Hermotimus of Colophon

Hermotimus of Colophon
Hermotimus of Colophon
Ερμότιμος
Occupation	mathematician

Hermotimus of Colophon^[a] (4th century BC) was an Ancient Greek mathematician who lived and worked in Colophon. He is known only from a single sentence by Proclus,^[1] probably summarizing a lost work of Eudemus of Rhodes. This sentence states that Hermotimus continued the research of Eudoxus and Theaetetus, discovered many of the propositions in Euclid's Elements, and wrote about theorems on loci.^[2]

Notes

^ Ancient Greek: Ερμότιμος, romanized: Hermotimus.

References

^ Asper, Markus (May 2019). "Personae at play. 'Men of Mathematics' in commentary". Historia Mathematica. 47: 4–15. doi:10.1016/j.hm.2019.02.003.
An English translation can be found in Heath, Thomas (1921). A History of Greek Mathematics. Vol. I, From Thales to Euclid. Oxford: Clarendon Press. pp. 320, 354.
"Eudoxus of Cnidos, a little younger than Leon, who had been associated with the school of Plato, was the first to increase the number of the so-called general theorems; he also added three other proportions to the three already known, and multiplied the theorems which originated with Plato about the section, applying to them the method of analysis. Amyclas [more correctly Amyntas] of Heraclea, one of the friends of Plato, Menaechmus, a pupil of Eudoxus who had also studied with Plato, and Dinostratus, his brother, made the whole of geometry still more perfect. Theudius of Magnesia had the reputation of excelling in mathematics as well as in the other branches of philosophy; for he put together the elements admirably and made many partial (or limited) theorems more general. Again, Athenaeus of Cyzicus, who lived about the same time, became famous in other branches of mathematics and most of all in geometry. These men consorted together in the Academy and conducted their investigations in common. Hermotimus of Colophon carried further the investigations already opened up by Eudoxus and Theaetetus, discovered many propositions of the Elements and compiled some portion of the theory of Loci. Philippus of Medma, who was a pupil of Plato and took up mathematics at his instance, not only carried out his investigations in accordance with Plato's instructions but also set himself to do whatever in his view contributed to the philosophy of Plato.

"Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende or Medma) is Euclid, who put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid; and further they say that Ptolemy once asked him if there was in geometry any shorter way than that of the Elements, and he replied that there was no royal road to geometry. He is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, the latter having been contemporaries, as Eratosthenes somewhere says."
^ Artmann, Benno (1999). "The Origin of Mathematics 1: The Testimony of Eudemus". Euclid—The Creation of Mathematics. Springer. pp. 11–16. doi:10.1007/978-1-4612-1412-0_3. ISBN 978-1-4612-1412-0.

External links

[1] Ancient Greek: Ερμότιμος, romanized: Hermotimus.

[2] Asper, Markus (May 2019). "Personae at play. 'Men of Mathematics' in commentary". Historia Mathematica. 47: 4–15. doi:10.1016/j.hm.2019.02.003.
An English translation can be found in Heath, Thomas (1921). A History of Greek Mathematics. Vol. I, From Thales to Euclid. Oxford: Clarendon Press. pp. 320, 354.
"Eudoxus of Cnidos, a little younger than Leon, who had been associated with the school of Plato, was the first to increase the number of the so-called general theorems; he also added three other proportions to the three already known, and multiplied the theorems which originated with Plato about the section, applying to them the method of analysis. Amyclas [more correctly Amyntas] of Heraclea, one of the friends of Plato, Menaechmus, a pupil of Eudoxus who had also studied with Plato, and Dinostratus, his brother, made the whole of geometry still more perfect. Theudius of Magnesia had the reputation of excelling in mathematics as well as in the other branches of philosophy; for he put together the elements admirably and made many partial (or limited) theorems more general. Again, Athenaeus of Cyzicus, who lived about the same time, became famous in other branches of mathematics and most of all in geometry. These men consorted together in the Academy and conducted their investigations in common. Hermotimus of Colophon carried further the investigations already opened up by Eudoxus and Theaetetus, discovered many propositions of the Elements and compiled some portion of the theory of Loci. Philippus of Medma, who was a pupil of Plato and took up mathematics at his instance, not only carried out his investigations in accordance with Plato's instructions but also set himself to do whatever in his view contributed to the philosophy of Plato.

"Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende or Medma) is Euclid, who put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid; and further they say that Ptolemy once asked him if there was in geometry any shorter way than that of the Elements, and he replied that there was no royal road to geometry. He is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, the latter having been contemporaries, as Eratosthenes somewhere says."

[3] Artmann, Benno (1999). "The Origin of Mathematics 1: The Testimony of Eudemus". Euclid—The Creation of Mathematics. Springer. pp. 11–16. doi:10.1007/978-1-4612-1412-0_3. ISBN 978-1-4612-1412-0.

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