Download PDF by Olaf Pedersen: A Survey of the Almagest: With Annotation and New Commentary

By Olaf Pedersen

ISBN-10: 0387848258

ISBN-13: 9780387848259

The Almagest, by way of the Greek astronomer and mathematician Ptolemy, is crucial surviving treatise on early mathematical astronomy, providing historians necessary perception into the astronomy and arithmetic of the traditional world.

Pedersen's 1974 book, A Survey of the Almagest, is the newest in an extended culture of partners to the Almagest. half paraphrase and half statement, Pedersen's paintings has earned the common compliment of historians and serves because the definitive introductory textual content for college students drawn to learning the Almagest.

during this revised variation, Alexander Jones, a distinctive authority at the background of early astronomy, presents supplementary info and observation to the unique textual content to account for scholarship that has seemed due to the fact 1974. This revision additionally comprises a number of corrections to Pedersen's unique textual content which have been pointed out for the reason that its publication.

This quantity is meant to supply scholars of the background of astronomy with a self-contained creation to the Almagest, assisting them to appreciate and enjoy Ptolemy's nice and classical paintings.

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Additional info for A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones (Sources and Studies in the History of Mathematics and Physical Sciences)

Sample text

Experience ; for instance, that clouds would be overtaken by the Earth and that we should always have a strong wind towards the East. Ptolemy is aware that the supporters of the hypothesis tried to avoid this difficulty by the assumption that the atmosphere takes part in the rotation with the same velocity; but that is refuted for reasons taken from the doctrine of the free fall of bodies. If a heavy body is thrown upwards along the vertical it is supposed to return to the Earth along the same geometrical line, thus striking the surface at a point different from that from which it started.

57 note 5). Compared with the additive Greek system the Babylonian positional system has two obvious advantages: first, the number of necessary symbols is reduced to no more than 2, regardless of how large numbers we want to write, and second, there are no particular problems connected with the notation of fractions. On the other hand the system has the disadvantage that not all fractions could be finite sexagesimal expressions. In fact, this was possible only in 'regular' fractions whose denominators could be written as 2 m • 3 m • 5P where m, n, and p are integers, whereas a simple fraction like 1/7 or 1/11 would lead to an infinite sexagesimal expansion, which had to be broken off somewhere.

In fact, we have 25;12, 10 - 60° = 1512°;10 25;12, 10 · 61 ° = 1537°;22,10 which is found by direct computation, perhaps aided by a multiplication table. Putting x = 60° in equation (A) we get 1515°;20,15 = 1512°;10 + 25;12,10{~ + ~} 2 60 60 or 3°;10,15 = 25;12,10{:0 + 6~2} Multiplication by 60 gives 190';15 = 25;12,1O{Y + 6~} (B) Now the process is repeated: we perform the second division and find y = 7' as the second quotient. Equation (B) is thereby reduced to z 13'-49 50 = 25-12 10 · "60 " Multiplying once more by 60 we get 829";50 = 25;12,10 · z (C) This gives the third quotient z = 33" and the complete solution is, to two sexagesimal places, 60°;7,33.

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A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones (Sources and Studies in the History of Mathematics and Physical Sciences) by Olaf Pedersen


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