A History of Greek Mathematics, Volume I: From Thales to Euclid by Sir Thomas Heath (PDF)

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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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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!

⭐There is still no better English reference for Greek mathematics than Heath. Since Heath, the only useful histories of Greek mathematics I have found are Dijksterhuis,

⭐, François Lasserre, “The Birth of Mathematics in the Age of Plato”, the translations of Books 4 and 7 of Pappus by Sefrin-Weis and Jones, Morrow’s translation of

⭐, the writings of Knorr,

⭐, Taisbak,

⭐, and Fowler,

⭐.There has been some good work on Greek astronomy, and it is worth saying that popular accounts of Greek astronomy emphasize epicycles but do not talk in depth about the spherical geometry and trigonometry that is used. Detailed studies of Greek astronomy are Toomer,

⭐, Pedersen,

⭐, Evans and Berggren,

⭐, and Neugebauer, “A History of Ancient Mathematical Astronomy”.This first volume covers Greek mathematics to Euclid. The best place for commentary on Euclid is Heath’s translation of the Elements, but for the following topics this volume is the best reference I know: (i) Hippocrates’ quadrature of lunes, (ii) the quadratrix of Hippias, (iii) the trisection of angles, (iv) the construction of two mean proportionals by Archytas (doubling the cube), (v) the geometry of spheres by Autolycus.

⭐Heath appears to have done it again. A really worthwhile book for the scholar and the dedicated hobbyist. If you are seriously interested in ancient Greek mathematics this is a must.

⭐A very interesting read …

⭐good and interesting!

⭐This book is really well written and researched by one of the premier translators and scholars of the subject in recent history. I like the often quoted greek words throughout the texts.

⭐this book is a great reference for math users. the customer service that i received while trying to get this book was very respectable. the book came in better condition than i thought it would and it came in time just before i needed to use it, giving me time to look over the book before i needed to use it for class. highly recommend it.

⭐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.

⭐A little dated, but extremely thorough. If you are doing any research on Greek mathematics I think this is the best place to start- I only wish I’d found it sooner!

⭐Pessima qualità di stampa. Sto procedendo col rimborso e al tempo stesso ho ordinato da amazon.com lo stesso testo, che sembra esser stampato degnamente e impaginato/con copertine differenti (le valutazioni degli utenti anglofoni sono inoltre tutte positive, quindi penso si tratti di una buona edizione).

⭐hard book

⭐i was looking for this after finding only volume 2 in Munich in an english bookstore. very happy with it, it arrived the week i ordered it.

⭐If you are interested in history of mathematics from the beginning, this is the book you need to read.

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