Product Description

Although not so well known today, Book 4 of Pappus’ Collection is one of the most important and influential mathematical texts from antiquity, both because of its content and because of its impact on early modern mathematics after 1600. As a kind of textbook in anthology format, the mathematical vignettes form a portrait of mathematics during the Hellenistic "Golden Age", illustrating central problems – for example, it discusses all three of the famous ancient problems in geometry: squaring the circle; doubling the cube; and trisecting an angle – varying solution strategies, and the different mathematical styles within ancient geometry.

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.

Historians of mathematics will find it useful for scholarly work on ancient geometry and its reception in the early modern era and it will also serve as a source book for exemplary arguments in ancient geometry. Pappus himself probably intended Collection 4 to be an introductory survey of the classical geometrical tradition – from the point of view of mathematical methods and strategies – for readers that had a basic training in elementary geometry (Elements I – VI). Likewise, this edition can be used as a textbook in advanced undergraduate and graduate courses on the history of ancient geometry.

Product Description
This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus' text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity. ... Read more

Customer Reviews (2)

Run-of-the-mill sociology of science
This predictable book betrays the author's eagerness to conform to the academic fashions of the day. Its predictable thesis is that "Pappus was not operating in a vacuum" (pp. 89-90); rather he had an "agenda" (e.g., p. 169) to "augment his prestige" (p. 200), etc., etc. In other words, the usual staple thesis of the pomo generation of historians. One impatiently awaits the day when the sterility and mediocrity of such flavour-of-the-month scholarship will be recognised. A typical passage may illustrate its futility:

"It is remarkable, I think, that in the case of book 4 the reader is left to fend for himself through a text difficult to understand even for skilled mathematicians ... while, in the case of book 5, the reader is not even expected to be acquainted with one of Archimedes' most famous discoveries ... These marked double standards ... can only be explained on the basis of two different kinds of intended readership." (p. 73)

There you have it---groundbreaking revelations of cutting-edge science studies research: some guy wrote for different audiences in different styles. If you find this "remarkable" then you're in for a treat.

As an additional illustration of Cuomo's tasteless catering to the establishment, we may quote the very first sentence of a section called "Mathematics and the stars":

"That astrological texts could be fruitfully used by ancient historians was an idea first put forwards by Lynn Thorndike, revived by Ramsay MacMullen and later applied with interesting results by Tamsyn Barton." (p. 10)

I for one would prefer if Cuomo put substance first and incestuous scholarly accolades and pedigrees second. But since Cuomo is clearly more concerned with fitting in with her peers than with addressing interesting and important historical questions, her backwards approach makes perfect sense.

Interesting project
Cuomo starts this book by suggesting we don't understand the late-classical era, that great confusing muddle which starts around 300 AD when Constantine transferred the capital of the Roman Empire to Constantinople and legalized Christianity. It ends with the Muslim conquest of Alexandria. In crude terms, it is what Gibbon called the 'fall of the Roman Empire.' Cuomo uses the 'Arch of Constantine' as a metaphoric reference. For most contemporary art historians, the arch is a pastiche of scavenged sculptures from earlier and finer artistic efforts. Scavenged is the key word here. The late-antiquity (according to Gibbon) was the moral equivalent of Sodom and Gomorrah.

I don't know how many people still take "Rome's Fall' as a moral litmus test, but I suspect the story still holds a lot of weight. It's this icon that Cuomo targets.

In general terms, I couldn't be more pleased with the project. Unfortunately, it doesn't really get off the ground. Cuomo isn't very forth coming on what she makes of the era. It seems she simply likes pastiche.

She starts her iconoclastic journey well, suggesting the subject of her book might never have existed. It is hard to argue the point. We know almost nothing about Pappus, the man. Unfortunately, the fictional Pappus concept seems to have been mentioned for shock value, and not pursued seriously. I would have been interested in hearing details on the process of putting mathematic lectures on scrolls for academic, social or bureaucratic purposes. Maybe ghost writing was a common practice. This emphasis on the 'media' itself seems critical to Cuomo's case (a role the Arch of Constantine served), but it is entirely ignored.

Cuomo then takes us down an entertaining bunny hole involving legal torture and highly paid astrologers. By taking this route, she hopes to convince us that mathematics was about as important to our late-classical delinquents as, well, ourselves. The legal discussion shows mathematical knowledge put one socially above those who could expect torture during any legal cross-examination. The astrological references show desperate young parents prayed for their off-spring to become mathematicians.

So far, so good, but Cuomo then launches into a book by book deconstruction of the works ascribed to Pappus (whoever he was), and in this the reader starts to wonder just what she wants to say. The less than stunning conclusion is that Pappus had careerist interests and said different things to target groups in hopes of enhancing his authority.

I was less than impressed.

One might surmise Cuomo has a bigger goal, but if it exists, it is very subtle. Of these subtle arguments, the chief seems to be that the standard historiography associates the development of Greek mathematics exclusively with Plato's philosophy (the Proclus (411-485) perspective). Cuomo points out contradictions in this line of reasoning made by Pappus (? 320 ?) and Iamblichus (250?-330?). In this, Cuomo hints at disputing the role of the Neo-Platonic synthesis. Proclus, as the heir to Plato's academy, plays a pivotal role in this. Cuomo seeks to uncover the real mathematician hidden by Proclus and later Neo-Platonic Christians.

If this is really what she hints at, I would be surprised. I am just grasping at straws... The unfortunate fate of the interested reader. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles!Pappus of Alexandria (Greek Πάππος ὁ Ἀλεξανδρεύς) (c. 290 - c. 350) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection (c. 340), and for Pappus's Theorem in projective geometry. Nothing is known of his life, except (from his own writings) that he had a son named Hermodorus, and was a teacher in Alexandria. Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's large-scale digitization efforts. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the original text that can be both accessed online and used to create new print copies. The Library also understands and values the usefulness of print and makes reprints available to the public whenever possible. This book and hundreds of thousands of others can be found in the HathiTrust, an archive of the digitized collections of many great research libraries. For access to the University of Michigan Library's digital collections, please see http://www.lib.umich.edu and for information about the HathiTrust, please visit http://www.hathitrust.org ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga posed and solved this famous problem in his work ??????; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them and each solution circle encloses or excludes the three given circles in a different way.In the 16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution does not use only straightedge and compass constructions. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius or expanded to infinite radius. ... Read more

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High Quality Content by WIKIPEDIA articles! n Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (ca. 262 BC ? ca. 190 BC) posed and solved this famous problem in his work ?????? (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2) and each solution circle encloses or excludes the three given circles in a different way. ... Read more