On the Sphere and the Cylinder, Book II
On the Sphere and the Cylinder, Book II
... were 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 ... <as> base, [the] <surface> equal to the surface of the sphere, and, <as> height, the radius of the sphere; (46) therefore the cone is equal to the sphere [(47) for the sphere has been...
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Eutocius’ Commentary to On the Sphere and the Cylinder II
... 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 theorems of the second ... is the same as the ratio which the cube on AM has to the <cube> on MH; (13) therefore the ratio of MtoMH, too, is the same as the ratio which the cube on AM has to the <cube> on ... unique point is the one demanded by the conditions of the problem – none of the above being made explicit. 26 Now – and only now – and E have become specific points. 27 Note also that the lines AE,...
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On the Sphere and the Cylinder, Book I
... side of the surface, or some on the same side, and some on < ;the surface> itself, but none on the other side. /5/ And, when a cone cuts a sphere, having a vertex at the center of the sphere, ... taken, the straight <lines> between the <two> points either all 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 ... 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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Cambridge.University.Press.The.Works.of.Archimedes.Volume.1.The.Two.Books.On.the.Sphere.and.the.Cylinder.Translation.and.Commentary.May.2004.pdf
... 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 ... 185Eutocius’ Commentary to On the Sphere andthe Cylinder I 243Eutocius’ Commentary to On the Sphere andthe Cylinder II 270Bibliography 369Index 371viiACKNOWLEDGMENTSWork on this volume was begun ... contribution to an ongoing commonstudy – and as a token of my gratitude.INTRODUCTION1 goal of the translationThe extraordinary influence of Archimedes over the scientific revolution wasdue in the...
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Eutocius’ Commentary to On the Sphere and the Cylinder I
... “curved lines,” and went on to discuss the expression on the same side” and its application for the definition of “concave in the same direction.” Only the diagram for to the definitions 245 B Γ ... 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 seeing that ... suffice for their being unequal, but also “when either: one is wholly contained by the other, or a part is contained, and a part it has common” (and the container is then greater than the contained)....
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the book report on the power and the glory by graham greene
... together in police station. Onewas the picture of an American bank robber who killed several policeofficers in Texas; the other was that of the priest. No one noticed the irony, including the ... he spent the night in a banana warehouse. The Englishmanager on the plantation allowed him to hide there .The following day,hoping to find safety from the police and from the revolutionary party ... to safety. There was one other priest in the region, Father Jose. But Father Jose was so coward, that herenounced the church up to the point of taking a wife, a shrewish oldwoman. The authorities...
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The student and the book
... desultory reading, and even The student and the book 7 then wrote verses.'' 30 The relationship between Poe and the world of books Johnston described aptly conveys the attitude toward ... childhood and adolescence. On one hand, books provided systems of knowledge, ways of organizing the world into knowable facts; on the other hand, books freed the imagination, allowing the reader ... quotations from Joseph Addison, Hugh Blair, Oliver Goldsmith, David Hume, and Samuel Johnson, among many others. The poetry section provided generous The student and the book 3 excerpts from the...
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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 ... answer on how its provisions relate to other international norms. First, one of the Final Provisions (Part XVI) of the Convention deals gener- ally with the relation of the Convention to ‘other conventions...
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Tài liệu Euphorion Being Studies of the Antique and the Mediaeval in the Renaissance - Vol. II pot
... which, the picture of the dying Roland and the picture of the dying Renaud, I would fain bring before you before speaking of the Euphorion, by Vernon Lee 14other Roland and the other Renaud, the ... repetition and alteration. Yet even these alterations could not make the tale of Siegfried survive among the Germans of the Middle Ages; nay, the more the alterations the less the interest; the want ... into the defile, heaped with corpses, and seeks for the bodies of the principal paladins, Ivon and Ivaire, the Gascon Engelier, Gérier and Gérin, Bérenger and Otho, Anseis and Salamon, and the...
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