Treatise on Conic Sections

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Cambridge University Press, 21 de nov. 2013 - 434 pàgines
Active in Alexandria in the third century BCE, Apollonius of Perga ranks as one of the greatest Greek geometers. Building on foundations laid by Euclid, he is famous for defining the parabola, hyperbola and ellipse in his major treatise on conic sections. The dense nature of its text, however, made it inaccessible to most readers. When it was originally published in 1896 by the civil servant and classical scholar Thomas Little Heath (1861-1940), the present work was the first English translation and, more importantly, the first serious effort to standardise the terminology and notation. Along with clear diagrams, Heath includes a thorough introduction to the work and the history of the subject. Seeing the treatise as more than an esoteric artefact, Heath presents it as a valuable tool for modern mathematicians. His works on Diophantos of Alexandria (1885) and Aristarchus of Samos (1913) are also reissued in this series.
 

Continguts

INTRODUCTION
xvii
ARISTAEUS AND EUCLID
xxxi
ARCHIMEDES
xli
INTRODUCTION TO THE CONIOS OF APOLLONIUS
lxviii
GENERAL CHARACTERISTICS
lxxxvii
THE METHons OF APOLLONIUS
ci
THE CONSTRUCTION OF A come BY MEANS
cxxx
THE THREELINE AND FOURLINE LOCUS
cxxxviii
ASYMPTOTES
53
TANGENTS CONJUGATE DIAMETERS AND AXES
64
EXTENSIONS OF PROPOSITIONS 1719
84
RECTANGLES UNDER SEGMENTS OF INTERSECTING
95
HARMONIC PROPERTIES OF POLES AND POLARS
103
INTERCEPTS MADE ON TWO TANGENTS BY A THIRD
109
THE LOCUS WITH RESPECT TO THREE LINES ETC
121
NORMALS AS MAXIMA AND MINIMA
139

THE CONSTRUCTION OF A come THROUGH FIVE
cli
APPENDIX NOTES ON THE TERMINOLOGY or GREEK eno
clvii
THE GONIOS OF APOLLONIUS
10
TANGENTS
22
PROPOSITIONS LEADING TO THE REFERENCE OF A CONIC
31
CONSTRUCTION OF OONICS FROM CERTAIN DATA
42
PROPOSITIONS LEADING IMMEDIATELY TO THE DETER
168
CONSTRUCTION OF NORMALS
180
OTHER PROPOSITIONS RESPECTING MAXIMA AND MINIMA
187
EQUAL AND SIMILAR CONICS
197
PROBLEMS
209
VALUES OF CERTAIN FUNCTIONS OF THE LENGTHS
221

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