Eutocius’ Commentary to On the Sphere and the Cylinder II
Eutocius’ Commentary to On the Sphere and the Cylinder I
... EUTOCIUS’ COMMENTARY TO ON THE SPHERE AND THE CYLINDER I TO BOOK 1 As I found that no one before us had written down a proper treatise on the books of Archimedes on Sphere and Cylinder, 1 and ... fall on the same side of the line, or some fall on the same side, and some on the line itself, but none on the other side.” And the same can be understood for surfaces as well. Then in the following ... argument. 248 eutocius’ commentary to sc i And if they be circumferences, 11 either the container or the contained or even both, the same can be understood. For taking on them < =on the given curved...
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Eutocius’ Commentary to On the Sphere and the Cylinder II
... EUTOCIUS’ COMMENTARY TO ON THE SPHERE AND THE CYLINDER II Now that the proofs of the theorems in the first book are clearly dis- cussed by us, the next thing is the same kind of study with the ... <ratio> of the <square> on AM to the <square> on MH and the <ratio> of AM to MH is the same as the ratio which the cube on AM has to the <cube> on MH; (13) therefore the ratio ... the <square> on O to the <square> on TY, so the height of YtoP. (1) Therefore the cylinder on the base O, having, <as> height, the <line> P, is equal to the < ;cylinder& gt;...
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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
... Book II 18 5Eutocius’ Commentary to On the Sphere andthe Cylinder I 24 3Eutocius’ Commentary to On the Sphere andthe Cylinder II 270Bibliography 369Index 371viiACKNOWLEDGMENTSWork on this volume ... translation 12 Preliminary notes: 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 ... reference: the footnotes and the 8introductioncommentary refer to constructions and to claims according to their letters ornumbers. Note that this is purely my editorial intervention, and that theoriginal...
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On the Sphere and the Cylinder, Book I
... reference is to SC I.42–3. 31 32 on the sphere and the cylinder i base equal to the greatest circle of the <circles> in the sphere, and a height equal to the diameter of the sphere, is, ... musical theory – well known to Archimedes and his audience – 4:3 and 3:2 are, respectively, the ratios of the fourth and the fifth.) 34 on the sphere and the cylinder i To return to the external ... consideration of the work. Once the groundwork is laid, in Propositions 1–22, the second half of the work is less constrained by strong deductive relations, one result leading to the next: the...
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On the Sphere and the Cylinder, Book II
... responsible for the creation of Greek mathematical writing. /1/ The 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 ... the segment the same ratio which: both the radius of the sphere and the 192 on the sphere and the cylinder ii height of the remaining segment, taken together, have to the height of the remaining ... therefore as to , the circle M to the circle around the diameter BZ. 33 (14) And is equal to the axis of the cone M; (15) therefore as to the axis of the cone M, so the circle M to the circle...
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United Nations Convention on the Law of the Sea and the polar marine environment
... Nations Convention on the Law of the Sea and the polar marine environment The 1982 United Nations Convention on the Law of the Sea (LOS Convention) was conceived as a framework convention ... United Nations Convention on the Law of the Sea. 2 34 1 The LOS Convention was negotiated through eleven sessions of the Third United Nations Conference on the Law of the Sea (UNCLOS III), in the period ... application of the LOS Convention. This provision belongs to Part XII of the Convention, which deals with the protection and preservation of the marine environment, and it aims at resolv- ing the...
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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
... begin to take on the responsibility for directing accounts in a mentored environment as theyprogress upwards. • Account Director: the responsibility of the account director is to manage the relationship ... 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 areoften involved in generating new business for the consultancy ... advice.Managers report to account directors and delegate work to the team.• Senior Account Manager: the senior manager role is related to the senior execrole in that it is a transition to the next level....
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Tài liệu COMMUNICATION FROM THE COMMISSION TO THE COUNCIL AND THE EUROPEAN PARLIAMENT Innovation in a knowledge-driven economy ppt
... target-setting, monitoring, evaluation and peer review ofregional and national programmes for enhancing innovation and of the bodies whichimplement them2001At the Union level, the Commission should ... innovation, 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, ... focus on the regulatory environment, in order to contribute to its adaptation to render it more26favourable to innovation and to regular reporting on progress in improving thisenvironment...
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An introduction to black holes information and the string theory
... struc-tureless bare 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 ... phenomenon involving a charge falling onto the stretchedhorizon. More generally, all of the information stored in the incident protonshould quickly be spread over the horizon. On the other hand, the ... region. The proton is like a tiny piece of ice thrown into a tub of veryhot water. The only reasonable expectation is that the constituents of the proton “melt” and diffuse throughout the horizon....
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