### The Resurgence of Archimedean Science: A Driver for Hydrostatics and Dynamics in the 16th and 17th Centuries
The European Renaissance, recognized for its revival of classical knowledge, experienced a significant revival in the examination of ancient Greek and Roman literature. Among these, the writings of Archimedes (287–212 BCE), the renowned Greek mathematician, physicist, and engineer, received renewed focus after being largely neglected during the medieval era. His manuscripts provided essential concepts that would greatly aid the emerging disciplines of physics, mechanics, and hydrostatics in the sixteenth century. Influential figures such as Benedetti (1530–1590), Simon Stevin (1548–1620), and Galileo Galilei (1564–1642) were particularly inspired by the rediscovered texts of Archimedes, especially his work, *On Floating Bodies*.
### Reviving Archimedes’ *On Floating Bodies*
Archimedes’ *On Floating Bodies* was initially printed and made more widely available through Nicolò Tartaglia’s (1499–1557) efforts, who released the text in both Italian and Latin. This distribution paved the way for its reexamination by mathematicians and physicists of the Renaissance. In 1565, Federico Commandino (1509–1575) further polished and corrected Tartaglia’s Latin translation. These editions ignited a transformation in the comprehension of fluid mechanics, with Archimedes’ principles becoming fundamental to the exploration of dynamics (the study of motion and forces) as well as hydrostatics—the examination of fluids at rest.
### Archimedes’ Impact on Hydrostatics
Archimedes’ *On Floating Bodies* is structured into two books. The first book outlines fundamental hydrostatic concepts, most prominently the “Principle of Archimedes,” a pivotal moment in the study of fluid mechanics. Proposition 7 from Book I states:
> “Solids that are denser than the fluid, when placed in the fluid, will be pushed downward until they have sunk as far as possible, and they will be lighter [when measured] in the fluid [than their weight in air] by the weight of the fluid that has the same volume as the solid.”
This principle, now commonly stated as *any object partially or wholly submerged in a fluid experiences an upward (buoyant) force equivalent to the weight of the fluid displaced by the object*, established the foundation for the contemporary understanding of buoyancy. Moreover, Archimedes also explored the shape taken by water due to gravitational forces, predicting that water would adopt a spherical form around the Earth—an insightful approximation derived from his mathematical grasp of fluids.
### In-Depth Hydrostatics in Book II
Book II of *On Floating Bodies* explores in greater detail the behaviors of floating objects, focusing specifically on right paraboloids. Archimedes conducted thorough analyses of their stable equilibrium configurations when submerged in a fluid. This work represented a conceptualization of ship hulls and stood out as one of Archimedes’ most remarkable mathematical accomplishments.
### Simon Stevin: The First Comprehensive Treatise on Hydrostatics
A key figure influenced by Archimedes was Simon Stevin, a Flemish engineer and mathematician. Stevin obtained a copy of Commandino’s edition and, in 1586, published *De Beghinselen des Waterwichts* (Principles on the Weight of Water). This publication was the first systematic treatise on hydrostatics since Archimedes and significantly broadened the utilization of hydrostatic concepts.
Similar to Archimedes, Stevin’s work consisted of two segments: a theoretical portion (*The Elements of Hydrostatics*) and a practical portion (*Preamble to the Practice of Hydrostatics*). One of Stevin’s notable contributions was his simplification of Archimedes’ principle, firmly establishing hydrostatics in practical mathematics.
Additionally, Stevin introduced novel ideas such as the *hydrostatic paradox*, a phenomenon that claims “any amount of liquid, no matter how small, can support any weight, no matter how large,” as long as the system is designed accordingly. He illustrated this concept by theorizing about the pressure at the bottoms of containers of various shapes and examining how vertical columns of fluid, irrespective of their lateral dimensions, exert uniform pressure based solely on their height.
### The Hydrostatic Paradox and Pascal’s Expansion
The hydrostatic paradox would later be further developed by subsequent thinkers, including Blaise Pascal (1623–1662), who expanded upon Stevin’s concepts. Pascal demonstrated the paradox by revealing how a small amount of water, when correctly arranged, could elevate objects of considerably greater mass. This concept, also referred to as Pascal’s Law, forms the foundation of hydraulic systems and modern mechanical engineering practices.
### Beyond Hydrostatics: Archimedes’ Influence on Dynamics
As Archimedes’ contributions to fluid mechanics were evolving into the formal domain of hydro