Hypsicles

Hypsicles (Greek: Ὑψικλῆς; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and the spurious 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 spurious Book XIV 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]

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.

Notes and references

↑ Evans, J., (1998), The History and Practice of Ancient Astronomy, page 90. Oxford University Press.
1 2 Boyer (1991). "Euclid of Alexandria". A History of Mathematics. 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 (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

External links

Ancient Greek astronomy

Astronomers	Acoreus 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) 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 Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac

Influences	Babylonian astronomy Egyptian astronomy

Influenced	Medieval European science Indian astronomy Medieval Islamic astronomy

Ancient Greek mathematics

Mathematicians	Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises	Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Elements (Euclid) On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) The Sand Reckoner

Problems	Problem of Apollonius Squaring the circle Doubling the cube Angle trisection

Centers	Cyrene Library of Alexandria Platonic Academy

Timeline of Ancient Greek mathematicians

Authority control	WorldCat Identities VIAF: 281628164 LCCN: nr96016542 ISNI: 0000 0001 0050 4784 GND: 119388006 SUDOC: 035529202 BNF: cb134836636 (data)

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