**Geminus** was a Stoic philosopher who wrote a number of astronomy texts including the influential *Isagoge* or *Introduction to Astronomy*. He attempted to prove Euclid's parallel postulate from the other axioms.

- Geminus, however, in spite of his name, was thoroughly Greek.
- Geminus is believed by many historians to have worked in Rhodes.
- For example, Geminus refers to Mt Atabyrius (today called Mt Attaviros) without giving any indication of where it is but when he refers to Mt Cyllene he is careful to indicate that it is the Peloponnesus.
- However, since Rhodes was at this time the centre for astronomical research, and was taken as the reference point for latitude in astronomical observations, it is quite possible that Geminus would assume his reader were familiar with the reference points of Rhodes such as Mt Atabyrius without further comment.
- Geminus was a Stoic philosopher and either a pupil, or perhaps a later follower, of Posidonius.
- Simplicius talks of a work by Geminus in which he merely reproduces the views of Posidonius but this is unfair on Geminus who, although holding similar views, shows his own independent point of view in many respects.
- Not all historians of science agree on the dates of Geminus that we have given.
- Several Isis festivals took place in Egypt and to date Geminus correctly by this argument the proper festival must be selected.
- it is clear that Geminus had in mind the Isis festivals which were celebrated in the Egyptian month Khoiak.
- Of course a date of 50 AD for the Isagoge Ⓣ(Introduction) means that Geminus could not have been a pupil of Posidonius who died in 50 BC as their lives would not have overlapped.
- In contrast the Isagoge itself contains not a single reference to this philosopher nor does the frequent mention of Rhodes (or its latitude) imply that Geminus was a pupil of Posidonius.
- Geminus wrote a number of astronomy texts, including the elementary text Isagoge or Introduction to Astronomy based on the work of Hipparchus which we referred to above.
- Geminus gave an historical account of earlier astronomical theories including those of Callippus and the Chaldeans.
- Geminus represents observational data for the motion of the moon in longitude by means of an arithmetical function.
- Geminus's mathematics text Theory of Mathematics is now lost but information about it is available from a number of sources.
- Proclus relies very heavily on the work of Geminus when he writes his own history of mathematics and it is fair to say that Geminus's books are the most valuable sources available to him.
- Geminus considers the concepts of 'hypothesis', 'theorem', 'postulate', 'axiom', 'line', 'surface', 'figure', 'angle' etc.
- Geminus is critical of Euclid's axioms in this work and he offers a 'proof' of the fifth postulate.
- The 'proof' which Geminus then gave of the parallel postulate is ingenious but it is false.
- It is interesting, however, that Geminus attempts to prove the parallel postulate and, although it is unlikely to be the first such attempt, at least it is the earliest one for which details have survived.
- The helix, namely the curve cutting the generators of a right circular cylinder at a constant angle, appears in this work by Geminus.
- Proclus suggests, however, that the curve goes back to Apollonius 150 years before Geminus.
- But Geminus proves an interesting classification theorem, namely that the helix, the circle and the straight line are the only curves with the property that any part of the curve will coincide with any other part of the same length.

Born about 10 BC, (possibly) Rhodes, Greece. Died about AD 60.

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Ancient Greek, Astronomy, Origin Greece, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive