Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics. ... Read more

Product Description
The book has no illustrations or index. It may have numerous typos or missing text. However, purchasers can download a free scanned copy of the original rare book from the publisher's website (GeneralBooksClub.com). You can also preview excerpts of the book there. Purchasers are also entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Original Publisher: Oxford, The Clarendon press; Publication date: 1921; Subjects: Mathematics, Greek; Mathematics, Greek; Science / General; Mathematics / History ... Read more

Product Description
This is an updated edition of a groundbreaking examination of early Greek mathematics. The author has revised parts of the text, updated the bibliography, and added a new appendix where he takes a strong position in the continuing debate about the nature and range of classical mathematics. ... Read more

Customer Reviews (3)

Why Books II and X of the Elements look like they do
This book claims that a major concern in ancient days was "anthyparesis," which is basically the Euclidean algorithm (though with subtraction in place of division and some other minor corrections for anachronisms). Given two quantities the anthyparesis algorithm gives as an output of series of numbers, namely the numbers corresponding to "how many times the smaller goes into the larger" reiterated with the remainder as the new "smaller." "On the one hand, there is the spectacular success of the anthypaireic exploration of the ratios of sides of squares sqrt(n):sqrt(m) in which a wide range of arithmetical and geometrical techniques are bound together into some apparently coherent whole. [See esp. ch. 3. Such ratios will always produce sequences that are periodic according to a general pattern; p. 75.] On the other hand, there is an equally spectacular lack of success in the search for any similar regular, predictable anthypaireic behaviour of any other geometrical ratios, apart from the extreme and mean ratio [which is the simples case anthypaireically: the case which produces periodic 1s; see section 3.5(b)]. Such a contrast might lead to the growth of an attitude in which these sides of squares come to be regarded as the basic underlying understandable geometric objects in terms of which everything else should be described." (pp. 166-167). It is proposed that the otherwise obscure Books II and X of Euclid's Elements be understood as partial attempts at these problems. There is no "smoking gun" evidence; the case is based primarily on showing that some of Euclid's proposition are reasonably well-suited to a research programme along these lines. Incidental evidence includes Euclid's focus on two dimensions ("he nowhere shows any interest in giving any similar results for cubes or other three-dimensional figures" (p. 190), even though this seems very obvious too us, e.g. a formula for (x+y)^3) and the lack of any evidence for the alleged "crisis" as a result of the discovery of incommensurable magnitudes (cf. 304).

A new landmark
"THE MATHEMATICS OF PLATO'S ACADEMY"
Second Edition
Fowler.

The first impression on receiving this book in your hands is the heavy weight.But this is not only true physically, due to the high quality of the cartridge paper, it is also true intellectually.Thus the second impression reinforces the first.The caliber of the scholarship exhibited in this tome is of the highest order, doing full justice to an investment in so expensive a paper.

Nothing less than the most complete exposition possible of ancient Greek mathematics as taught at the Platonic Academy in Athens, is presented, based on all currently available sources.

The author labors to guide the reader with diagrams, definitions, explanations, cross-references, commentaries and modern mathematical symbols to provide a clear, detailed and thorough account.He even starts from the photographic plates of Greek papyri.This is a major work of scholarship that itself deserves to become a classic; a model of its kind.

Just in case amazon readers accuse me of obsequious flattery, abject servility and distasteful onesidedness, allow me one criticism.The influence of the Ionian philosopher-mathematicians, Thales, Anaxagoras, Anaximander and Anaximenes on Plato's Academy is not covered.

A magnificent twenty-one page bibliography testifies to the author's detailed background research, and whets the reader's appetite for further reading.

Finally, three separate indexes show that the author is making every effort to help his reader as much as he can.Could one ask for more ?

A brilliant, sprawling book
Two things are certain if you really want to know what mathematics was done in Plato's Academy, and before Euclid: Your heart will break at the lack of evidence, and you will have to read this book.

Fowler details how thin the surviving evidence is, even for such basics as when Euclid's ELEMENTS were written. Drawing on other careful classicists he demolishes now traditional stories about the Pythagoreans and the irrational, Plato's Academy, even Euclid's own style in the Elements. He shows them coming from heavy interpretations of extremely vague (and often late) sources. Plates in the book show how desperately scanty are the physical remains of any mathematical writing within centuries of Plato's death. Even the first and second century AD leave us only a few scraps of Euclid.

On the positive side, Fowler gives a persuasive account of a method of reciprocal subtraction which he calls "anthyphairesis". It lay within the grasp of Athenian geometers, and suits some remarks Plato makes on mathematics, and suits traditions on geometers Plato knew, and goes far to unify and explain much of Euclid. It was apparently cited by Aristotle (under the name "antanairesis"). Probably, it really was used in the period. It also makes some very pretty geometry. Regular pentagons make a lot of sense anthyphairetically. Anyone trying to read the later books of Euclid, especially books X and XIII, will get tremendous help from this book. Conversely, you can hardly read much of this book without reading Euclid.

The book is not well organized. It spends many pages at a time on mathematical reconstructions that could not possibly have been used by the Greeks, so as to show beyond question that they could not have been. And it probably pushes its point too far. That is what classicists do. They push a point for all it is worth and perhaps more. These flaws are inevitable when you work on such important questions on so little evidence. Fowler assembles enormous amounts of classical textual evidence and later scholarship. He gives some nice mathematics including an appendix on the later arithmetized incarnation of anthyphairetic methods as continued fractions.

If you are determined to ask what math Plato knew and promoted, and what existed before Euclid--and so you are determined to break your heart--then you must read this book. ... Read more

Product Description
From the reviews of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."

(European Mathematical Society)

"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises. ... Read more

Customer Reviews (4)

An intellectually satisfying history of mathematics
This is a brilliant book that conveys a beautiful, unified picture of mathematics. It is not an encyclopedic history, it is history for the sake of understanding mathematics. There is an idea behind every topic, every section makes a mathematical point, showing how the mathematical theories of today has grown inevitably from the natural problems studied by the masters of the past.

Math history textbooks of today are often enslaved by the modern curriculum, which means that they spend lots of time on the question of rigor in analysis and they feel obliged to deal with boring technicalities of the history of matrix theory and so on. This is of course the wrong way to study history. Instead, one of the great virtues of a history such as Stillwell's is that it studies mathematics the way mathematics wants to be studied, which gives a very healthy perspective on the modern customs. Again and again topics which are treated unnaturally in the usual courses are seen here in their proper setting.This makes this book a very valuable companion over the years.

Another flaw of many standard history textbooks is that they spend too much time on trivial things like elementary arithmetic, because they think it is good for aspiring teachers and, I think, because it is fashionable to deal with non-western civilisations. It gives an unsound picture of mathematics if Gauss receives as much attention as abacuses, and it makes these books useless for understanding any of the really interesting mathematics, say after 1800. Here Stillwell saves us again. The chapter on calculus is done by page 170, which is about a third of the book. A comparable point in the more mainstream book of Katz, for instance, is page 596 of my edition, which is more than two thirds into that book.

Petty details aside, the main point is the following: This is the single best book I have ever seen for truly understanding mathematics as a whole.

Relationship between algebra and geometry
It is a very good book.It has presented very clearly some difficult-to-understand relationship especially the link between algebra and geometry.It is a very good balance - history, Mathmatics, biography all mixed very well together.Highly recommended.

concise and well written summary of mathematics
Stillwell covers a lot of ground in a short undergraduate text intended to unify various mathematical disciplines.Naturally, _Mathematics_and_its_History_ begins with the early Greeks and in particular geometry (which is how mathematics was typically expressed then).The development of algebra and polynomial forms is described followed by perspective geometry.The invention of calculus and the closely related discovery of infinite series provide the backdrop for short biographies of prominent mathematicians (mostly dead white males to multicultural deconstructionists).The development of elliptic integrals (used in solving functions with specified boundary conditions such as a Neumann problem found in fluid mechanics).The treatment then diverges to physical problems including the vibrating string and hydrodynamics, together with a note on the renown Bernoulli family.Then Stillwell returns to the esoteric in complex numbers, topology, group theory and logic with some comments on computation at the end.Some mathematicians may find the overview to lack comprehensiveness, but the book's brevity for each topic and biographical notes present a balanced approach to the more casual reader about this important field of study and how it developed.

see below
This is an overall good text. It offers a very in depth history of many many mathematical ideas.It gets quite technical at times, which can be a good or bad thing, depending on what you are looking for. ... Read more

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

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There is a great divide between species that makes extrapolation of biochemical research from one group to another utterly invalid. In their previous book, "Sacred Cows and Golden Geese: The Human Cost of Experiments on Animals", the Greeks showed how an amorphous but insidious network of drug manufacturers, researchers dependent on government grants to earn their living, even cage-manufacturers have perpetuated animal research in spite of its total unpredictability when applied to humans. (Cancer in mice, for example, has long been cured. Chimps live long and relatively healthy lives with AIDS. There is no animal form of Alzheimer's disease.) In doing so, the Greeks challenged the "specious science" we have been culturally conditioned to accept. This book takes these revelations one step further. In accessible language, it provides the scientific underpinning for the Greeks' philosophy of "do no harm to any animal, human or not," by examining paediatrics, diseases of the brain, new surgical techniques, in vitro research, the human genome and proteome projects, and an array of scientific and technological breakthroughs. ... Read more

Customer Reviews (4)

They've done it again!
I definitely recommend reading "Sacred Cows and Golden Geese" before this as it gives a wide overview. Specious Science gets more down to the nitty gritty and scientific details of the problems with nonhuman animal research while still keeping things general enough for the public to grasp. I have a background in psych and cog neuro but found the places in this book that stepped outside my realm of study completely understandable.

Great book showing how the continuation of nonhuman animal research is unethical, unscientific, and plain criminal.

Another ground-breaker!! But can you handle the truth?
Dr. Greek has again put forth the most powerful, insightful, and rational reference work in the scope of human health issues. What entities control the way you approach disease and illness, its treatments, and the prevention of it? Here you will find overwhelmingly documented sources and information on how we can finally equip ourselves to understand why Americans have one of the world's worst health records while simultaneously spending more than any other country on 'treatment'. Where is so much of our money being wasted and whom is pocketing the rest? Can you really handle the truth? You can allocate many, many years researching and trying to uncover the answers on your own and still come up far short, or you can save several tens of thousands of dollars and invest less than [price] in an advanced compilation of documentation, which is written, by the way, in lay person's terms. Your co-workers or friends will never return this book to you if you lend it out though---it is that good, I'll attest to this, as I am on my third copy.

Specious Science exposes animal model's fundamental flaws
Finally, an antidote to the incessant and self-serving claims of the animal research industry!

Specious Science excels in at least three areas. First, it's a great primer in the fundamental tenets of sound science. Second, it shows how animal-modelled research fails to meet these basic requirements in theory and in practice. Third, it explains how human-focused medical research, which competes with animal experiments for funding, is superior in its scientific rigor, relevancy, and predictive value.

How many times have we heard that a mouse is the "best" model for studying human disease? One look at a mouse should make you skeptical. The Greeks probe deeper and investigate significant differences between humans and animals at the cellular, sub-cellular, and molecular levels - the arenas in which both the agents of and treatments for disease operate. They explain how small interspecies differences in genetic layout lead to substantial divergences in responses among species. In other words, Evolution 101! The animal model, no matter how strenuous or creatively its proponents argue otherwise, fails this lesson.

"Best animal model" is a fairly meaningless term. Extrapolating from one species to another is fated to be inexact and misleading. Our "hit rate" for medical discoveries is higher in every other type of scientifically-grounded medical research, and for this reason, as the book points out, money squandered on the crude and antiquated animal model harms humans.

Specious Science should be required reading for any life science major, or anyone interested in how charities and the Federal Government spends their health research dollars.

Crystal Therapy, Pyramid Power and Faith Healing.
Those with a vested interest frequently claim that biomedical research using animals is a necessary evil. Specious Science demonstrates that those who make such claims have wandered from the fact-based rationality that drives real science.

The Greeks use current knowledge of genetics and evolution to explain why animal-modeled science should be viewed with the same skepticism that most educated people view crystal therapy, pyramid power, and faith healing.

Once they have presented a theory for why members of other animal species are not productive models of human disease, the Greeks go on to examine the evidence and demonstrate that their theory is sound. Using the history of medical advancement as their test bed, the authors look at the record and debunk the claims we have all heard about animal research being the source of all cures - claims made by the vested interests that turn out to be spin-doctoring and myth.

With much scholarship and research, the Greeks have uncovered the roots and behind-the-scenes stories of the discoveries that have changed medicine through time into a science. They explain the lost chances and delays that a faith in the animal model has repeatedly caused. They expose the fatal catastrophes that have resulted when scientists have chosen to value animal data over human, and they have explained the surprising histories of the medical miracles that have arisen from doctors trying to help human patients.

The book also points out recent breakthroughs and advances in medicine that are stemming from human biology, genetics, epidemiology, chemistry, physics, and mathematics. We learn that computers are screening chemicals at astonishing rates and predicting their efficacy and toxicity as drugs at a rate and degree of accuracy that will embarrass everyone with a stake in the archaic practice of animal experimentation.

Together, Specious Science and their earlier work, Sacred Cows and Golden Geese, present a cogent and compelling argument that explains why animal experiments continue and why they continue to retard real medicine progress and result in continued human suffering.

Anyone wishing to understand the science of medicine and the debate surrounding the theory of animal models will find this book essential reading. ... Read more

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History of geometry. Egyptian mathematics, Babylonian mathematics, Indian mathematics, Chinese mathematics, Greek mathematics, Mathematics in medieval Islam, List of geometry topics, List of important publications in mathematics, List of interactive geometry software, History of mathematics, Flatland ... Read more

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High Quality Content by WIKIPEDIA articles! Almagest is the Latin form of the Arabic name ( al-kitabu-l-mijisti, in English The Great Book) of a mathematical and astronomical treatise proposing the complex motions of the stars and planetary paths, originally written in Greek Ptolemy of Alexandria, Egypt, written in the 2nd century. Its geocentric model was accepted as correct for more than a thousand years in Islamic and European societies through the Middle Ages and early Renaissance. The Almagest is the most important source of information on ancient Greek astronomy. The Almagest has also been valuable to students of mathematics because it documents the ancient Greek mathematician Hipparchus's work, which has been lost. Hipparchus wrote about trigonometry, but because his works have been lost mathematicians use Ptolemy's book as their source for Hipparchus' works and ancient Greek trigonometry in general. ... Read more

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Ancient Greece was the birthplace of science, which developed in the Hellenized culture of ancient Rome. This book, written by seventeen international experts, examines the role and achievement of science and mathematics in Greek antiquity through discussion of the linguistic, literary, political, religious, sociological, and technological factors which influenced scientific thought and practice. ... Read more

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This is the first edition of the original text of the advanced part of the most important work on conic sections written in antiquity and one of the most influential works in mathematics. It is also the first literal English translation of it ever to be published. The purpose of the work is to make available, to those interested in the history of science and to mathematicians, a version of the work as close to the original as possible. This part of Apollonius' Conics is lost in the original Greek, and only an Arabic translation made in the 9th century survives. This text has never been published previously, and all "editions" of this part of Apollonius' work are based on the Latin translation from the Arabic published by Edmund Halley in 1710, which suffers from Halley's insufficient knowledge of Arabic and his use of a single manuscript. The present edition is based on all known manuscripts. Its other improvements over Halley's edition are: 1) the Arabic text with a full critical apparatus; 2) an accurate English translation (until now only a loose paraphrase, based on Halley's translation, has been available in English); 3) a commentary to elucidate both mathematical and historical difficulties. This book will replace Halley's edition and all its derivatives as the standard edition of this part of Apollonius' work. ... Read more