Editing Archimedes (section)

==== ''On Floating Bodies'' ====
{{Main|On Floating Bodies}}
There are two books of ''On Floating Bodies''. In the first book, Archimedes spells out the law of [[wikt:equilibrium|equilibrium]] of fluids and proves that water will adopt a spherical form around a center of gravity.<ref>{{Cite journal |last=Berggren |first=J. L. |date=1976 |title=Spurious Theorems in Archimedes' Equilibrium of Planes: Book I |journal=Archive for History of Exact Sciences |volume=16 |issue=2 |pages=87–103 |doi=10.1007/BF00349632 |jstor=41133463}}</ref>  

This may have been an attempt at explaining the theory of contemporary Greek astronomers such as [[Eratosthenes]] that the Earth is round.{{cn|date=April 2025}} The fluids described by Archimedes are not {{nowrap|self-gravitating}} since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.{{cn|date=April 2025}}

[[Archimedes' principle]] of buoyancy is given in this work, stated as follows:<ref>{{cite book |last=Netz |first=Reviel |chapter=Archimedes' Liquid Bodies |title=ΣΩΜΑ: Körperkonzepte und körperliche Existenz in der antiken Philosophie und Literatur |year=2017 |pages=287–322 |editor1-first=Thomas |editor1-last=Buchheim |editor2-first=David |editor2-last=Meißner |editor3-first=Nora |editor3-last=Wachsmann |isbn=978-3-7873-2928-1 |place=Hamburg |publisher=Felix Meiner |chapter-url=https://books.google.com/books?id=rQ2KDwAAQBAJ&pg=PA287 |chapter-url-access=limited}}</ref>

<blockquote>Any body wholly or partially immersed in fluid experiences an upthrust equal to, but opposite in direction to, the weight of the fluid displaced.</blockquote>

In the second part, he calculates the equilibrium positions of sections of paraboloids. This 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.<ref>{{cite book |last=Stein |first=Sherman |chapter=Archimedes and his floating paraboloids |editor1-first=David F. |editor1-last=Hayes |editor2-first=Tatiana |editor2-last=Shubin |title=Mathematical Adventures for Students and Amateurs |publisher=Mathematical Association of America |place=Washington |year=2004 |pages=219–231 |isbn=0-88385-548-8 |chapter-url=https://archive.org/details/mathematicaladve0000unse/page/219 |chapter-url-access=limited}} {{pb}} {{cite journal |last=Rorres |first=Chris |year=2004 |title=Completing Book II of Archimedes's on Floating Bodies |journal=The Mathematical Intelligencer |volume=26 |number=3 |pages=32–42 |doi=10.1007/bf02986750}} {{pb}} {{cite journal |last1=Girstmair |first1=Kurt |last2=Kirchner |first2=Gerhard |title=Towards a completion of Archimedes' treatise on floating bodies |journal=Expositiones Mathematicae |volume=26 |number=3 |year=2008 |pages=219–236 |doi=10.1016/j.exmath.2007.11.002 |doi-access=free}}</ref>