Treatise on Conic SectionsCambridge 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 |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
apex Apollonius Archimedes Archytas Aristaeus asymptotes axes axial triangle base bisected Book central conic centre chords parallel circle cone conic sections conjugate diameters conjugate hyperbola construction corresponding definition determined draw drawn parallel ellipse equal equation Eratosthenes Euclid Eutocius figure find finding first fixed point follows four-line locus geometrical Hence intersection Join latus rectum lemma length mean proportionals meet the asymptotes meet the axis meet the curve Menaechmus method middle point minimum straight line normal opposite branch ordinate Pappus parabola parallel to QQ parallelogram parameter perpendicular plane problem Proclus produced proof Prop Proposition proved quadrilateral ratio rectangle reference respectively rfis right angles right cone segment side similar triangles similarly solution square straight line drawn Suppose tangent at Q theorems treatise vertex whence