Book contents
- Frontmatter
- PREFACE
- LIST OF THE PRINCIPAL WORKS CONSULTED
- Contents
- INTRODUCTION
- THE WORKS OF ARCHIMEDES
- ON THE SPHERE AND CYLINDER, BOOK I
- ON THE SPHERE AND CYLINDER, BOOK II
- MEASUREMENT OF A CIRCLE
- ON CONOIDS AND SPHEROIDS
- ON SPIRALS
- ON THE EQUILIBRIUM OF PLANES, BOOK I
- ON THE EQUILIBRIUM OF PLANES, BOOK II
- THE SAND-RECKONER
- QUADRATURE OF THE PARABOLA
- ON FLOATING BODIES, BOOK I
- ON FLOATING BODIES, BOOK II
- BOOK OF LEMMAS
ON CONOIDS AND SPHEROIDS
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- PREFACE
- LIST OF THE PRINCIPAL WORKS CONSULTED
- Contents
- INTRODUCTION
- THE WORKS OF ARCHIMEDES
- ON THE SPHERE AND CYLINDER, BOOK I
- ON THE SPHERE AND CYLINDER, BOOK II
- MEASUREMENT OF A CIRCLE
- ON CONOIDS AND SPHEROIDS
- ON SPIRALS
- ON THE EQUILIBRIUM OF PLANES, BOOK I
- ON THE EQUILIBRIUM OF PLANES, BOOK II
- THE SAND-RECKONER
- QUADRATURE OF THE PARABOLA
- ON FLOATING BODIES, BOOK I
- ON FLOATING BODIES, BOOK II
- BOOK OF LEMMAS
Summary
Introduction.
“Archimedes to Dositheus greeting.
In this book I have set forth and send you the proofs of the remaining theorems not included in what I sent you before, and also of some others discovered later which, though I had often tried to investigate them previously, I had failed to arrive at because I found their discovery attended with some difficulty. And this is why even the propositions themselves were not published with the rest. But afterwards, when I had studied them with greater care, I discovered what I had failed in before.
Now the remainder of the earlier theorems were propositions concerning the right-angled conoid [paraboloid of revolution]; but the discoveries which I have now added relate to an obtuseangled conoid [hyperboloid of revolution] and to spheroidal figures, some of which I call oblong (παραμάκεα) and others flat (ἐπιπλατέα).
I. Concerning the right-angled conoid it was laid down that, if a section of a right-angled cone [a parabola] be made to revolve about the diameter [axis] which remains fixed and return to the position from which it started, the figure comprehended by the section of the right-angled cone is called a right-angled conoid, and the diameter which has remained fixed is called its axis, while its vertex is the point in which the axis meets (ἅπτεται) the surface of the conoid.
- Type
- Chapter
- Information
- The Works of ArchimedesEdited in Modern Notation with Introductory Chapters, pp. 99 - 150Publisher: Cambridge University PressPrint publication year: 2009First published in: 1897
- 2
- Cited by