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
QUADRATURE OF THE PARABOLA
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
“Archimedes to Dositheus greeting.
“When I heard that Conon, who was my friend in his lifetime, was dead, but that you were acquainted with Conon and withal versed in geometry, while I grieved for the loss not only of a friend but of an admirable mathematician, I set myself the task of communicating to you, as I had intended to send to Conon, a certain geometrical theorem which had not been investigated before but has now been investigated by me, and which I first discovered by means of mechanics and then exhibited by means of geometry. Now some of the earlier geometers tried to prove it possible to find a rectilineal area equal to a given circle and a given segment of a circle; and after that they endeavoured to square the area bounded by the section of the whole cone and a straight line, assuming lemmas not easily conceded, so that it was recognised by most people that the problem was not solved. But I am not aware that any one of my predecessors has attempted to square the segment bounded by a straight line and a section of a rightangled cone [a parabola], of which problem I have now discovered the solution.
- Type
- Chapter
- Information
- The Works of ArchimedesEdited in Modern Notation with Introductory Chapters, pp. 233 - 252Publisher: Cambridge University PressPrint publication year: 2009First published in: 1897
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