Showing papers in "Archive for History of Exact Sciences in 1999"

Against Chandrasekhars Interpretation of Newtons Treatment of the Precession of the Equinoxes

Abstract: L'interpretation de l'astrophysicien S Chandrasekhar sur le traitement de la precession des equinoxes dans le livre des principes de Newton est analysee

The Making of Peacocks Treatise on Algebra: A Case of Creative Indecision

Abstract: Peacock occupe une place importante dans la litterature de l'histoire des mathematiques du XIX e siecle grâce a son traite d'algebre, premier ouvrage traitant d'algebre publie en Angleterre

Galileo and Leibniz: Different Approaches to Infinity

Abstract: L'A. discute la theorie de Galilee pour comprendre pourquoi et comment Leibniz est revenu au concept traditionnel des mathematiques pour la notion d'indivisible

The first modern definition of the sum of a divergent series: An aspect of the rise of 20th century mathematics

Abstract: A travers l'article, l'A. definit la somme des series divergentes en analysant son concept et demontre qu'il a conduit a l'emergence des mathematiques du XX e siecle

David Hilbert between Mechanical and Electromagnetic Reductionism (1910–1915)

Abstract: L'A. demontre la similarite entre l'equation de la gravitation presentee par D. Hilbert et celle presentee par Einstein, avec une possible influence de Hilbert sur Einstein et la question de la priorite de cette decouverte

Archimedes Transformed: The Case of a Result Stating a Maximum for a Cubic Equation

Abstract: L'A. demontre comment Eutocius s'eloigne des mathematiques d'Archimede en utilisant l'expression de ses theories arithmetiques et geometriques

Acronychal Risings in Babylonian Planetary Theory

Abstract: The Astronomical Diaries (ADT), and a few known collections for individual planets, contain observations of five synodic phenomena of superior planets: heliacal rising (F), first station (), acronychal rising (0), second station (^), and heliacal setting (£2). A date is given for each, in the case of F often both an observed date and a 'true' or 'ideal' date on which the rising is considered to have occurred even if it was not observed, as due to clouds, found by a measurement of the interval in degrees of time between the rising of the planet and the rising of the sun. However, location is recorded differently for each class of phenomena. Heliacal risings and settings, F and £2, are located by zodiacal sign, or by beginning or end of zodiacal sign. In some cases F contains a measured distance from a nearby 'normal' (standard) star or planet, for conjunctions of planets with stars or with each other were considered ominous. But it does not appear that measurements of distances from stars at F were used to establish location more precisely than by zodiacal sign, and distances from planets cannot be used to establish location. First and second stations, and ^, usually contain a measured distance from a normal star, presumably to determine when the planet was stationary, but sometimes only a location by zodiacal sign. Acronychal rising 0 contains no location at all. It could have been assumed that the planet was in the zodiacal sign opposite the sun, but no location for the sun is given in the Diaries. (It is curious that acronychal risings were observed at all since there are no omens associated with them. Yet an acronychal rising of Jupiter appears already in the second earliest known Diary, ADT -567, and one may wonder why.) Sometimes observations contain the remark 'not observed' (nu pap), which presumably indicates an inference of the date and location from nearby preceding or following observations. The dates and longitudes of the same phenomena reported in the Diaries are computed in the ephemerides to a degree of precision exceeding the observations in the Diaries. The ephemerides are published in ACT, and the further analysis in HAMA is essential. In a recent study of Babylonian planetary theory (Swerdlow, 1998), I set out a method by which the parameters of the ephemerides can be derived from synodic times between phenomena, recoverable from the dates in the Diaries, and locations no more precise than by zodiacal sign. The method depends upon a constant difference between synodic time and synodic arc, AT - AX = C, found in the ephemerides of all planets except Venus, which allows A X to be found from AT. With the exception of 0 and ^ of Mars, which occur in the retrograde arc, the ephemerides use the same functions for computing all phenomena of the superior planets by complete synodic arcs and synodic times even though the synodic arcs and times between consecutive heliacal risings or settings, which

Eulers “Harmony” Between the Principles of “Rest” and “Least Action”: The Conceptual Making of Analytical Mechanics

Abstract: In 1751, LEONHARD EULER established “harmony” between two principles that had been stated by PIERRE-LOUIS-MOREAU DE MAUPERTUIS a few years earlier. These principles are intended to be the foundations of Mechanics; they are the principle of rest and the principle of least action.

A Likely Source of an Observation Report in Ptolemy's Almagest

Abstract: In a recently published volume of Greek papyri from Oxyrhynchus (mod Bahnasa, Egypt) containing astronomical texts, tables, and horoscopes, I gave pride of place to a remarkable fragment of a theoretical work on planetary theory that, as I there remarked, is "nearer in genre to Ptolemy's Almagest than any hitherto known"1 The text, published under the number P Oxy LXI 4133, contains the report of an observation of Jupiter's position in AD 104/105, and refers also to another observation of Jupiter made 344 years earlier, the report of which was in the lost part of the text preceding the extant portion I gave reasons in my commentary for tentatively identifying the author of the treatise as Menelaus of Alexandria, and for identifying the earlier observer more confidently with an anonymous observer of Jupiter cited by Ptolemy in the Almagest Only more recently did I realize that a rather obvious corollary of my analysis of the papyrus is that the treatise from which it comes was very likely Ptolemy's immediate source for that Jupiter observation The planetary observations that Ptolemy utilizes fall chronologically into two widely separated groups: (a) observations from his own time (specifically AD 127-141) by himself and by someone named Theon; and (b) observations from the third century BC by Timocharis, by unnamed Hellenistic observers using a special calendar "according to Dionysius," and by anonymous Babylonian observers In general it may be said that Ptolemy only uses observations from before his time when he wishes to establish longterm properties of his planetary models (his practice is different in his lunar theory) The older planetary observations can be grouped as follows: Mercury: six Dionysian observations from 265-257 BC (two of them are only four days apart), and two Babylonian observations from 245 and 237 BC Venus: two observations, four days apart, by Timocharis in 272 BC Mars: one Dionysian observation, 272 BC Jupiter: one Dionysian observation, 241 BC Saturn: one Babylonian observation, 229 BC For each planet, Ptolemy uses one old observation together with one from his own time to establish accurate mean motions His procedure makes no special demands on the

On the history of Souslin's problem

Abstract: De nombreux essais ont ete entrepris pour comprendre et resoudre le probleme du mathematicien russe Souslin (M.) sur les intervalles. L'A. porte une attention particuliere aux travaux developpes par Kurepa (D.) entre 1934 et 1937