Continuity Eleven sketches from the past of Mathematics.pdf

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J ERZ Y M I O D USZ E WS K I
CONTINUITY
E L E V E N S K E TC H ES
FRO M TH E PAST O F M ATH EM ATI CS
T R A N S L AT E D 20 0 8 —2015
BY PROFESSOR ABE SHENITZER
KATOWICE 2016
CONTINUITY
E L E V E N S K E TC H ES
FR O M T H E PA ST O F M AT H EM AT I CS
Kup książkę
NR 3451
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j ERz y M I O d uSz E wS K I
CONTINUITY
E L E V E N S K E TC H ES
FRO M TH E PAST O F M ATH EM ATI CS
T R A N S L AT E d 20 0 8 —2015
By PROFESSOR ABE SHENITzER
KATOWICE 2016
Kup książkę
Table of contents
From the author
Introduction
Chapter I
The flying arrow • Aristotle’s view of the aporia of Zeno • Its influence on the
evolution of geometry and on the science of motion • Democritus’s version
of this aporia • On mathematical atomism
Chapter II
Aporia of the wanderer • The Archimedean postulate • The Eudoxian exhaustion
lemma • Non-Archimedean continua • Another Zeno’s difficulty: Stadium
Chapter III
Number • On idealism in mathematics • Its two varieties: Pythagoreism
and Platonism • Discovery of incommensurable segments • The Euclidean
algorithm • On some possible meanings of the proportion of segments
Chapter IV
On geometric magnitudes • Comparison of polygons from the point of view
of area • Comparison through complementation • Comparison through finite
decomposition • The role of Archimedean postulate • On quadratures
Chapter V
The Eudoxian theory of proportions • The role in it of the Archimedean postulate • The
theorem on interchanging terms in a proportion • On Tales’s theorem • Comparison
with Dedekind theory • Inequality of proportions • On the area of a circle • On
Greek geometric algebra • The
Elements
as an attempt to geometrize arithmetic
7
9
15
27
35
51
63
5
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