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A History of Greek Mathematics, Vol. 1: From Thales to Euclid Paperback – May 1, 1981

ISBN-13: 978-0486240732 ISBN-10: 0486240738 Edition: New edition

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A History of Greek Mathematics, Vol. 1: From Thales to Euclid + A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics) + The Thirteen Books of the Elements, Vol. 2: Books 3-9
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Product Details

  • Paperback: 464 pages
  • Publisher: Dover Publications; New edition edition (May 1, 1981)
  • Language: English
  • ISBN-10: 0486240738
  • ISBN-13: 978-0486240732
  • Product Dimensions: 8.3 x 5.6 x 0.9 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #424,001 in Books (See Top 100 in Books)

Editorial Reviews

From the Back Cover

"As it is, the book is indispensable; it has, indeed, no serious English rival."—Times Literary Supplement.
"Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century."—Professor W. H. Stahl
"Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry."
The perspective that enabled Sir Thomas Heath to understand the Greek genius—deep intimacy with languages, literatures, philosophy, and all the sciences—brought him perhaps closer to his beloved subjects and to their own ideal of educated men, than is common or even possible today. Heath read the original texts with a critical, scrupulous eye, and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English.
"Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes' proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition:
It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations. 
Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.  
Unabridged (1981) republication of the original 1921 edition published by Oxford University Press.

About the Author

Thomas Little Heath: Bringing the Past to Life
Thomas Little Heath (1861–1940) was unusual for an authority on many esoteric, and many less esoteric, subjects in the history of mathematics in that he was never a university professor. The son of an English farmer from Lincolnshire, Heath demonstrated his academic gifts at a young age; studied at Trinity College, Cambridge, from 1879 to 1882; came away with numerous awards; and obtained the top grade in the 1884 English Civil Service examination. From that foundation, he went to work in the English Treasury, rose through the ranks, and by 1913, was permanent secretary to the Treasury, effectively the head of its operations. He left that post in 1919 at the end of the first World War, worked several years at the National Debt office, and retired in 1926.
During all of that time, however, he became independently one of the world's leading authorities on the history of mathematics, especially on the history of ancient Greek mathematics. Heath's three-volume edition of Euclid is still the standard, it is generally accepted that it is primarily through Heath's great work on Archimedes that the accomplishments of Archimedes are known as well as they are.
Dover has reprinted these and other books by Heath, preserving over several decades a unique legacy in the history of mathematical scholarship.

In the Author's Own Words:
"The works of Archimedes are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader." — Thomas L. Heath

Customer Reviews

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It should be noted that this is one of a two volume set.
newton fisher
Sir Thomas Heath shows all Greek mathematics and Greek mathematics is a good place to start; although, it must be said, that mathematics started with the Greeks.
flashgordon
This book assumes that the reader is familiar with the Euclidean geometry which was standard in schools in Heath's time.
Alan U. Kennington

Most Helpful Customer Reviews

36 of 38 people found the following review helpful By Paris Chavez on November 1, 2000
Format: Paperback
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.
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6 of 6 people found the following review helpful By Alan U. Kennington on November 20, 2012
Format: Paperback
I have to give this book 5 stars because it is such an important work. Many other mathematics history books are derived very substantially from this work (i.e. from both volumes I and II). The fact that Heath wrote more than 100 years ago does not in any way imply that his history is less worthy or less scholarly than modern accounts. In fact, many modern accounts of ancient Greek mathematics are no more than diluted versions of the Heath books. One may as well read the source material upon which most modern histories of Greek mathematics are based.

My constant impression when I read this book (both volumes in their entirety) was that we must be enormously grateful to Thomas Little Heath for his total devotion to the translation and interpretation of the surviving manuscripts, and for helping to bring them to light. (He is perhaps best known for his Archimedes translations and interpretations.) Heath had a thorough familiarity with the full range of manuscripts at his time, and the range has not increased inordinately since then. He makes clear that the majority of our sources for ancient Greek mathematics actually date to the first millennium AD.

The majority of this book is about geometry, since other mathematics topics in ancient Greek times were largely seen through the perspective of geometry. Even if you know a lot about modern advanced geometry, and even if you learned Euclidean geometry in the traditional fashion at high school (as I did), the proofs of theorems in this book are very hard work. The Greek genius for mathematics is breathtaking.
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6 of 7 people found the following review helpful By flashgordon on November 7, 2012
Format: Paperback Verified Purchase
Or, at least, Sir Thomas Heath's "A History of Greek Mathematics(in two volumes; i just finished volume 1)" is a good place to start a real technical history of mathematics.

Recently, William Duham and John Stillwell, have tried to make histories of mathematics with the books stuffed with the actual mathematics; the only problem with those books, is they cast the ancient mathematics in terms of modern mathematics. I don't totally disagree with this approach; i absolutely agree that we should see the connections between ancient and modern mathematics; but, those books can only show so much of the ancient mathematics. Sir Thomas Heath shows all Greek mathematics and Greek mathematics is a good place to start; although, it must be said, that mathematics started with the Greeks.

Certainly, mathematics started tens of thousands of years before with much the same cultures that made the European cave paintings. Archaeologists have unearthed tally bones; animal bones(like coyotes) with number markings. The next great mathematical ages were perhaps with 1) those who made Stonehenge, the Pyramids, and 2) the Mesopotamians in general; the Summarians and the Babylonians. A thousand years before the great Greek rational culture effort, the Babylonians discovered the Pythagorean theorem(but did not prove it), used the quadratic formula(once again, did not prove it; has anyone seen an actual proof of the quadratic formula? Seems to me the geometric algebra proofs in Euclid's Elements are the only real proofs of the quadratic formula!), infinit series(of perhaps primitive state), even systems of equations!
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A History of Greek Mathematics, Vol. 1: From Thales to Euclid
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