Hypsicles

Hypsicles (Template:Lang-grc-gre; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and the Book XIV of Euclid's Elements.

Life and work

Although little is known about the life of Hypsicles, it is believed that he authored the astronomical work On Ascensions (Ἀναφορικός and sometimes translated On Rising Times). In this work, 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.^[1] It is thought that this is the work from which the division of the circle into 360 parts may have been adopted^[2] since it divides the day into 360 parts, a division possibly suggested by Babylonian astronomy.,^[3] although this is a mere speculation and no actual evidence is found to support this.

Hypsicles is more famously known for possibly writing the apocryphal 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 volumes, the ratio being ${\sqrt {\tfrac {10}{3(5-{\sqrt {5}})}}}$ .^[2]

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.^[4]

"Basilides of Tyre, O Protarchus, when he came to Alexandria and met my father, spent the greater part of his sojourn with him on account of the bond between them due to their common interest in mathematics. And on one occasion, when looking into the tract written by Apollonius (Apollonius of Perga) about the comparison of the dodecahedron and icosahedron inscribed in one and the same sphere, that is to say, on the question what ratio they bear to one another, they came to the conclusion that Apollonius' treatment of it in this book was not correct; accordingly, as I understood from my father, they proceeded to amend and rewrite it. But I myself afterwards came across another book published by Apollonius, containing a demonstration of the matter in question, and I was greatly attracted by his investigation of the problem. Now the book published by Apollonius is accessible to all; for it has a large circulation in a form which seems to have been the result of later careful elaboration." "For my part, I determined to dedicate to you what I deem to be necessary by way of commentary, partly because you will be able, by reason of your proficiency in all mathematics and particularly in geometry, to pass an expert judgment upon what I am about to write, and partly because, on account of your intimacy with my father and your friendly feeling towards myself, you will lend a kindly ear to my disquisition. But it is time to have done with the preamble and to begin my treatise itself."

Notes

^ Evans, J., (1998), The History and Practice of Ancient Astronomy, page 90. Oxford University Press.
^ ^a ^b Boyer (1991). "Euclid of Alexandria". A History of Mathematics. pp. 130–131. 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 (1991). "Greek Trigonometry and Mensuration". A History of Mathematics. 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
^ Thomas Little Heath (1908). "The thirteen books of Euclid's Elements".

References

Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7.
Heath, Thomas Little (1981). A History of Greek Mathematics, Volume I. Dover publications. ISBN 0-486-24073-8.

External links

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

[Boyer_Apocrypha-2] Boyer (1991). "Euclid of Alexandria". A History of Mathematics. pp. 130–131. 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 (1991). "Greek Trigonometry and Mensuration". A History of Mathematics. 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

[4] Thomas Little Heath (1908). "The thirteen books of Euclid's Elements".

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v t e Ancient Greek astronomy
Astronomers	Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis
Works	Almagest (Ptolemy) Catasterismi (Eratosthenes) On Sizes and Distances (Hipparchus) On the Sizes and Distances (Aristarchus) On the Heavens (Aristotle)
Instruments	Antikythera mechanism Armillary sphere Astrolabe Dioptra Equatorial ring Gnomon Mural instrument Triquetrum
Concepts	Callippic cycle Celestial spheres Circle of latitude Counter-Earth Deferent and epicycle Equant Geocentrism Heliocentrism Hipparchic cycle Inferior and superior planets Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac
Influences	Babylonian astronomy Egyptian astronomy
Influenced	Medieval European science Indian astronomy Medieval Islamic astronomy

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National	Germany United States France BnF data Italy Czech Republic Portugal Netherlands Norway Greece Sweden Poland Vatican Israel Belgium
Academics	zbMATH
People	Trove Deutsche Biographie DDB
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Life and work

Hypsicles letter

See also

Notes

References

External links