"From Ta Physika to Contemporary Physics – Section XXXII"

“From Ta Physika to Contemporary Physics – Section XXXII”


**The Revival of Hydrostatics: The Legacy of Archimedes and Its Evolution in the Sixteenth and Seventeenth Centuries**

The renewed fascination with Archimedes’ contributions during the Renaissance significantly altered the course of physics and mechanics in the sixteenth century, resulting in revolutionary advancements in both dynamics and hydrostatics. Largely disregarded for much of the medieval era, Archimedes’ works—especially his treatise *On Floating Bodies*—emerged as a foundational resource for the scientific inquiries of influential figures such as Niccolò Tartaglia, Simon Stevin, Galileo Galilei, and eventually Pascal.

At the core of this resurgence was the revival of Archimedean concepts, which established a solid basis for grasping buoyancy and equilibrium. This essential work not only contested Aristotelian physics but also spurred entirely new methodologies in both practical and theoretical explorations of hydrostatics and mechanics.

### Archimedes’ *On Floating Bodies*: A Revival

Written in ancient Greece, Archimedes’ *On Floating Bodies* consists of two volumes filled with deep insights on fluid mechanics. In Book I, Archimedes outlines general principles regarding equilibrium and fluid properties, introducing his groundbreaking idea of hydrostatic pressure. Here, he famously posited the connection between fluid pressure and weight, demonstrating that still water takes on a spherical form around a central gravitational force.

The centerpiece of Book I is Proposition 7, which embodies the widely acclaimed “Principle of Archimedes”:

> “Solids heavier than the fluid, when thrown into the fluid, will be driven downward as far as they can sink, and they will be lighter [when weighed] in the fluid [than their weight in air] by the weight of the portion of fluid having the same volume as the solid.”

In modern terms, this is often articulated as:

> “Any object totally or partially submerged in a fluid experiences an upward force (buoyancy) equivalent to the weight of the fluid displaced.”

Book II delves further into the geometry of floating bodies, particularly examining the equilibrium of right paraboloids within fluids. This intricate mathematical examination, while complex for many contemporary readers, is widely regarded as one of Archimedes’ greatest accomplishments in mathematics and its relation to the physical sciences. Scholars believe that this analysis reflected Archimedes’ practical interests in ship design and stability at sea.

### The Renaissance Resurgence: Tartaglia to Commandino

The significant influence of Archimedes on early modern science was made achievable by the Italian mathematician Niccolò Tartaglia, who released the first printed translations of *On Floating Bodies* in both Latin and Italian. This crucial publication exposed Archimedes’ hydrostatic concepts to a larger European readership eager for advancements in scientific thought.

Federico Commandino, a distinguished Renaissance scholar and translator, enhanced Tartaglia’s work by rectifying mistakes in the Latin text and issuing a revised edition in 1565. Commandino’s thorough work ensured that Archimedes’ treatise could function as a vital reference for the developing scientific community. This greater availability marked the onset of an Archimedean revival, prompting mathematicians and physicists to find ways to weave his concepts into their own studies.

### Simon Stevin and the Progression of Hydrostatics

Among those influenced by Archimedes, Simon Stevin from Bruges emerged as a crucial figure. Stevin not only reinforced Archimedean principles but also brought forth notable progressions in hydrostatics. His 1586 publication, *De Beghinselen des Waterwichts* (*Principles on the Weight of Water*), was the first organized treatise on hydrostatics since ancient times, seamlessly merging theoretical concepts with practical applications.

Stevin diverged from Archimedes’ conclusions in significant aspects. For example, while Archimedes believed water adapted to a spherical Earth, Stevin contended that water surfaces could be considered flat for practical usage. Through a compelling perpetual motion argument, Stevin demonstrated that water instinctively reaches equilibrium in various-shaped containers.

Stevin articulated Archimedes’ principle of buoyancy in more straightforward, applicable language:

> “The gravity of any solid body is as much lighter in water than in air as is the gravity of the water having the same volume.”

Stevin’s contributions also introduced the “hydrostatic paradox,” a revolutionary concept that illustrated how the pressure at the bottom of a fluid is determined solely by the height of the fluid column above it, independent of the vessel’s shape or width. This revelation would later be examined and affirmed by prominent figures, including Blaise Pascal.

### Beyond Stevin: A Continuous Development

The enduring nature of Archimedes’ hydrostatic principles arose from their versatility across various fields and periods, gaining momentum well into the seventeenth century. For