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Ipsicle (Ὑψικλῆς; 190 a.C. – 120 a.C.) è stato un matematico e astronomo greco antico noto per le sue Ascensioni (Ἀναφορικός) e per il libro XIV degli Elementi di Euclide..

Sebbene si sappia poco sulla sua vita si ritiene che sia l'autore delle Ascensioni, in cui Ipsicle dimostra alcune proposizioni riguardo le progressioni aritmetiche ed utilizza i risultati per calcolare valori approssimati per il tempo necessario ai segni zodiacali per elevarsi sopra l'orizzonte.^[1] Si pensa che sia in quest'opera che è stata adottata la divisione del cerchio in 360 gradi^[2] poiché divide il giorno in 360 parti, soluzione forse suggerita dall'astronomia babilonese.^[3]

Ipsicle è noto per lo più per essere il possibile autore dell'apocrifo Libro XIV degli 'Elementi' di Euclide, che potrebbe essere stato scritto sulla base di un trattato di Apollonio di Perga. 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 volumes, the ratio being ${\sqrt {\tfrac {10}{3(5-{\sqrt {5}})}}}$ .^[2]

Note

^ Evans, J., (1998), The History and Practice of Ancient Astronomy, pagina 90. Oxford University Press.
^ ^a ^b Boyer, Euclid of Alexandria, in 1991, pp. 118–119.
«In ancient times it was not uncommon to attribute to a celebrated author works that were not by him; thus, some versions of Euclid's Elements include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal. The so-called Book XIV continues Euclid's comparison of the regular solids inscribed in a sphere, the chief results 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 volumes, the ratio being that of the edge of the cube to the edge of the icosahedron, that is, ${\scriptstyle {\sqrt {\frac {10}{3(5-{\sqrt {5}})}}}}.$ 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.)»
^ Boyer, Greek Trigonometry and Mensuration, in 1991, p. 162.
«It is possible that he took over from Hypsicles, who earlier had divided the day into 360 parts, a subdivision that may have been suggested by Babylonian astronomy.)»

[1] Evans, J., (1998), The History and Practice of Ancient Astronomy, pagina 90. Oxford University Press.

[Boyer_Apocrypha-2] Boyer, Euclid of Alexandria, in 1991, pp. 118–119.
«In ancient times it was not uncommon to attribute to a celebrated author works that were not by him; thus, some versions of Euclid's Elements include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal. The so-called Book XIV continues Euclid's comparison of the regular solids inscribed in a sphere, the chief results 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 volumes, the ratio being that of the edge of the cube to the edge of the icosahedron, that is, ${\scriptstyle {\sqrt {\frac {10}{3(5-{\sqrt {5}})}}}}.$ 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.)»

[3] Boyer, Greek Trigonometry and Mensuration, in 1991, p. 162.
«It is possible that he took over from Hypsicles, who earlier had divided the day into 360 parts, a subdivision that may have been suggested by Babylonian astronomy.)»

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