Book Description

Customer Reviews (2)

more than just history
It should be noted that this is one of a two volume set. This author also compiled and commented upon The Elements ofEuclid in three volumes [also available here].

Theseworkswere first brought to my attention by my Greeklanguage professor nearly 40 years ago as the best English language source on Greek Mathematics.

Just as the Greeks did not view `pure' mathematics or geometry as a lifes-work so to younger readers [through collage] the methods of logic may prove most useful.

For we retired `geezers' not quite ready for Oprah reruns and made for T.V. `romances' it may be the stimulation ofthe brain by the problems [which are documented and solved infull], the history andthe `awe' of how much these did `without computers';

Academically great
This is not a terribly exciting book to read, but it is a superior reference for looking up Greek mathematicians.It is apparent that the author is partial to Euclid, as his section is close to a third of the book, (see the author's version of the Elements)but being a Euclid fan myself I can forgive this easily.Even the most obscure mathematicians are covered in good detail along with what they proved, as well as how they proved it.For those interested in historical mathematics, this book is invaluable. Note:This is a two volume set.I thought it was only one and I only purchased the second.Be sure to get both. ... Read more

Product Description
This Elibron Classics book is a facsimile reprint of a 1921 edition by the Clarendon Press, Oxford. ... Read more

Product Description
This Elibron Classics book is a facsimile reprint of a 1921 edition by the Clarendon Press, Oxford. ... Read more

Book Description

Customer Reviews (2)

On 'arithmos' and 'general magnitude'
It's hard to say something about this wonderful book without sounding pompous.Generally, I try to avoid terms like 'classic' and 'essential', but they keep coming to mind.

The original was written in the mid 1930s.As Klein writes in this version's preface, "This study was originally written and published in Germany during rather turbulent times."

The late Jacob Klein spent his post war years teaching Platonic philosophy at St. John's College.There, he was known as something of a lovable elitist.Professors tell a story about Klein being partial to the number 12.He claimed that there were an exclusive 12 philosophers, 7 Greek and 5 German.The word got out and he soon received a letter from 4,000 American philosophers begging to differ with his opinion.

While many might call this book 'philosophy of math,' I doubt Dr. Klein would agree.The book is without much in the way of serious math.It is more concerned with the symbols of math and how they are used.Quoting from the first paragraph of the introduction:

"Creation of a formal mathematical language was of decisive significance for the constitution of modern mathematical physics. If the mathematical presentation is regarded as a mere device, preferred only because the insights of natural science can be expressed by "symbols" in the simplest and most exact manner possible, the meaning of the symbolism as well as of the special methods of the physical disciplines in general will be misunderstood. True, in the seventeenth and eighteenth century it was still possible to' express and communicate discoveries concerning the "natural" relations of objects in non mathematical terms, yet even then -or, rather, particularly then - it was precisely the mathematical form, the mos geometricus, which secured their dependability and trustworthiness. After three centuries of intensive development, it has finally become impossible to separate the content of mathematical physics from its form. The fact that elementary presentations of physical science which are to a certain degree nonmathematical and appear quite free of presuppositions in their derivations of fundamental concepts (having recourse, throughout, to immediate "Intuition") are still in vogue should not deceive us about the fact that it is impossible, and has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form. Thence arise the insurmountable difficulties in which discussions of modern physical theories become entangled as soon as physicist or nonphysicists attempt to disregard the mathematical apparatus and to present the results of scientific research in popular form. The intimate connection of the formal mathematical language with the content of mathematical physics stems from the special kind of conceptualization which is a concomitant of modern science and which was of fundamental importance in its formation."

While this iconoclastic promise is a bit difficult to extract from the somewhat professional philosophic prose, there is a wonderful essay in "Biographies of Scientific Objects," edited by Lorraine Daston that serves as an excellent commentary.The essay called "Mathematical Entities in Scientific Discourse" credits Klein with a new perspective from which to interpret the transition of ancient and medieval traditions to the new mathematical physics of the seventeenth century. His was the seemingly narrow-but only deceptively so-perspective of the ancient concept of "arithmos", compared to the concept of number in its modern, symbolic sense. In Klein's own words, the underlying thematics of the book never loses sight of the "general transformation, closely connected with the symbolic understanding of number, of the scientific consciousness of later centuries."

Although the Greek conceptualization of mathematical objects was indeed based upon the notion of arithmos, this notion should not be thought of as a concept of "general magnitude." It never means anything other than "a definite number of definite objects," or an "assemblage of things counted". Likewise, geometric figures and curves, commensurable and incommensurable magnitudes, ratios, have their own special ontology which directs mathematical inquiry and its methods.

In contradistinction to Greek parlance, "general magnitude," according to Klein, is clearly a modern concept.Proving this case is the project of both books.

I think you will find reading this material an interesting journey.

Klein's work is a masterpiece of philosophical exegesis.
Klein's work examines the generally unsuspected foundations of modern algebraic mathematics.He charts the development of a new kind of intentionality which lies at the heart of modern mathematical practice, with an explicit affirmation that this mode of intentionality is exemplary for all of modern thought.Beginning from the classical foundations of mathematics, he follows the subject carefully through every turn of ideation until he has completed his thesis. On the basis of this thorough-going evaluation and exegesis of mathematical thought, he identifies Francois Viete as the true founder of this modern symbolic intentionality.But he does not rest with this, proceeding to show how Descartes, Stevin, and Wallis each draw out of this foundation conclusions which are familiar to the modern thinker.This reader knows of no other work of this kind that has so deeply penetrated the foundations of what we call modernity. ... Read more

Book Description

Book Description
This book provides a way to understand a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests on a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.Download Description
The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Product Description
A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author s intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonianmetric algebra,a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets.The book s use ofmetric algebra diagramsin the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstractlettered diagramsin the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author s comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics. ... Read more

Book Description
Professor Aaboe gives here the reader a feeling for the universality of important mathematics, putting each chosen topic into its proper setting, thus bringing out the continuity and cumulative nature of mathematical knowledge. The material he selects is mathematically elementary, yet exhibits the depth that is characteristic of truly great thought patterns in all ages. The success of this exposition is due to the author's unique approach to his subject. He wisely refrains from attempting a general survey of mathematics in antiquity, but selects, instead, a few representative items that he can treat in detail. He describes Babylonian mathematics as revealed from cuneiform texts discovered only recently, as well as more familiar topics developed by the Greeks. Although each chapter can be read as a separate unit, there are many connecting threads. Aaboe stays as close to the original texts as is comfortable for a modern reader, and the bibliography enables the interested student to delve more deeply into any aspect of ancient mathematics that catches his or her fancy. ... Read more

Customer Reviews (1)

Early and timeless beauty in mathematics
While mathematics has a long history, in many ways it was not until the publication of Euclid's Elements that it became an abstract science. Babylonian mathematics, the topic of the first chapter, largely dealt with counting and the focus in this book is on the notations the Babylonians used to represent numbers, both integers and fractions. Although their notation had its' limits, we still use it today for time and angle measure.
And then there was Euclid, and all was ordered. There is no reason to believe one way or another that Euclid was the first to prove the theorems in his classic work, but there is no doubt as to his organizational genius. His "rigorous" setting down of the principles of geometric thought was truly a turning point in abstract mathematics, If you are not impressed when reading the material of the second chapter, taken from Euclid, then you have no aesthetic appreciation for what mathematics is. While the mathematics has been cleaned, the beauty has never been topped.
The next chapter is about the greatest genius before Newton, Archimedes. In fact, had he been blessed with better notation, it is possible that he would have invented, or at least pre-invented calculus. If even half of the legends about his mechanical skill are true, they are still amazing. Apparently, entire armies and navies were terrified at the rumor that one of his mechanical devices was about to be used. The crispness of his theorems and the logical progression will be just as instructive thousands of years from now.
The final chapter describes how Ptolemy was able to construct trigonometric tables. Using the chords of circles, he was able to construct tables that can still be used today. Civilization improves and mathematicians continue to expand the mathematical field and refine earlier work. However, the elegance of earlier work still shines through, and in this book you can experience some of the earliest mathematical diamonds, hewn from thought and destined to survive as long as humans do. ... Read more

Customer Reviews (1)

Make no mistake, this is a math book -
A comparable book might be an Introduction to Algebra book.Complete with descriptions and examples of usage (and of course history).Ifyou're interested in knowing more about Babylonian sexagesimal notation, Egyptian fractions, poetic numbers, Pythagoras, Plato or Hellenistic science interest you then this is a good source for the material and thankfully it has been translated into English.While I believe the translation was accurate, this can be a sleeper if you're not fond of numbers or their manipulation. ... Read more

Book Description

Product Description
"The best treatment of the subject in English" (Carl Boyer, History of Mathematics, p. 680). Blue cloth with gilt spine lettering & gilt cover seal. ... Read more