Editing Archimedes (section)

==== ''The Sand Reckoner'' ====
{{Main|The Sand Reckoner}}
In this treatise, also known as '''''Psammites''''', Archimedes finds a number that is greater than the [[Sand|grains of sand]] needed to fill the universe. This book mentions the [[Heliocentrism|heliocentric]] theory of the [[Solar System]] proposed by [[Aristarchus of Samos]], as well as contemporary ideas about the size of the Earth and the distance between various [[celestial bodies]], and attempts to measure the apparent diameter of the [[Sun]].<ref>{{Cite journal |last=Osborne |first=Catherine |date=1983 |title=Archimedes on the Dimensions of the Cosmos |url=https://www.jstor.org/stable/233105 |journal=Isis |volume=74 |issue=2 |pages=234–242 |doi=10.1086/353246 |jstor=233105 |issn=0021-1753}}</ref><ref name=":7">{{Citation |last1=Rozelot |first1=Jean Pierre |title=A brief history of the solar diameter measurements: a critical quality assessment of the existing data |date=2016 |arxiv=1609.02710 |last2=Kosovichev |first2=Alexander G. |last3=Kilcik |first3=Ali}}</ref> By using a system of numbers based on powers of the [[myriad]], Archimedes concludes that the number of grains of sand required to fill the universe is 8{{e|63}} in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. ''The Sand Reckoner'' is the only surviving work in which Archimedes discusses his views on astronomy.<ref>{{cite web |year=2002 |title=English translation of ''The Sand Reckoner'' |publisher=[[University of Waterloo]] |url=http://www.math.uwaterloo.ca/navigation/ideas/reckoner.shtml |archive-date=2002-06-01 |archive-url=https://web.archive.org/web/20020601231141/https://www.math.uwaterloo.ca/navigation/ideas/reckoner.shtml |url-status=dead}} Adapted from {{cite book |last=Newman |first=James R. |title=The World of Mathematics |volume=1 |publisher=Simon & Schuster |location=New York |year=1956}}</ref>

Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as [[Aristarchus of Samos|Aristarchus]]' heliocentric model of the universe, in the ''Sand-Reckoner''.<ref>{{Cite encyclopedia |last1=Toomer |first1=G. J. |last2=Jones |first2=Alexander |date=7 March 2016 |title=Astronomical Instruments |encyclopedia=Oxford Research Encyclopedia of Classics |doi=10.1093/acrefore/9780199381135.013.886 |isbn=9780199381135 |quote="Perhaps the earliest instrument, apart from sundials, of which we have a detailed description is the device constructed by Archimedes for measuring the sun's apparent diameter; this was a rod along which different coloured pegs could be moved."}}</ref> Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves),<ref>{{Cite journal |last=Evans |first=James |date=1 August 1999 |title=The Material Culture of Greek Astronomy |journal=Journal for the History of Astronomy |volume=30 |issue=3 |pages=238–307 |bibcode=1999JHA....30..237E |doi=10.1177/002182869903000305}}</ref> applying correction factors to these measurements, and finally giving the result in the form of upper and lower bounds to account for observational error.<ref>{{Cite journal |last=Shapiro |first=A. E. |date=1975 |title=Archimedes's measurement of the Sun's apparent diameter. |journal=Journal for the History of Astronomy |volume=6 |issue=2 |pages=75–83 |bibcode=1975JHA.....6...75S |doi=10.1177/002182867500600201}}</ref> 

[[Ptolemy]], quoting Hipparchus, also references Archimedes' [[solstice]] observations in the ''Almagest''. This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years.<ref name="Acerbi2008" />