a new edition of the Greek text, based on a fresh transcription from the main manuscript and offering an alternative to Hultsch’s standard edition; notes to facilitate understanding of the steps in the mathematical argument; a commentary highlighting aspects of the work that have so far been neglected, and supporting the reconstruction of a coherent plan and vision within the work; bibliographical references for further study. The whole of Book II (the former part of which is lost, the existing fragment beginning in the middle of the 14th proposition) discusses a method of multiplication from an unnamed book by Apollonius of Perga. Drag-and-drop file blocks to change the order. Thus our Euclidean version is essentially equivalent to the full Pappus’s Theorem and not just a special case of it. In Book V, after an interesting preface concerning regular polygons, and containing remarks upon the hexagonal form of the cells of honeycombs, Pappus addresses himself to the comparison of the areas of different plane figures which have all the same perimeter (following Zenodorus's treatise on this subject), and of the volumes of different solid figures which have all the same superficial area, and, lastly, a comparison of the five regular solids of Plato. Prime members enjoy FREE Delivery and exclusive access to music, movies, TV shows, original audio series, and Kindle books. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. The 13-digit and 10-digit formats both work. cases of circles touching one another and inscribed in the figure made of three semicircles and known as arbelos ("shoemakers knife") form the first division of the book; Pappus turns then to a consideration of certain properties of Archimedes's spiral, the conchoid of Nicomedes (already mentioned in Book I as supplying a method of doubling the cube), and the curve discovered most probably by Hippias of Elis about 420 B.C., and known by the name, τετραγωνισμός, or quadratrix. Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere. This volume provides an English translation of Collection 4, in full, for the first time, including: a new edition of the Greek text, based on a fresh transcription from the main manuscript and offering an alternative to Hultsch’s standard edition, notes to facilitate understanding of the steps in the mathematical argument, a commentary highlighting aspects of the work that have so far been neglected, and supporting the reconstruction of a coherent plan and vision within the work, bibliographical references for further study. instance of Pappus’s Theorem to the above situation. Yadav & Man Mohan: Ancient Indian Leaps into Mathematics, This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. These beautifully …, Carol Parikh: The Unreal Life of Oscar Zariski, Oscar Zariski’s work in mathematics permanently altered the foundations of algebraic geometry.


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