Treatise on Conic SectionsActive 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. |
Contents
CONTENTS | xvii |
ARISTAEUS AND EUCLID | xxxi |
ARCHIMEDES | xli |
INTRODUCTION TO THE CONICS OF APOLLONIUS | lxviii |
GENERAL CHARACTERISTICS | lxxxvii |
THE METHODS OF APOLLONIUS | ci |
THE CONSTRUCTION OF A CONIC BY MEANS | cxxx |
POINTS | cli |
TANGENTS CONJUGATE DIAMETERS AND AXES | 64 |
EXTENSIONS OF PROPOSITIONS 1719 | 84 |
RECTANGLES UNDER SEGMENTS OF INTERSECTING | 95 |
HARMONIC PROPERTIES OF POLES AND POLARS | 102 |
INTERCEPTS MADE ON TWO TANGENTS BY A THIRD | 109 |
THE LOCUS WITH RESPECT TO THREE LINES ETC | 119 |
INTERSECTING CONICS | 126 |
NORMALS AS MAXIMA AND MINIMA | 139 |
APPENDIX NOTES ON THE TERMINOLOGY OF GREEK GEO | clvii |
THE CONE | 1 |
THE DIAMETER AND ITS CONJUGATE | 15 |
TANGENTS | 22 |
PROPOSITIONS LEADING TO THE REFERENCE OF A CONIC | 31 |
CONSTRUCTION OF CONICS FROM CERTAIN DATA | 42 |
ASYMPTOTES | 53 |
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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Common terms and phrases
Apollonius Archimedes Archytas Aristaeus asymptotes axes axial triangle axis bisected Book CA² CB² CD² central conic centre circle cone conic sections conjugate diameters conjugate hyperbola corresponding CP² draw drawn parallel ellipse equal equation Euclid Eutocius figure follows four-line locus geometrical given Hence intersection Join latus rectum M₁H meet the curve Menaechmus MH² middle point normal opposite branch ordinate P₁ Pappus parabola parallelogram parameter perpendicular plane PN² problem Proclus produced proof Prop Proposition proved quadrilateral QV² ratio rectangle reference respectively right angles right cone segment similar triangles similarly solution square straight line Suppose tangent tangent at Q vertex whence αἱ ἄρα δὲ ἐπὶ καὶ ΜΗ πρὸς τὸ ἀπὸ τὰ τῇ τὴν τῆς τοῦ τῷ τῶν ὑπὸ ὡς