The carnival of calculation in .NET Deploy Code39 in .NET The carnival of calculation

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The carnival of calculation using visual .net toaccess barcode 3/9 with web,windows application Microsoft Official Website Posidonius, the .net vs 2010 3 of 9 philosopher active at Rhodes, chooses a calculation that juxtaposes Rhodes with the great center of Mediterranean life to which Rhodes still referred, even as late as the rst century that of Alexandria. With both, the limits of one s political horizon could be used by reference to the stars as a launching pad for a daring ight of imagination, right around the globe.

Going beyond the Alexandrian world, one could say something about the earth as a whole. Of course this is not an isolated moment in Hellenistic cultural life. This is a civilization of expansion, whose very moment of inception is marked by an urge to reach out for the totality of the earth.

Even prior to Eratosthenes or Posidonius trying to measure the earth based on the observations at Alexandria, one had to set up Alexandrias across the known world and to build power that reached as far as such exotic places as Syene. This moment of Alexandrian conquest also coincided, as is well known, with Pytheas travels into the Atlantic, reaching into a northern extreme untouched by Alexander himself. Alexander and Pytheas, as well as Eratosthenes and Posidonius, all tried to capture the earth.

We have considered already the meaning of this effort as an attempt to capture the unbounded. Here I want to emphasize the gigantic aspect of this effort. This at least is surely clear: Eratosthenes and Posidonius cared about size.

Size is an appropriate theme with which to sum up the evidence considered in this chapter. It is evident in a series of cosmic measurements not only those of the earth just seen here, but also those of the cosmos offered by Aristarchus at least once, in the Sizes and Distances of the Sun and the Moon (and perhaps once again in the treatise where the Heliocentric thesis was put forth), as well as by Archimedes in the Sand-Reckoner. And beyond the cosmic lies the divine and the mythical: the fantastically huge number representing the fancifully described cattle of Helios (in Archimedes Cattle Problem), the extraordinarily large number arising from trying to mathematize the excellent power of Artemis.

One is tempted to bring into this context the problem of nding two mean proportionals between two given. On Pytheas see, e.g. critically Strabo ii.

. . Little is known of substance of Pytheas travels, except that they de nitely took him into the Northern Atlantic.

For a recent survey of the evidence, see Magnani . The reception of Pytheas from antiquity down to the present day is fascinated with the problems of authenticity: what did Pytheas actually do More relevant to us is what cultural role he was trying to assume. Magnani s speculative summary ends up with the image of Pytheas (pp.

) as engaged primarily in the autoptic con rmation of Eudoxean mathematical geography. In other words, what Pytheas represents is the desire to make the theoretical, universal reach of mathematics concrete. See more on mostly the later, Renaissance history of such cosmic measurements in Henderson .

Likely, Hipparchus himself was once again a key contributor to this domain, though in this case as in so many others his achievement is only indirectly reported (Swerdlow ).. A fascination with size lines that is be ing reinterpreted by Eratosthenes, in a fragment preserved by Eutocius (as well as in his Platonicus) as a problem of doubling the cube the form in which it is still familiar to us today. Let us quote Eratosthenes, then, addressing the king:. Eratosthenes to barcode code39 for .NET king Ptolemy, greetings. They say that one of the old tragic authors introduced Minos, building a tomb to Glaucos, and, hearing that it ought to be a hundred cubits long in each direction, saying: You have mentioned a small precinct of the tomb royal; Let it be double, and, not losing this beauty, Quickly double each side of the tomb.

This seems to have been mistaken; for, the sides doubled, the plane becomes four times, while the solid becomes eight times. And this was investigated by the geometers, too: in which way one could double the given solid, the solid keeping the same shape; and they called this problem duplication of a cube : for, assuming a cube, they investigated how to double it..

One notices not only the mythical dimensions inserted by Eratosthenes, but a more basic point still: a sober geometrical exercise in nding proportional lines is presented, by Eratosthenes, as a problem of making something bigger indeed making something bigger precisely in the context, well understood by a Ptolemaic audience, of royal architectural grandeur. This reinterpretation of the problem of two mean proportionals as one of doubling the cube has become so successful that we have now come to think of it as the natural mathematical representation but we must be aware of its speci c Alexandrian origins. The Sand-Reckoner with its measuring out of the universe by grains of sand reminds us that these two are interconnected: the fantastically big and the fantastically small.

In a precise way, it is their combination that creates the sense of size. Measured in earth circumferences, for instance, the earth comes out as having the size of , not at all a remarkable result . .

. For us to be impressed by Eratosthenes and Posidonius numbers, measure has to be provided in stades. And so we should also follow the measurements of the fantastically small as an exercise in fantastically big numbers.

The obvious example is in the attempt to provide a precise calculation of the ratio of the circumference of the circle to its diameter, in Archimedes Measurement of Circle. But is the focus on the extremely small not at the very heart of Hellenistic mathematics For even at its most sober, geometrical moments, its achievements are those of precise curvilinear measurements based on the method of exhaustion, whose essence is the.
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