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A History of Greek Mathematics, Vol. 1: From Thales to Euclid, by Sir Thomas Heath
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"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.��
- Sales Rank: #388247 in Books
- Published on: 1981-05-01
- Released on: 1981-05-01
- Original language: English
- Number of items: 1
- Dimensions: 8.26" h x .91" w x 5.65" l, 1.06 pounds
- Binding: Paperback
- 464 pages
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
Most helpful customer reviews
0 of 0 people found the following review helpful.
This is screwball.
By Pamela H.
I am trapped must give review before reading can't cancel. So here I am. Angry. I hate this book. I did not choose the five stars either. And I can't change. I would give zero.
10 of 10 people found the following review helpful.
Really serious history for serious mathematicians
By Alan U. Kennington
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. Heath shows clearly through his explanations of Greek mathematical thinking, and their proofs of theorems, that they were not intellectually inferior to modern mathematicians, (These comments apply even more to volume II, which contains much deeper mathematics than volume I.)
Time after time, I found myself surprised that the ancient Greeks discovered or invented concepts which I had thought were first developed after 1600 AD. Even within the period 450 BC to 150 BC, I was surprised by how much Greek mathematics was known centuries earlier than I had thought. The account of Euclid's Elements, in particular, makes clear that the theories of proportion and conic sections were already very advanced well before the time of Apollonius.
This book assumes that the reader is familiar with the Euclidean geometry which was standard in schools in Heath's time. The presentation of geometrical proofs often skips substantial steps which the modern mathematician would not typically be familiar with.
It is probably best to read this book with a pen and paper to work out the proofs and constructions. Unlike many other Greek mathematics history books, this one is mathematically quite demanding. The reader is not spared the arduous details of the ancient Greek achievements in mathematical thinking. But if Heath had omitted those arduous details, one would not appreciate how awesome their abilities were.
PS. 2013-1-13. I forgot to mention that the index for Volume 1 is in Volume 2. In other words, Volume 1 has no index (unless you also buy Volume 2).
8 of 9 people found the following review helpful.
a real technical history of mathematics
By flashgordon
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! Sir Thomas Heath's accounts of Greek mathematics came before the decoding of all this; Van Der Waerden(student of Emmy Noether) wrote an updated account of the beginnings of matheamtics "Science Awakening" which updates Sir Thomas Heath's account taking account that the Greeks clearly didn't work in a vacuum. One could say that the Greeks took the Babylonian mathematics and proved them deductively; they then went far beyond in trigonometry and conics - also the three delian problems, number theory; that's where mathematics stalled due to the Greeks geometrizing algebra and hence being limited to three dimensions, the calculus of Archimedes(really Eudoxus) was severelly limited due to this geomtric algebra. But, that's another story well beyond the purposes of these books.
But, what wonders this geometric algebra! How can any real intellectual not find the scholarship of Sir Thomas Heath and the findings of Greek mathematics boring? I'd hate to get into this much further; but, I'm more and more disillusioned about the state of today's idea of what it means to be intellectual.
Sir Thomas Heath shows the real history of mathematics in full technical glory as I've already said beyond William Dunhem and John Stillwell. Those are good books in their own right; but, Sir Thomas Heath also shows the modern algebraic formulations of many of the great mathematics and many things not shown by those contemporary authors. People like to make books that show hints of modern mathematics like Ian Stuart and a hundred years ago Rouse Ball; seems to me that reading Sir Thomas Heath's "A History of Greek Mathematics"(with his Euclid's Elements in handy) is the best mathematics puzzle book that can introduce people to 'real' mathematics; one could read it before one knows how to do the modern algebraic formulations; and then, when you learn enough algebra and a first semester of calculus, one can go back and rework those modern accounts of Greek mathematics. Sir Thomas Heath's account serves as the true starting point for those who want to become mathematicians!
I'd like to further note that I read Van Der Waerden's "Algebra from Al Kowarizmi to Emmy Noether"; in it, he mentions that Vieta(a very underrated mathematician; read E.T. Bell's account of him in his "Development of Mathematics"; i do believe its the chapter titled transition to modern mathematics; and then Van Der Waerden's account in the book just mentioned!) solved some problems the Greeks diddn't finish - namely that of the relation between trisection and the solution of the cubic equation; Sir Thomas Heath shows the solution; although, he leaves some gaps of the reasoning; he suggest that Newton cut his teeth by studying Vieta, and if you want to see the gaps left unsaid(or couldn't figure it out youself; i couldn't; but, I got the rest), look up the collective mathematical papers of Isaac Newton volume one I do believe(there's eight volumes!); this is just one example of the great scholarship that goes into Sir Thomas Heath's "A History of Greek Mathematics." Again, how any real intellectual could get bored with this . . . is out of his/her collective mind!
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