Hypsicles (; c. 190 – c. 120 BCE) was an ancient Greeks mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.
Life and work
Although little is known about the life of Hypsicles, it is believed that he authored the astronomical work
On Ascensions. The mathematician
Diophantus of Alexandria noted on a definition of polygonal numbers, due to Hypsicles:
On Ascensions
In
On Ascensions (Ἀναφορικός and sometimes translated
On Rising Times), Hypsicles proves a number of propositions on arithmetical progressions and uses the results to calculate approximate values for the times required for the signs of the zodiac to rise above the
horizon.
[Evans, J., (1998), The History and Practice of Ancient Astronomy, page 90. Oxford University Press.] It is thought that this is the work from which the division of the
circle into 360 parts may have been adopted
since it divides the day into 360 parts, a division possibly suggested by Babylonian astronomy,
although this is mere speculation and no actual evidence is found to support this. Heath 1921 notes, "The earliest extant Greek book in which the division of the circle into 360 degrees appears".
This work by Hypsicles is believed to represent the earliest extant Greek text to use the Babylonian division of the zodiac into 12 signs of 30 degrees each.[Montelle, Clemency (2016), "The Anaphoricus of Hypsicles of Alexandria", in Steele, John M., The Circulation of Astronomical Knowledge in the Ancient World, Time, Astronomy, and Calendars: Texts and Studies, 6, Leiden: Brill, pp. 287–315, ]
Euclid's Elements
Hypsicles is more famously known for possibly writing the Book XIV of Euclid's
Elements. The book may have been composed on the basis of a treatise by Apollonius. The book continues Euclid's comparison of
regular solids inscribed in
spheres, with the chief result being that the ratio of the surfaces of the
dodecahedron and
icosahedron inscribed in the same sphere is the same as the
ratio of their
, the ratio being
.
[}. It is thought that this book may have been composed by Hypsicles on the basis of a treatise (now lost) by Apollonius comparing the dodecahedron and icosahedron. (Hypsicles, who probably lived in the second half of the second century B.C., is thought to be the author of an astronomical work, De ascensionibus, from which the division of the circle into 360 parts may have been adopted.)}}]
Heath further notes, "Hypsicles says also that Aristaeus, in a work entitled Comparison of the five figures, proved that the same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere; whether this Aristaeus is the same as the Aristaeus of the Solid Loci, the elder (Aristaeus the Elder) contemporary of Euclid, we do not know."
Hypsicles letter
Hypsicles letter was a preface of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements, featuring a treatise.
Notes
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