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 th...

Ngày tải lên: 01/11/2013, 10:20

... 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...

Ngày tải lên: 01/11/2013, 10:20

... 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 an...

Ngày tải lên: 21/09/2012, 11:00

... 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 t...

Ngày tải lên: 01/11/2013, 10:20

... 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 cy...

Ngày tải lên: 01/11/2013, 10:20

... 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 prov...

Ngày tải lên: 01/11/2013, 09:20

... is related to the senior exec role 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 they progress ... Director: the responsibility of the account director is to manage the relationship with the client and ensure best performance is achieved for both client and...

Ngày tải lên: 13/12/2013, 04:15

... 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. EN 19 In addition to the simplification and harmonisation of their legislative an...

Ngày tải lên: 16/01/2014, 16:33

... 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 transitions from the bare proton to a state with an X-boson and a positron. The com- plicated history of...

Ngày tải lên: 19/01/2014, 13:57

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Ngày tải lên: 18/02/2014, 11:20