Mathematicians and their Contributions

Geminus

Geminus

about 10 BC - about 60

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.

It may be surprising that Geminus's name seems to be Latin rather than Greek but as Heath writes [3]:-

The occurrence of a Latin name in a centre of Greek culture need not surprise us, since Romans settled in such centres in large numbers during the last century BC. Geminus, however, in spite of his name, was thoroughly Greek.

Geminus is believed by many historians to have worked in Rhodes. Certainly his astronomy text uses mountains on Rhodes to make specific points but, as Dicks points out in [1], this is not proof that he worked there. 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. He wrote to defend the Stoic view of the universe, and in particular to defend mathematics from attacks which had been made on it by Sceptic philosophers and by Epicurean philosophers. 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. Some favour dates of 130 BC - 60 BC which are based largely on a calendar which appears in his Introduction to Astronomy called the Isagoge Ⓣ and seems to suggest a date of around 70 BC for the date when the text was written. Dicks in [1] seems convinced by this argument which becomes certain only if the date of the Egyptian Isis festival is known with certainty. Several Isis festivals took place in Egypt and to date Geminus correctly by this argument the proper festival must be selected. Neugebauer in [4] believes that the selection which give the date of 70 BC is incorrect and he favours a date for the Isis festival which leads to a date of 50 AD for Geminus's text:-

... it is clear that Geminus had in mind the Isis festivals which were celebrated in the Egyptian month Khoiak. This places him in the first century AD. The duration of the festival and the possible insecurity of the date of the Winter Solsticeprevent us from establishing a more accurate date, but ... the first half of the century [is] more likely that the latter part. ... we thus consider a date around 50 AD as fairly secure for the Isagoge Ⓣ ...

Of course a date of 50 AD for the Isagoge Ⓣmeans that Geminus could not have been a pupil of Posidonius who died in 50 BC as their lives would not have overlapped. Neugebauer comments in [4]:-

A much discussed question is the dependence of Geminus on the famous stoic philosopher Posidonius of Rhodes (who died around 50 BC). The assumption of such a dependence mainly rests on close parallels between passages in the Isagoge and the writings of Cleomedes who repeatedly refers to Posidonius as his source. 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.