Download A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath
By reviewing this book A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath, you will get the most effective point to get. The brand-new point that you do not need to invest over cash to reach is by doing it on your own. So, what should you do now? Visit the link page as well as download guide A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath You could obtain this A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath by on the internet. It's so very easy, isn't really it? Nowadays, innovation truly sustains you activities, this on-line publication A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath, is as well.
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath
Download A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath
A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath. In undergoing this life, many people consistently attempt to do as well as get the most effective. New expertise, experience, driving lesson, and also everything that could boost the life will be done. Nevertheless, lots of people often really feel perplexed to obtain those things. Feeling the restricted of encounter as well as resources to be better is one of the does not have to possess. Nevertheless, there is a really easy point that could be done. This is exactly what your instructor consistently manoeuvres you to do this. Yeah, reading is the response. Reviewing an e-book as this A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath and also various other referrals could enrich your life top quality. Exactly how can it be?
Below, we have numerous publication A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath and collections to check out. We additionally serve variant types as well as type of guides to search. The enjoyable publication, fiction, past history, unique, scientific research, and also various other kinds of e-books are readily available here. As this A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath, it becomes one of the recommended e-book A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath collections that we have. This is why you are in the ideal site to see the amazing publications to own.
It will not take more time to obtain this A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath It won't take even more cash to print this e-book A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath Nowadays, individuals have been so smart to use the innovation. Why do not you utilize your device or various other device to conserve this downloaded and install soft documents publication A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath In this manner will certainly allow you to always be come with by this e-book A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath Of course, it will be the most effective buddy if you read this publication A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath until finished.
Be the very first to download this e-book now and get all reasons you require to review this A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath Guide A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath is not simply for your duties or requirement in your life. Publications will consistently be an excellent close friend in each time you review. Now, allow the others understand about this page. You could take the perks and share it additionally for your good friends and also people around you. By in this manner, you could really get the meaning of this book A History Of Greek Mathematics, Volume II: From Aristarchus To Diophantus (Dover Books On Mathematics), By Sir Thomas Heath profitably. What do you think of our idea right here?
"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." — Prof. 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's 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: #327319 in Books
- Brand: Heath, Thomas Little, Sir
- Published on: 1981-05-01
- Released on: 1981-05-01
- Original language: English
- Number of items: 1
- Dimensions: 8.26" h x 1.06" w x 5.64" l, 1.34 pounds
- Binding: Paperback
- 608 pages
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
7 of 7 people found the following review helpful.
Even more onerous, and important, than volume 1
By Alan U. Kennington
Volume 2 is even more onerous to wade through than Volume 1. I would not recommend reading every word of either of the two volumes. But Volume 2 is right off the scale in mathematical difficulty, both in quality and quantity. Quite often, it is more like a database to be mined by academic historians than a book to be read cover to cover. However, it is of enormous importance, demonstrating even more than volume 1 the depth and dexterity of ancient Greek mathematical thought.
The world must be grateful that a scholar such as Heath has made such Herculean efforts to locate and present the maximum of information about the history of Greek mathematics. Most maths history books gloss over the mathematical nitty-gritty, trying to keep everything as non-technical as possible so as not to scare off the reader. Heath writes as if his subject is important in itself, which it is.
The range of ancient Greek mathematics may seem narrow by modern standards. It is mostly the geometry of lines, circles, ellipses, hyperbolas, parabolas, spirals, cones, cylinders, spheres, and a handful of more adventurous curves, surfaces and solids. The non-integer numerical side of ancient Greek mathematics was mostly expressed in terms of geometry, although in the later, dying centuries of Greek mathematics, Diophantus did develop a purely arithmetical framework free of geometry. Heath makes it quite clear that the later number theory in Greek mathematics was often tedious, repetitive and somewhat shallow compared to what we now call number theory. Heath's exhausting "conspectus" of the "Arithmetica" by Diophantus, on pages 484 to 514, adequately demonstrates this.
Heath assumes that the reader has a good understanding of Euclidean geometry, such as is not available in schools and universities these days. It is nowadays almost a lost craft. It is lucky that Heath was writing at a time when old-style ruler-and-compass Euclidean geometry was still taken seriously as an academic subject. A modern historian would skim over this historical material because of its difficulty and unfamiliarity. Heath also seems to assume that the reader is fluent in Greek, Latin, French and German, because he provides no translations for most text in these languages. Once again, this was usual in his time but is difficult for modern readers. (I do read Latin, French and German, but I had to buy a better dictionary for the Greek.)
My overall impression of ancient Greek mathematicians from this book, especially from Volume 2, is that they were enormously more intelligent than I had ever suspected. Modern mathematicians would have great difficulty reproducing or even comprehending much of ancient Greek geometry. The ancient ingenuity and sophistication were truly impressive. Heath demonstrates this particularly in the case of the three-dimensional geometry of Apollonius and others around his time.
Apart from famous stars such as Archimedes, Apollonius, Ptolemy, Pappus and Diophantus, Heath also gives extensive coverage in Volume 2 of Aristarchus, Nicomedes, Geminus, Nicomachus, Theodosius, Hipparchus, Menelaus and Heron, who also made impressive, and often surprisingly modern, contributions to the progress of mathematics. While reading in this book how much of post-Renaissance mathematics was merely a repeat or continuation of ancient Greek mathematics, I wondered how advanced the world would be now if the Dark Ages had not interrupted the progress of mathematics for more than a thousand years. Heath's descriptions of ancient astronomy and optics in particular made me think that humanity could have reached the Moon 1000 years earlier if Greek mathematics had not been interrupted for so long.
2 of 2 people found the following review helpful.
Proto-algebraic view of geometry
By Viktor Blasjo
In continuation of my review of Volume 1, I shall in this review extract the contents of this volume pertaining to the theme of constructions discussed there.
A main theme in this later era of Greek mathematics is the increasing importance of an essentially algebraic point of view. The theory of conic sections is a case in point.
Menaechmus introduced conic sections for the purpose of using them to double the cube (110), but within only a generation or so systematic treatises were written on conics (116), followed later by the more abstract treatise by Apollonius that has come down to us (126). This was clearly a matter of theory for theory's sake, independently of their function in solving construction problems or any other use.
Altogether the volume of writings the Greeks produced on conics outweigh by a mile the scraps they wrote on any other curves except lines and circles, even though, as we saw in Volume 1, they knew many other curves that were about as useful as conics as far as applications were concerned. The only explanation for this is that conics are curves of degree two: they are algebraically the simplest next step beyond line and circle. In an algebraically oriented mode of mathematics conics will be ubiquitous and eminently treatable.
That this is the reason why they are so prominent in Greek mathematics is seen also by the uses the Greeks made of them. For instance, Archimedes derived the rotational volumes of conics (56), the centers of gravity (78) and areas (85) of parabolic segments, and the hydrostatics of paraboloids (94). There is no need or motivation for any of these results. Rather Archimedes is simply doing it because he can, and he can because they are second-degree curves which makes them susceptible to quasi-algebraic treatment and thus feasible to work with.
Another important and thoroughly algebraic use of conics is for solving cubic equations. Archimedes came upon a problem equivalent to a cubic equation in the context of studying the volumes of sections of spheres (43). He solved it by the intersection of two conic sections (45), as did Dionysodorus (46) and Diocles (47).
Now, as we recall from Volume 1, construction by conics was evidently not held is very high regard, since Menaechmus's use of them to double the cube was followed by a barrage of later methods that used other means. This suggests clearly that when they are used for Archimedes's cubic problem this is very much algebra through and through.
It is in this context, I think, that we must understand Pappus's famous division of problems:
"Those problems which can be solved by means of a straight line and a circumference of a circle may properly be called plane; for the lines by means of which such problems are solved have their origin in a plane. Those, however, which are solved by using for their discovery one or more of the sections of the cone have been called solid; for their construction requires the use of surfaces of solid figures, namely cones. There remains a third kind of problem, that which is called linear; for other lines (curves) besides those mentioned are assumed for the construction, the origin of which is more complicated and less natural, as they are generated from more irregular surfaces and intricate movements." (117)
This division seems the be essentially algebraic in character, since it gives a central place to conics while ignoring the various ruler-tool-based constructions that were evidently preferred for the duplication of the cube. The latter are not constructions by intersections of curves, so they do not fit Pappus's classification scheme. It seems thus that Pappus has allowed increasing algebraic awareness to trump more intuitive means of judging solutions. Why else would he insist only on constructions by intersections of curves, as so many earlier mathematicians doubling the cube evidently did not?
This interpretation also fits with the fact than Pappus's algebraically oriented notion of purity of method clashes with actual usage even by such luminaries as Archimedes and Apollonius:
"It seems to be a grave error into which geometers fall whenever any one discovers the solution of a plane problem by means of conics or linear (higher) curves, or generally solves it by means of a foreign kind, as in the case e.g. with the problem in the fifth Book of the Conics of Apollonius relating to the parabola, and when Archimedes assumes in his work on the spiral a neusis of a 'solid' character with reference to a circle; for it is possible without calling in the aid of anything solid to find the proof of the theorem given by Archimedes." (68)
Despite this last point, Pappus actually does precisely what he says is not needed: he proves the construction using conics instead of the neusis (386). It seems clear that the point of this is to prove that Archimedes's solution is in fact "solid," i.e., to map Archimedes's use of neusis into Pappus's algebraic hierarchy of methods. Rather than postulating that Archimedes was a fool, it seems more reasonable to conclude that Archimedes was working with a pre-algebraic, more intuitive way of judging construction methods than that used by Pappus.
Pappus's remark that Archimedes used "a neusis of a 'solid' character" hints at the fact that some uses of neusis can be reduced to ruler and compass, others not. This can perhaps be seen as another indication of the mismatch between intuitive and algebraic classifications of constructions. Apollonius in fact wrote a lost treatise discussing at some length which instances of neusis are reducible to ruler and compass constructions (189), which was possibly a step toward the more algebraic conception, although it also makes sense within an intuitive framework.
In the interest of full disclosure I must note a few items that do not fit my algebra-oriented interpretation. Perseus studied sections of a torus by analogy with sections of a cone (203), and Dionysodorus found the volume of a torus by analogy with Archimedes's determination of volumes of solids of revolution of conics (219). There were no applications of this. One must admit that here it is the geometrical generation of the conics rather than their algebraic properties that are at the forefront. In a somewhat similar vein, Pappus finds the quadratix by projections of 3D curves: once using a cylindrical helix and once using a cylinder with spiral base (380). This peculiar way of legitimising the quadratrix is in odd contrast with the algebraic modes of thought that were becoming so central, and together with the work of Perseus it seems instead to suggest an odd notion that the conics were somehow legitimated because they were part of a three-dimensional surface.
0 of 1 people found the following review helpful.
I also have vol I - a great book - if you are interested in how the ...
By kookie womblat
I also have vol I - a great book - if you are interested in how the ancients thought - there's nothing better than Heath - his commentaries on such works is outstanding - does anyone study these topics anymore? A gem of mathematical thinking, well before our time of calculators etc.
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath PDF
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath EPub
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath Doc
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath iBooks
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath rtf
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath Mobipocket
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics), by Sir Thomas Heath Kindle
Tidak ada komentar:
Posting Komentar