Greek angles from Babylonian numbers

Models of planetary motion as observed from Earth must account for two principal anomalies: the nonuniform speed of the planet as it circles the zodiac, and the correlation of the planet’s position with the position of the Sun. In the context of the geometrical models used by the Greeks, the practical difficulty is to somehow isolate the motion of the epicycle center on the deferent from the motion of the planet on its epicycle. One way to isolate the motion of the epicycle center is to determine the longitude and time of oppositions of the planet with the mean Sun. A Greek astronomer might have realized that the predictions of mean oppositions by Babylonian models could serve as useful proxies for real empirical observations. It is shown that a Greek astronomer with a reasonable understanding of Babylonian System A models for the outer planets and the Sun–Moon could have used those models to estimate approximate values for the eccentricity e and longitude of apogee A required for geometrical models. The same method would work for the inner planets if conjunctions were observable, but they are not, and the variation of the observable synodic events—first and last morning and evening visibilities—is dominated more by the motion of the planet in latitude than the nonuniform motion of the epicycle center.     

Length of the year in pre-epicyclic planetary theory

An estimate is made of the length of the year implied in the pre-epicyclic planetary theory of the Pañcasiddhntik. It is shown that this could be the same as the year-length of the corresponding Babylonian theory.     

The motion of Mars in Egyptian planetary tables

B. L. van der Waerden's thesis, that the motion of Mars in the Stobart Tables has been computed by linear methods based on the assumption of a piece-wise constant velocity, is discussed in this paper, and some further evidence presented.     

Reconstruction of a Greek table of chords

Summary R. R. Newton has shown that Ptolemy's table of solar declinations (Almagest I, 15) was not computed from Ptolemy's own table of chords. Newton explains this by assuming that Ptolemy copied his table of declinations from an earlier source, and that originally the table has been computed by means of a less accurate table of chords.In the present paper I shall venture a tentative reconstruction of the method of computation of this ancient table of chords. The clue to this reconstruction is a recursion formula which allows a rapid calculation of the chords belonging to arcs of 1°, 2°, ... in a circle. This recursion formula, which was suggested to me by a verse in the ryabhtya of ryabhata, can be deduced from a theorem of Archimedes concerning a certain sum of chords in a circle. I suppose that this recursion formula was used by Apollonius of Perga in order to obtain a table of chords, and that this table of chords was used by a Greek author (possibly Apollonios himself or Hipparchos) to calculate the table of solar declinations used by Ptolemy. If this hypothesis is adopted, the errors in Ptolemy's table can be explained.     

Structures and strategies in ancient Greek and Roman technical writing: An Introduction

Most of our knowledge of Greek and Roman scientific practice and its place in ancient culture is derived from our study of ancient texts. In the last few decades, this written evidence—ancient technical or specialist literature—has begun to be studied using tools of literary analysis to help answer questions about, for instance, how these works were composed, their authors’ intentions and the expectations of their readers.This introduction to Structures and strategies in ancient Greek and Roman technical writing provides an overview of recent scholarship in the area, and the difficulty in pinning down what ‘technical/specialist literature’ might mean in an ancient context, since Greek and Roman authors communicated scientific knowledge using a wide variety of styles and forms of text (e.g. poetry, dialogues, letters).An outline of the three sections is provided: Form as a mirror of method, in which Sabine Föllinger and Alexander Mueller explore ways in which the structures of texts by Aristotle and Plutarch may reflect methodological concerns; Authors and their implied readers, with contributions by Oliver Stoll, David Creese, Boris Dunsch and Paula Olmos, which examines what ancient texts can tell us about the place of technical knowledge in antiquity; Science and the uses of poetry, with articles by Jochen Althoff, Michael Coxhead and Laurence Totelin, and a new English translation of the Aetna poem by Harry Hine, which explores the (to us) unexpected roles of poetry in ancient scientific culture.     

Greek astronomical calendars I. The parapegma of Euctemon

Summary In view of the striking similarities noted in the subsection A, B, C we are bound to conclude that Euctemon was influenced by Babylonian astronomy. However, his parapegma was not just a translation of a Babylonian text: it was an improvement in many respects. His dates of annual risings and settings were more accurate than the Babylonian dates. In most cases he recorded true risings, or he recorded both the true and the visible phaenomena. This distinction is not made in the text MUL APIN.