jc-search.com/includes/2019-07-31/xyhe-dealscom-e-commerce-studie.php This can again be understood against the assumption that there are strong continuities between past and present.
If the mathematical enterprise is fundamentally the same across the centuries, we do not need to be overly concerned with the circumstances in which Euclid put together the Elements , or why. It should be almost self-explanatory, or so similar to what we do today, that we should be able to understand it on the basis of our values, criteria for rationality, and common sense. Given all this, it is perhaps surprising that Heath makes space for mathematicians who were competent, but not the absolute peak of mathematical genius.
Possibly because he was a mathematician by training, but not someone who spent his life discovering theorems, Heath is not judgemental of greater or lesser mathematical achievement. I certainly could find no trace in History of his contemporary G. The field is very much in flux. On the whole, because more and more historians of mathematics today have a background not in mathematics, but in history, we no longer feel the need to apologize for our interest in figures about whom Heath had little to say.
In other words, many historians today albeit by no means all think that the past is a different country, and to a large extent, that is the very point of studying it. If mathematicians were ultimately engaged in the same enterprise, the universe they were referring to is the same and unalterable, therefore perfect translation is achievable.
Moreover, Heath says in the preface that he was keen to reproduce at least some of the procedures I, viii. Modern translations, in being shorter and snappier, make that an easier task.
Occasionally, he expands on terminological differences between past and present II, Something is always lost in translation, especially from a dead language into a live one. Was it metaphorical or concrete, and how can we tell? And is it feasible for a translator to engage in controversies about the philosophy of language, mathematics and history, while trying to produce something readable by as wide an audience as possible? We lose the fact that Greek mathematics was significantly less abstract, for instance, or that nouns referring to geometrical objects could often be elided and referred to only by the letters of the diagram accompanying a proposition.
On the other hand, a literal translation will still not be ancient Greek, and the sense of alienation generated by having something vaguely familiar the volume of a sphere, say expressed in completely different language may obfuscate, without producing any dividends. Let us take the case of Apollonius. The Conics is particularly under-studied. I cannot help thinking that this must have to do with the fact that it contains incredibly long and convoluted propositions.
Frankly, without the help of modern notation, Apollonius becomes such hard work that it is off-putting see II, And yet, one has to ask: how on earth did anyone in antiquity read Apollonius? He has several addressees; he mentions more than one edition; his manuscript has after all survived. The fact that Eutocius wrote commentaries on him is testament not simply to the difficulty of the Conics , but also to their reputation.
A History of Greek Mathematics, Volume I and millions of other books are available for Amazon Kindle. A History of Greek Mathematics, Vol. 1: From Thales to Euclid Paperback – May 1, A History of Greek Mathematics, Volume II: From Aristarchus to. of the history of Greek mathematics in about pages of vol. i. While no one would wish to disparage so great a monument of indefatigable research, it was.
A relatively significant number of people must have read Apollonius. However did they do that?
To me, then, the problem becomes that translating Apollonius into modern notation leaves completely unsolved the mystery of how ancient readers made it through his books. That may be seen as a purely historical problem. Sometimes, however, modern notation costs us some interesting mathematics. The practice of using a moving ruler to find a neusis a line of given length, inserted between given lines and verging towards a given point was a procedure peculiar to Greek mathematics. By writing that the solution of a particular neusis problem is equivalent to the solution of a cubic equation I, ; he only mentions the sliding ruler at II, 66 , and then turning it entirely into algebra, Heath is in effect producing homogeneity out of a difference that the readers may have found stimulating or intriguing, had they been allowed to see it.
Connected to this is the much-disputed issue of geometric algebra.
Hence, geometric algebra: the idea is that the Greeks expressed in geometric language the same things that we express in algebraic terms. Given his assumptions of continuity, it is not surprising that Heath uses the term unproblematically and, one might say, innocently e. I, , , , — he only manifests a speck of doubt at II, You may send this item to up to five recipients. The name field is required.
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Be the first. In the case of the central conics, the base of the rectangle is 'the transverse side of the figure' or the transverse diameter the diameter of reference , and the rectangle is equal to the square on the diameter conjugate to the diameter of reference. Again, if we take up a textbook of geometry written in accordance with the most modern Education Board circular or University syllabus, we shall find that the phraseology used except where made more colloquial and less scientific is almost all pure Greek.
The Greek tongue was extraordinarily well adapted as a vehicle of scientific thought.