Hipsikle

Hipsikle (grčki: Υψικλής odn. Υψικλής ο Αλεξανδρεύς, latinski: Hypsicles; rođen oko 190. pne., umro oko 120. pne.). Starogrčki matematičar i astronom, poznat po delu čiji latinski naziv glasi De ascensionibus i po sumnjivoj Knjizi XIV Euklidovih Elemenata.

Život i delo uredi

O Hipsiklovom životu se malo zna, ali veruje se da je on napisao astronomsko delo De ascensionibus. On u ovom delu dokazuje više stavova o aritmetičkoj progresiji i koristi dobijene rezultate da izračuna približne vrednosti potrebnih vremena da se znakovi zodijaka uzdignu iznad horizonta^[1]. Misli se da je baš iz ovog dela prihvaćena podela kruga na 360 stepeni, a što je moguće da potiče iz vavilonske astronomije^[2]

Hipsikle je poznatiji kao mogući pisac apokrifne Knjige XIV Euklidovih "Elemenata". Ova knjiga sumnjivog autorstva je mogla biti sastavljena na osnovu traktata Apolonija iz Perge. Ona nastavlja Euklidovo poređenje pravilnih tela upisanih u sferu, s glavnim rezultatom da je odnos površina dodekaedra i ikosaedra upisanih u istu sferu isti kao odnos njihovih površina, pri čemu taj odnos iznosi: ${\sqrt {\tfrac {10}{3(5-{\sqrt {5}})}}}$ .^[3]

Izvori uredi

(na engleskom:)

Boyer, Carl B. (1991). A History of Mathematics (Second Edition izd.). John Wiley & Sons, Inc.. ISBN 0471543977.
Heath, Thomas Little (1981). A History of Greek Mathematics, Volume I. Dover publications. ISBN 0486240738.

Citati i fusnote (na engleskom) uredi

↑ Evans, J., (1998), The History and Practice of Ancient Astronomy, page 90. Oxford University Press.
↑ Boyer (1991). „Greek Trigonometry and Mensuration”. str. 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.)«
↑ Boyer (1991). „Euclid of Alexandria”. str. 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.)«

Eksterni linkovi uredi

(na engleskom:)

The mac-tutor biography of Hypsicles

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

[2] Boyer (1991). „Greek Trigonometry and Mensuration”. str. 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.)«

[Boyer_Apocrypha-3] Boyer (1991). „Euclid of Alexandria”. str. 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.)«

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