Editing Volume (section)

=== Calculus and standardization of units ===
{{Further|History of calculus|Apothecaries' system}}
[[File:"How to Measure" diagram, with graduated cylinder measuring fluid drams, 1926.jpg|alt=Pouring liquid to a marked flask|left|thumb|Diagram showing how to measure volume using a graduated cylinder with [[fluid dram]] markings, 1926]]
In the [[Middle Ages]], many units for measuring volume were made, such as the [[sester]], [[Amber (unit)|amber]], [[Coomb (unit)|coomb]], and [[Seam (unit)|seam]]. The sheer quantity of such units motivated British kings to standardize them, culminated in the [[Assize of Bread and Ale]] statute in 1258 by [[Henry III of England]]. The statute standardized weight, length and volume as well as introduced the peny, ounce, pound, gallon and bushel.<ref name="Imhausen-2016" />{{Rp|page=|pages=73–74}} In 1618, the ''[[London Pharmacopoeia]]'' (medicine compound catalog) adopted the Roman gallon<ref name="RPS-2020">{{Cite web |date=4 Feb 2020 |title=Balances, Weights and Measures |url=https://www.rpharms.com/Portals/0/MuseumLearningResources/11%20Balances%20Weights%20and%20Measures.pdf |access-date=13 August 2022 |website=[[Royal Pharmaceutical Society]] |page=1 |archive-date=20 May 2022 |archive-url=https://web.archive.org/web/20220520094140/https://www.rpharms.com/Portals/0/MuseumLearningResources/11%20Balances%20Weights%20and%20Measures.pdf |url-status=live }}</ref> or ''[[congius]]''<ref>{{Cite book |last=Cardarelli |first=François |title=Scientific Unit Conversion: A Practical Guide to Metrication |date=6 Dec 2012 |publisher=[[Springer Science+Business Media]] |isbn=978-1-4471-0805-4 |edition=2nd |location=London |pages=151 |oclc=828776235}}</ref> as a basic unit of volume and gave a conversion table to the apothecaries' units of weight.<ref name="RPS-2020" /> Around this time, volume measurements are becoming more precise and the uncertainty is narrowed to between {{Cvt|1–5|mL|USoz impoz|sigfig=1}}.<ref name="Imhausen-2016" />{{Rp|page=8}}

Around the early 17th century, [[Bonaventura Cavalieri]] applied the philosophy of modern integral calculus to calculate the volume of any object. He devised [[Cavalieri's principle]], which said that using thinner and thinner slices of the shape would make the resulting volume more and more accurate. This idea would then be later expanded by [[Pierre de Fermat]], [[John Wallis]], [[Isaac Barrow]], [[James Gregory (mathematician)|James Gregory]], [[Isaac Newton]], [[Gottfried Wilhelm Leibniz]] and [[Maria Gaetana Agnesi]] in the 17th and 18th centuries to form the modern integral calculus, which remains in use in the 21st century.<ref name="Treese-2018" />{{Rp|page=404}}