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 FLOATING BODIES, BOOK I
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
Postulate 1.
“Let it be supposed that a fluid is of such a character that, its parts lying evenly and being continuous, that part which is thrust the less is driven along by that which is thrust the more; and that each of its parts is thrust by the fluid which is above it in a perpendicular direction if the fluid be sunk in anything and compressed by anything else.”
Proposition 1.
If a surface be cut by a plane always passing through a certain point, and if the section be always a circumference [of a circle] whose centre is the aforesaid point, the surface is that of a sphere.
For, if not, there will be some two lines drawn from the point to the surface which are not equal.
Suppose O to be the fixed point, and A, B to be two points on the surface such that OA, OB are unequal. Let the surface be cut by a plane passing through OA, OB. Then the section is, by hypothesis, a circle whose centre is O.
Thus OA = OB; which is contrary to the assumption. Therefore the surface cannot but be a sphere.
Proposition 2.
The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth.
Suppose the surface of the fluid cut by a plane through O, the centre of the earth, in the curve ABCD.
- Type
- Chapter
- Information
- The Works of ArchimedesEdited in Modern Notation with Introductory Chapters, pp. 253 - 262Publisher: Cambridge University PressPrint publication year: 2009First published in: 1897
- 2
- Cited by