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A History of Greek Mathematics, Vol. 1: From Thales to Euclid
"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 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
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 .
"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 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
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 .
464 pages, Paperback
First published January 1, 1921
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November 21, 2011Available online - http://www.archive.org/details/cu3192...
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August 2, 2016
A comprehensive history of Greek mathematics, divided by topics -- after a couple of introductory chapters on terminology, numerals and notation, it deals with Pythagorean arithmetic, the beginnings of geometry, Pythagorean geometry, the elements of geometry before Plato, math in Plato, the elements between Plato and Euclid, more advanced problems, and ends up with Euclid. Much of Greek geometry is just algebra in disguise. This first book covers the theory of incommensurables (irrationals) and the discovery of conic sections. It seems the Greeks were more advanced in some areas than I was aware of.
February 11, 2017
Great resource for complex geometry and measurement of shape.
Awesome content on art resources and applications of form to be drawn on a plane.
Awesome content on art resources and applications of form to be drawn on a plane.
November 27, 2024
Quite an interesting read. While dated, Heath's book is full of interesting details about how the Ancient Greeks did math, how math progressed, and some interesting math on its own. Heath will sometimes put in full math proofs from the Greek perspective, which I appreciate, but many others may wish to skip. If you skip such sections the book is still readable. Overall, I found it interesting because I am interested in the history of mathematics; if you have a similar interest well worth your time.
July 3, 2019
This was one of the most boring books I've ever read. Maybe that's what you should expect from a book on this subject, but I think that a lot of the subject matter of the book was actually pretty interesting. The presentation was just confusing and boring. Maybe it's because the book, written about 98 years ago (1921), is at this point a historical text itself. Heath uses words like 'trapezium' instead of 'trapezoid', 'mean proportional' instead of 'geometric mean', and 'extreme and mean ratio' for the golden ratio. The use of archaic/British terms in what is already a dense and difficult book makes things just that more annoying and confusing. He also frequently uses Greek/Latin phrases without giving any translation, and words written purely in Greek (with no transliteration) occur very frequently throughout the text (so I suggest you know how to read Greek if you want to read this book). Heath also constantly refers to several methods of Greek proof (such as the method of exhaustion) without ever defining them until the last chapter - WHY?!?! One of the things I found most annoying was how Heath constantly refers to various ancient Greek, Roman, and medieval commentators on ancient Greek math without giving any context (not even a date) of when, where, or why that person was writing about ancient Greek math. He just tosses out funny-sounding names left and right, sometimes adjacent to each other, and I have no idea if they're an ancient Greek writing at the Library of Alexandria, an ancient Roman guy, or some medieval monk. I wish that he would have gone over the history of the various scholars who recorded, analyzed, and transmitted the ancient Greek texts.
So pretty much, if I were to commission a modern re-write of this book, I would want the author to go much more into the general non-mathematical history of how and why the ancient texts and their succeeding commentaries were written. It would have been interesting for Heath to have put the mathematical discoveries into more of a historical context. He doesn't approach history with a holistic view at all (it probably wasn't the fashion back then?).
There were some good parts of the book. First of all, it was very thorough. I doubt he left anything out between Thales and Euclid. Second of all, the subject matter itself is super interesting. The Greeks were masters at geometry, and their accomplishments were pretty amazing. Most of the proofs in the book are actually accessible, and I found the proofs of Hipprocates's squaring of the lunes to be really cool. I was also really impressed by how the Greeks discovered irrational numbers and incorporated them into their general theories. Some of the Greeks' general scientific theories were also super impressive, if wrong - for example, their model of the heavens as revolving spherical shells (Heraclides of Pontus determined that Venus and Mercury revolve around the sun). The Greeks also wrestled with the troubling concepts of infinity and infinite divisibility pretty successfully, I think (Zeno's Four Arguments) - they pretty much came to the conclusion that there are no indivisible units of time and space. They didn't figure out the derivative though, unfortunately. Another concept I think was impressive was how Plato thought that material objects were instantiations of perfect, eternal forms. That idea pretty much forms the basis of all of our more technical sciences.
It was also interesting that the Greeks didn't have the number 0 - this was actually somewhat problematic for them, because without 0 you can't write 10! or 100, or 1000, etc. So for every power of 10 they needed a new set of 10 symbols, and they needed to memorize how to add/multiply all of the symbols together.
The Pythagoreans were also very interesting. The fact that there was an ancient cult that worshiped numbers is pretty cool. Some of their beliefs about numbers were just mystical and not productive ("such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on... all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature"), but their veneration of numbers also led them to make tons of important contributions to mathematics that may have been frivolous back then but laid the foundations for all of geometry.
So, the subject matter was interesting, but the book was incredibly boring.
So pretty much, if I were to commission a modern re-write of this book, I would want the author to go much more into the general non-mathematical history of how and why the ancient texts and their succeeding commentaries were written. It would have been interesting for Heath to have put the mathematical discoveries into more of a historical context. He doesn't approach history with a holistic view at all (it probably wasn't the fashion back then?).
There were some good parts of the book. First of all, it was very thorough. I doubt he left anything out between Thales and Euclid. Second of all, the subject matter itself is super interesting. The Greeks were masters at geometry, and their accomplishments were pretty amazing. Most of the proofs in the book are actually accessible, and I found the proofs of Hipprocates's squaring of the lunes to be really cool. I was also really impressed by how the Greeks discovered irrational numbers and incorporated them into their general theories. Some of the Greeks' general scientific theories were also super impressive, if wrong - for example, their model of the heavens as revolving spherical shells (Heraclides of Pontus determined that Venus and Mercury revolve around the sun). The Greeks also wrestled with the troubling concepts of infinity and infinite divisibility pretty successfully, I think (Zeno's Four Arguments) - they pretty much came to the conclusion that there are no indivisible units of time and space. They didn't figure out the derivative though, unfortunately. Another concept I think was impressive was how Plato thought that material objects were instantiations of perfect, eternal forms. That idea pretty much forms the basis of all of our more technical sciences.
It was also interesting that the Greeks didn't have the number 0 - this was actually somewhat problematic for them, because without 0 you can't write 10! or 100, or 1000, etc. So for every power of 10 they needed a new set of 10 symbols, and they needed to memorize how to add/multiply all of the symbols together.
The Pythagoreans were also very interesting. The fact that there was an ancient cult that worshiped numbers is pretty cool. Some of their beliefs about numbers were just mystical and not productive ("such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on... all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature"), but their veneration of numbers also led them to make tons of important contributions to mathematics that may have been frivolous back then but laid the foundations for all of geometry.
So, the subject matter was interesting, but the book was incredibly boring.
October 21, 2023
The Ancient Greeks did a lot for mathematics. Sir Thomas Little Heath explains these contributions in the first volume of a two-volume set. He covers the period from Thales to Euclid in this first volume.
The Ancient Greeks are most famous for their contributions to Geometry. They used figures and drawings to demonstrate their proofs and solutions. In the field of Geometry, they emphasized rigor and logic. Supposedly, they invented the Pythagorean Theorem, but Heath acknowledges the other Ancient Civilizations that discovered it at the same period. In Number Theory, Pythagoras and his followers explored the integers.
Heath discusses the three intractable problems: squaring the circle, trisecting any angle, and doubling the cube. Squaring the circle means making a square with an area of pi. Trisecting any angle refers to splitting an arbitrary angle into thirds. Doubling the cube is where you make a cube with double the volume of the original. As stated, the problems are impossible with the tools provided.
Heath was a scholar. He discusses how the Ancient Greeks wrote their numbers and how they manipulated them to reach their answers. The book is fascinating.
It isn't perfect. The book includes portions of text in the Greek language, and I can't read Greek. However, Heath wrote the book at a time when any educated person had to have a passing knowledge of Greek. Furthermore, he writes a translation for the word right next to it.
I enjoyed the book. Thanks for reading my review, and see you next time.
The Ancient Greeks are most famous for their contributions to Geometry. They used figures and drawings to demonstrate their proofs and solutions. In the field of Geometry, they emphasized rigor and logic. Supposedly, they invented the Pythagorean Theorem, but Heath acknowledges the other Ancient Civilizations that discovered it at the same period. In Number Theory, Pythagoras and his followers explored the integers.
Heath discusses the three intractable problems: squaring the circle, trisecting any angle, and doubling the cube. Squaring the circle means making a square with an area of pi. Trisecting any angle refers to splitting an arbitrary angle into thirds. Doubling the cube is where you make a cube with double the volume of the original. As stated, the problems are impossible with the tools provided.
Heath was a scholar. He discusses how the Ancient Greeks wrote their numbers and how they manipulated them to reach their answers. The book is fascinating.
It isn't perfect. The book includes portions of text in the Greek language, and I can't read Greek. However, Heath wrote the book at a time when any educated person had to have a passing knowledge of Greek. Furthermore, he writes a translation for the word right next to it.
I enjoyed the book. Thanks for reading my review, and see you next time.
February 15, 2022
I remember reading Heath's first volume of Euclid's Elements as a teenager and being spellbound by the historical discussion of the text, but not so much by the commentary after each proposition, which seemed all over the place. I am not at my best right now, so maybe if I were more refreshed I would have found more interest in tackling the examples he selects for each author and era of early Greek mathematics. As it is, I found them fairly tedious and dry, and the book as a whole is very up and down. Heath certainly exercised his imagination or lack thereof as a textual critic in a fairly unrestrained fashion, finding it impossible to believe that X early figure could have failed to realize Y, or that Z would have expressed himself in A fashion unless B, and I seldom believe him. Still, the ups are good, and it is a slice through a critical aspect and time of human thought.
Displaying 1 - 7 of 7 reviews