A History of Greek Mathematics: Volume 2. From Aristarchus by Sir Thomas Heath

By Sir Thomas Heath

"As it really is, the booklet is vital; it has, certainly, no critical English rival." — Times Literary Supplement
"Sir Thomas Heath, optimal English historian of the traditional unique sciences within the 20th century." — Prof. W. H. Stahl
"Indeed, in view that a lot of Greek is arithmetic, it really is controversial that, if one might comprehend the Greek genius totally, it'd be a superb plan to start with their geometry."
The standpoint that enabled Sir Thomas Heath to appreciate the Greek genius — deep intimacy with languages, literatures, philosophy, and all of the sciences — introduced him maybe towards his liked topics, and to their very own excellent of expert males than is usual or perhaps attainable at the present time. Heath learn the unique texts with a severe, scrupulous eye and taken to this definitive two-volume background the insights of a mathematician communicated with the readability of classically taught English.
"Of all of the manifestations of the Greek genius none is extra notable or even awe-inspiring than that that's published by means of the background of Greek mathematics." Heath documents that heritage with the scholarly comprehension and comprehensiveness that marks this paintings as evidently vintage now as while it first seemed in 1921. The linkage and cohesion of arithmetic and philosophy recommend the description for the full historical past. Heath covers in series Greek numerical notation, Pythagorean mathematics, 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 dedicated to the heritage and research of well-known difficulties: squaring the circle, perspective trisection, duplication of the dice, and an appendix on Archimedes's evidence of the subtangent estate of a spiral. The insurance is all over the place thorough and sensible; yet Heath isn't content material with simple exposition: it's a illness within the present histories that, whereas they country regularly the contents of, and the most propositions proved in, the nice treatises of Archimedes and Apollonius, they make little try to describe the technique through which the consequences are got. i've got for that reason taken pains, within the most vital situations, to teach the process the argument in enough element to let a reliable mathematician to understand the tactic used and to use it, if he'll, to different comparable investigations.
Mathematicians, then, will have fun to discover Heath again in print and obtainable after a long time. Historians of Greek tradition and technological know-how can renew acquaintance with a typical reference; readers typically will locate, rather within the vigorous discourses on Euclid and Archimedes, precisely what Heath capacity by means of impressive and awe-inspiring.

Show description

Read Online or Download A History of Greek Mathematics: Volume 2. From Aristarchus to Diophantus PDF

Best science & mathematics books

Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications: Proceedings of an Ams Special Session Held May 22-23, 1991 in

This e-book is the 1st set of lawsuits to be committed solely to the idea of hypergeometric services outlined on domain names of positivity. many of the medical components during which those capabilities are utilized comprise analytic quantity conception, combinatorics, harmonic research, random walks, illustration conception, and mathematical physics---are represented the following.

Homotopy Theory of Function Spaces and Related Topics: Oberwolfach Workshop, April 5-11, 2009, Mathematisches Forschungsinstitut, Oberwolfach, Germany

Those 14 unique study articles conceal localisation & rational homotopy conception, review subgroups, unfastened loop areas, Whitehead items, areas of algebraic maps, guage teams, loop teams, operads & string topology

Additional info for A History of Greek Mathematics: Volume 2. From Aristarchus to Diophantus

Example text

N Um euch die Übungsaufgabe nicht wegzunehmen, geben wir nun eine andere offene Überdeckung an und zeigen zunächst, dass diese eine offene Überdeckung des Intervalls (0, 1) ist und danach, dass diese Überdeckung keine endliche Teilüberdeckung besitzt, die das Intervall (0, 1) überdeckt. Hieraus ergibt sich, dass (0, 1) nicht überdeckungskompakt und damit nicht kompakt ist. Wir behaupten als erstes, dass ∞ n=1 1 1 , n+2 n =:Un eine offene Überdeckung vom Intervall (0, 1) ist. Dazu ist zu zeigen, dass für alle 1 x ∈ (0, 1) ein n ∈ N mit x ∈ Un existiert.

Mithilfe der Parallelogrammungleichung kann man sich schnell überlegen, ob eine Norm durch ein Skalarprodukt induziert werden kann. In Abb. 12 haben wir versucht, diese Beziehungen noch einmal zusammenzufassen. Zum Abschluss noch zu einem Gegenbeispiel, das zeigt, wieso einige Umkehrungen in Abb. 12 nicht richtig sind. Beispiel 19 Die diskrete Metrik aus Beispiel 1 wird nicht durch eine Norm induziert. Das Paradebeispiel für die Notwendigkeit einer Topologie ist die Konvergenz in RR , also die punktweise Konvergenz von Funktionenfolgen.

Sei weiterhin k ⊂ M. Dann gäbe es ein ε > 0, sodass für alle n ∈ N Punkte xn und xn existieren mit dM (xn , xn ) < 1 n und dN (f (xn ), f (xn )) ≥ ε. Da K kompakt ist, existiert eine Teilfolge (xnk )k∈N , die gegen ein x ∈ K konvergiert. Wegen dM xnk , xnk < 1 nk gilt dann aber auch limk→∞ xnk = x. Da f andererseits stetig ist, folgt aus der Dreiecksungleichung lim dN f (xnk ), f (xnk ) ≤ lim dN f (xnk ), f (x) + lim dN f (x), f (xnk ) = 0. k→∞ k→∞ k→∞ Dies ist aber ein Widerspruch zu dN f (xnk ), f (xnk ) ≥ ε und beweist damit die Behauptung.

Download PDF sample

Rated 4.32 of 5 – based on 43 votes