Editing Archimedes (section)

==== ''On the Equilibrium of Planes'' ====
{{Main|On the Equilibrium of Planes}}
There are two books to ''On the Equilibrium of Planes'': the first contains seven [[Axiom|postulates]] and fifteen [[proposition]]s, while the second book contains ten propositions. In the first book, Archimedes proves the law of the [[lever]],<ref>{{Cite journal |last=Goe |first=G. |date=1972 |title=Archimedes' theory of the lever and Mach's critique |journal=Studies in History and Philosophy of Science Part A |volume=2 |issue=4 |pages=329–345 |doi=10.1016/0039-3681(72)90002-7 |bibcode=1972SHPSA...2..329G}}</ref> which states that:

{{Blockquote|text=[[Magnitude (mathematics)|Magnitudes]] are in equilibrium at distances reciprocally proportional to their weights.}}

Earlier descriptions of the principle of the lever are found in a work by [[Euclid]] and in the ''[[Mechanics (Aristotle)|Mechanical Problems]],'' belonging to the [[Peripatetic school]] of the followers of [[Aristotle]], the authorship of which has been attributed by some to [[Archytas]].<ref name="lever clagett">{{cite book |first=Marshall |last=Clagett |url=https://books.google.com/books?id=mweWMAlf-tEC&q=archytas%20lever&pg=PA72 |title=Greek Science in Antiquity |publisher=Dover Publications |isbn=978-0-486-41973-2 |year=2001}}</ref>

Archimedes uses the principles derived to calculate the areas and [[center of mass|centers of gravity]] of various geometric figures including [[triangle]]s, [[parallelogram]]s and [[parabola]]s.<ref name="works">{{cite book |author=Heath, T.L. |url=https://archive.org/details/worksofarchimede029517mbp |title=The Works of Archimedes |year=1897 |publisher=Cambridge University Press}}</ref>