Apollonius of Perga, Treatise on Conic Sections: Edited in modern notation with Introductions including an Essay on the earlier History of the subject by T. L. HeathCUP Archive, 1896 - 254 pagine |
Sommario
INTRODUCTION | xvii |
CHAPTER II | lxxxvii |
THE METHODS OF APOLLONIUS | ci |
CHAPTER IV | cxxx |
THE THREELINE AND FOURLINE LOCUS | cxxxviii |
THE CONSTRUCTION OF A CONIC THROUGH FIVE | cli |
APPENDIX | clvii |
THE CONE | 1 |
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 | 121 |
NORMALS AS MAXIMA AND MINIMA | 139 |
PROPOSITIONS LEADING IMMEDIATELY TO THE DETER | 168 |
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 |
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 |
Altre edizioni - Visualizza tutto
Apollonius of Perga, Treatise on Conic Sections: Edited in modern notation ... Apollonius (Pergaeus) Visualizzazione completa - 1896 |
Apollonius of Perga, Treatise on Conic Sections: Edited in modern notation ... Apollonius (Pergaeus) Visualizzazione completa - 1896 |
Parole e frasi comuni
Apollonius Archimedes Archytas Aristaeus asymptotes axes axial triangle axis bisected Book CB² CD² central conic centre circle cone conic sections conjugate diameters conjugate hyperbola construction corresponding CP² draw drawn parallel ellipse equal equation Euclid Eutocius figure follows four-line locus geometrical given Hence intersection Join latus rectum M₂H meet the curve Menaechmus MH² middle point normal opposite branch ordinate P₁ Pappus parabola parallel to QQ 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 Suppose tangent at Q theorems treatise vertex whence αἱ ἄρα δὲ ἐπὶ καὶ πρὸς τὸ ἀπὸ τὰ τῇ τὴν τῆς τοῦ τῶν ὑπὸ ὡς