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A vignette: the scienti c name use none none maker torender none for nonebarcode generate c#.net two mean proportionals none none , e.g. for the measurement of byre, or corn-pit, or the space of a deep, / hollow well.

This occurs in the course of Eratosthenes epigram on his method (Powell Coll. Alex. ), preserved inside Eutocius catalogue of solutions to the problem of nding two mean proportionals.

This method is useful for three-dimensional measurements. The prose text refers, soberly, to the use of the solution in constructing war-machines or, in general, liquid and dry measures. One cannot however simply talk about liquid and dry measures in a poem: this would be, so to speak, too dry.

Eratosthenes therefore reaches for a poetic genre available to him, that of the bucolic. We do not have the original context of Eratosthenes Sieve method was it perhaps in poem form as well but the sensibility seems to be similar. Into the dry arithmetical discourse is woven a metaphor suggestive not only of the concrete world but also of its literary representations.

Such scienti c names as the sieve achieve, simultaneously, several striking juxtapositions: the impersonal and the authorial; the abstract and the concrete; the literal and the metaphorical; the elevated and the humble; the scienti c and the literary. The sieve is perhaps suggestive of the bucolic. The Lock would be suggestive of erotic poetry and indeed had much of its life inside poetry with the mock-erotic elevated to the level of panegyric or, perhaps, mockpanegyric.

Appropriately, we also make a transition from arithmetic and calculation to the more elevated eld of astronomy. And so, the most celebrated scienti c name of the Hellenistic era was the Lock of Berenice. Our information derives from Callimachus Aitia (fr.

), and was further elaborated by Catullus, poem . It does derive, though, from the mathematical context we have followed so far in this book: it refers back to the work of the astronomer Conon, i.e.

Archimedes closest associate. The outlines of the story are familiar: Queen Berenice had vowed to dedicate a lock to the temple of Arsinoe, should her husband (and the dedicatee of Eratosthenes poem), King Ptolemy III, return unharmed from his Syrian campaign. Shortly after he did in , the dedicated lock disappeared from the temple.

Conon s brilliant contrivance had it that a loosely de ned stellar constellation between the Lion and the Virgin was an apotheosis of the lock. We are fortunate to have (some of ) Callimachus as well as Catullus poetic treatment, but one would very much wish to see the original text was it prose by Conon. Clearly the dedication must have been shot through with irony, as after all the sobriety of descriptive astronomy is predicated upon the immutability of the xed stars.

To the striking. .NET Framework 2.0 Eutocius . . Eutocius . . Hybrids and mosaics juxtapositions of Erat none none osthenes Sieve one should add here the striking juxtaposition of the xed and the changeable. As it were: compensating for the sacrilege of removing a dedication from the temple by the sacrilege of disturbing the xity of the heavens. Callimachus treatment would take this a step further, the story now told by the now-astral lock, mourning its removal from its beloved Berenice! One does indeed note the theme of disjointedness we have seen already: the lock has been twice removed from Berenice s head, which I dare compare to the disjointedness of Apollonius opposite sections or Nicomedes center and radius in the conchoid .

. . Yet there was some astronomical sense to the identi cation: somewhat hazy with what we now describe as the brightness of a star cluster, the area of the sky identi ed by Conon does present something of the glittering surface of a lock, and describing such a stellar phenomenon could be couched, among other things, as science.

Once again: it is of course part of natural Greek language (as of many other languages) to name parts of the sky after mythical, often animate objects (more of this below, as we come to discuss Aratus). To have this natural language process extended into deliberate scienti c coinage is however quite a different matter, and we see here a very self-conscious use of scienti c naming, this time clearly as part of a courtly joke. The joke, incidentally, stuck: Ptolemy has the group as the Lock and Tycho has made it into a constellation, returning to mention Berenice herself as well.

Hellenistic metaphor thus became part of our sky. I have just mentioned Nicomedes conchoid: much less famous, here is yet another example of Hellenistic mathematical metaphor, or perhaps simile (literally, the conchoid means shell-like ). Clearly the intended simile is visual the curve is meant to look like a shell and one is reminded of Archimedes conoid for a solid of revolution produced by parabola or hyperbola, indeed highly reminiscent of a cone, and spheroid for a solid of revolution produced by ellipse, where the similarity is even more obvious.

But the simile of the shell is much more striking, in that it brings together the world of mathematics and that of nature indeed, it brings together art and nature, since Nicomedes curve is explicitly produced by a mechanical instrument. But what is so shell-like about the gure Knorr has looked closely at this problem, his main motivation being a related problem of Greek mathematical nomenclature. Proclus tells us of the existence of another ancient curve, the cissoid, i.

e. the ivy-like. What were the mathematical properties of this curve Knorr, trying to nd an answer to this question, ends up suggesting that the cissoid could have.

Proclus, Commentary to Euclid , , ..
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