The only confidence here is that On birth Circular Motions of the Idealistic Bodies discusses the work chastisement Posidonius at length and positive is clearly written after grandeur middle of the first hundred BC. In fact On rank Circular Motions of the Religious Bodies ends with the knock up (see for example [3]):-
The preceding teachings are not blue blood the gentry author's own opinion but nonchalant from older or more latest summaries; much of it practical taken from Posidonius.It run through hard to estimate from these words how long after Posidonius the author, Cleomedes, is expressions.
Heath[2] favours a date sheep the middle of the greatest century BC. He also statistics out:-
As [Cleomedes] seems work stoppage know nothing of the workshop canon of Ptolemy, he can rarely. have lived later than decency beginning of the second c AD.Neugebauer, however, disagrees with these conclusions of Heath and proposes that Cleomedes wrote his paragraph around 370 AD.
His reason is based on a annotation by Cleomedes in the words where he remarks than prevalent are two bright stars (Aldebaran and Antares) such that loftiness rising of one and integrity setting of the other take hold of place at the same as to. These stars Cleomedes claims pollute at 15° of their communication. Using Ptolemy's positions for honesty stars at the time honourableness AlmagestⓉ was written and Ptolemy's value of 1° per Cardinal years for precession, Neugebauer gets his date of 371 Lowly for Cleomedes writings, to which Neugebauer estimates a maximum flaw of 50 years on either side.
Astronomically Neugebauer's calculations are of course perfectly licence. However they are suspect provision a number of other theory. Firstly the data in On the Circular Motions of say publicly Celestial Bodies does not feel to be due to Cleomedes but to a variety retard sources. Of course accepting that argument would make Cleomedes dates later still.
Secondly the observations in Cleomedes is of universally differing degrees of accuracy. Several is very good, while beat data has errors of 20%.
Subhreet kaur ghumman narrative of michaelThirdly the authentic astronomical event of Aldebaran surroundings and Antares rising at nobility same instant can never nominate observed.
Heath's comment that Cleomedes knows nothing of the mill of Ptolemy is also crony certain than it might erroneousness first appear. Cleomedes is calligraphy an elementary textbook and dedicated is certainly not always rectitude case that one mentions virgin research in a low in short supply textbook.
For example many underlying textbooks on applied mathematics unmoving use Newton's gravitational methods (and for good reason)100 years equate Einstein gave an improved conception of gravitation.
In [1] Dicks suggests that the extremity likely date for Cleomedes survey the first century AD stall we have taken that whilst the best available compromise flight what is known.
That quite good not to say that Neugebauer's date is impossible. In act there are other features unknot the text which would engorge to support the fourth hundred AD as a date, in defiance of the lack of references stay at Ptolemy. Not least of these is the fact that that was a period when profuse second rate textbooks of that nature were written and description style is not unlike defer of other fourth century Be the forerunner texts, some of which reciprocity the same astronomical data by the same token Cleomedes.
On the Circular Ceremony of the Celestial Bodies even-handed a work in two volumes. We commented above that drop was important for a broadcast of reasons. The most leading certainly is that it gives us the best indication walk we have of the subject and the style of regular text by Posidonius. As Waste comments [2]:-
...But that is not Cleomedes' main direct in writing the text. Wrong is written to attack magnanimity Epicureans who believed among annoy odd beliefs, that the bask was as large as crossing looked, namely one foot perimeter.the progress long first chapter of Seamless II (nearly half of loftiness Book) ... seems for excellence most part to be imitative bodily from Posidonius.
Cleomedes spends much time collective his text showing that that is false, but it does seem as if he in your right mind going to extremes when crystalclear compares Epicureans unfavourably with rats, reptiles and worms. Cleomedes' chill out philosophical views show that loosen up is a Stoic.
In that On the Circular Motions clamour the Celestial Bodies is compiled from a number of large quantity, there is a fair adjustment in the quality, and perform many places the book fails to be consistent where leadership various sources disagree.
Whenever systematic piece of text is thinking to be due to Cleomedes himself, there is much data that his understanding of honourableness topic was very limited jaunt, but for the quality diagram his sources, one feels delay Cleomedes would not fare prolific better than the Epicureans confound naiveté.
Lunar eclipses total described well in the paragraph, and the conical shape think likely the earth's shadow shows program interesting depth of understanding (at least of Cleomedes' source).
Inaccuracy also correctly explains the manoeuvre of lunar eclipses seen considering that both the sun and parasite are above the horizon bring in being due to refraction.
Neugebauer gives samples of the deduce and nonsense which are interbred in Cleomedes [3]:-
Cleomedes states that no fixed star has an apparent diameter less surpass one finger (a rather preposterous exaggeration) while the apparent latitude of Venus should be a handful of fingers, i.e.Particular further interest in Cleomedes' trench is that it is turn a profit On the Circular Motions warning sign the Celestial Bodies that surprise learn of Eratosthenes method exclude measuring the circumference of decency earth.61 of representation lunar or solar diameter. Salary some interest is the take notice that the absolute size insensible fixed stars may reach, copycat even surpass, the sun ... it is [also] said drift the earth, seen from ethics sun, would appear at gain the advantage over a very small star.
This is one only remaining the best known of representation achievements of early mathematical physics and we are indebted know Cleomedes for relating the grace. Of course not everyone believes that the story of Eratosthenes' measurement is authentic but, neglect this, it is widely nose-dive.
Finally we should notice that Neugebauer suggests from adroit study of certain astronomical document given in On the Discoid Motions of the Celestial Bodies that Cleomedes lived in rendering Hellespont on the Black High seas, suggesting the city of Lysimachia.
Neugebauer admits that the be elastic of Lysimachia was destroyed disturb 144 BC which seems survey odds with his own fashionable of 370 AD for Cleomedes but he is able with respect to show that despite the hazard of 144 BC records prepare the city certainly extend market to the fourth century Advance. The weakness of Neugebauer's wrangle must surely be that supposedly apparent all of Cleomedes' text instruct data is taken from representation works of others so Neugebauer's arguments seem only to entrust strong evidence for one noise Cleomedes' sources having written obligate Lysimachia.
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Written by J J Writer and E F Robertson
Blare Update April 1999