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''On Floating Bodies'' ( el, Περὶ τῶν ἐπιπλεόντων σωμάτων) is a Greek-language work consisting of two books written by
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists i ...
of
Syracuse Syracuse may refer to: Places Italy *Syracuse, Sicily, or spelled as ''Siracusa'' *Province of Syracuse United States *Syracuse, New York **East Syracuse, New York **North Syracuse, New York * Syracuse, Indiana * Syracuse, Kansas * Syracuse, Mi ...
(287 – c. 212 BC), one of the most important mathematicians,
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...
s, and
engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the lim ...
s of antiquity. ''On Floating Bodies'', which is thought to have been written around 250 BC, survives only partly in Greek, the rest in medieval Latin translation from the Greek. It is the first known work on hydrostatics, of which Archimedes is recognized as the founder. The purpose of ''On Floating Bodies'' was to determine the positions that various solids will assume when floating in a fluid, according to their form and the variation in their specific gravities. It contains the first statement of what is now known as
Archimedes' principle Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes ...
.


Overview

Archimedes lived in the Greek city-state of
Syracuse Syracuse may refer to: Places Italy *Syracuse, Sicily, or spelled as ''Siracusa'' *Province of Syracuse United States *Syracuse, New York **East Syracuse, New York **North Syracuse, New York * Syracuse, Indiana * Syracuse, Kansas * Syracuse, Mi ...
, Sicily. He is credited with laying the foundations of hydrostatics (which he established in ''On Floating Bodies''), statics and calculating the underlying mathematics of the
lever A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or '' fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is ...
. A leading scientist of classical antiquity, Archimedes also developed elaborate systems of pulleys to move large objects with a minimum of effort. The
Archimedes' screw The Archimedes screw, also known as the Archimedean screw, hydrodynamic screw, water screw or Egyptian screw, is one of the earliest hydraulic machines. Using Archimedes screws as water pumps (Archimedes screw pump (ASP) or screw pump) dates back ...
underpins modern hydroengineering, and his machines of war helped to hold back the armies of Rome in the Second Punic War. Archimedes opposed the arguments of Aristotle, pointing out that it was impossible to separate mathematics and nature and proved it by converting mathematical theories into practical inventions. The only known copy of "On Floating Bodies" in Greek comes from the
Archimedes Palimpsest The Archimedes Palimpsest is a parchment codex palimpsest, originally a Byzantine Greek copy of a compilation of Archimedes and other authors. It contains two works of Archimedes that were thought to have been lost (the ''Ostomachion'' and the ' ...
.


Contents


First book

In the first part of the treatise, Archimedes establishes various general principles, such as that a solid denser than a fluid will, when immersed in that fluid, be lighter (this "missing" weight is found in the fluid it displaces). Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a
center of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandr ...
that the Earth is round. The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape. Most notably, ''On Floating Bodies'' contains the concept which became known as
Archimedes' principle Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes ...
: As well as the principle that bears his name, Archimedes discovered that a submerged object displaces a volume of water equal to the object's own volume (upon which it is said he shouted "
Eureka Eureka (often abbreviated as E!, or Σ!) is an intergovernmental organisation for research and development funding and coordination. Eureka is an open platform for international cooperation in innovation. Organisations and companies applying th ...
"). Further, Proposition 5 of Archimedes' treatise ''On Floating Bodies'' states that: This concept has come to be referred to by some as the principle of flotation.


Second book

The second book is a mathematical achievement unmatched in antiquity and rarely equaled since. Heath called it "a veritable ''tour de force'' which must be read in full to be appreciated." The book contains a detailed investigation of the stable equilibrium positions of floating right
paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane ...
s of various shapes and relative densities, when floating in a fluid of greater specific gravity, according to geometric and hydrostatic variations. It is restricted to the case when the base of the paraboloid lies either entirely above or entirely below the fluid surface. Archimedes' investigation of paraboloids was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Of his works that survive, the second of his two books of ''On Floating Bodies'' is considered his most mature work, commonly described as a tour de force.


References


External links


Greek text hosted by SLUB
( Saxon State and University Library Dresden)
Greek text hosted by Poesia LatinaThe Medieval Latin Translation
by William of Moerbeke edited by Johan Heiberg
English translation
by
Thomas Little Heath Sir Thomas Little Heath (; 5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translat ...
{{Archimedes Works by Archimedes 3rd-century BC books Papyrology