A History of Greek Mathematics, Vol. 1: From Thales to Euclid (Volume 1) Revised ed. Edition

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, Archimedes (Princeton Legacy Library), 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 Proclus: A Commentary on the First Book of Euclid's Elements, the writings of Knorr, Textual Studies in Ancient and Medieval Geometry, Taisbak, Euclid's Data: The Importance of Being Given (Acta Historica Scientiarum Naturalum et Medicinalium), and Fowler, The Mathematics of Plato's Academy: A New Reconstruction.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, Ptolemy's Almagest, Pedersen, A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones (Sources and Studies in the History of Mathematics and Physical Sciences), Evans and Berggren, Geminos's "Introduction to the Phenomena": A Translation and Study of a Hellenistic Survey of Astronomy, 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.

I am on my way to study the grec thought. Aristotales was brilliant and has not been surpassed until Descartes. Grec geometry was okay but grec arithmetic lagged substantialy with respect to grec philosophy. It would be nice to discover why. Then after I will study grec medicine(Galen).

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.

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.

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.

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.

A very interesting read ...

I have both Volume I and II - these are superb references with lots of great commentary and even modern analogies for some of the geometrical problems solved by the ancient mathematicians. I think both are a must-have for those interested in both historical math and general interest in maths. Highly recommended! Thanks!

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.

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).

Fascinating account of a subject of which i knew little. Quite heavy going and detailed in place - the reader does have to have a bit of maths, and I daresay some knowledge of Ancient Greek would add to the interest (I dont have any). I do wonder how he found the time to do his day job ( running the Treasury!).

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