relationship with the client and ensure best performance is achieved for bothclient and consultancy. The account director ... client work at a high-level –day -to- day running of the account is left to the manager – but it is still up to the director to know what is going on and to ensure the client is happy. Directors...
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Tài liệu COMMUNICATION FROM THE COMMISSION TO THE COUNCIL AND THE EUROPEAN PARLIAMENT Innovation in a knowledge-driven economy ppt
... for dialogue on innovation policies in the Union, and their coordination,– Work to improve the availability of statistics relating to innovation,– Organisation of “peer reviews” on topics of ... while taking other objectives, such as the global reduction of State aid, into consideration.EN19In addition to the simplification and harmonisation of their legislative and administrativerules, ... as to lead to the dynamic conditions, and hence growth and quality jobs, thatinnovation can bring. The general climate for innovation in Member States is conditioned by national and regionalinnovation...
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An introduction to black holes information and the string theory
... 1.12).Finally, the quantum Xerox principle closes out the last possibility. The information conservation principle requires all information to be returned to the outside in Hawking radiation. The equivalence ... proton. The interactions cause it to make virtual transitionsfrom the bare proton to a state with an X-boson and a positron. The com-plicated history of the proton is described by Feynman diagrams ... ∼2P∆τ∼2PMGet/4MGThus, if the proton size depends on the time resolution according to equa-tion 10.0.3, it will spread over the horizon exponentially fast. The idea of information spreading as the resolving time...
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