In book II of his De Caelo, Aristotle mentions that he had observed an occultation of Mars by the Moon. In his Astronomia Nova, Johannes Kepler provides the earliest known dating for this Aristotelian observation, and dates it to April 4 357 B.C. In fact, there was no occultation on that day, and modern calculations date the phenomenon to May 4 357 B.C., 1 month after the date provided in Astronomia Nova. In this paper, I will show that Kepler had indeed found the correct time and date for the phenomenon in his preliminary work for the Astronomia Nova, and I will propose a reasonable cause for the incorrect date given in the final edited text.
In this paper we analyse and comment on the genesis and proof of the theorem that Girard Desargues presented in the last pages of his Brouillon project, and discuss the characterization of the foci of conic sections as fixed points of a certain involution on the principal axis that he tacitly used to establish this theorem.
Hipparchus based an estimate of the minimum possible value for the rate of precession on measurements of the distance of Spica from the Moon in mid-eclipse-an eclipse observed by himself on April 21, 146 BCE and another observed by Timocharis, on an unspecified date. This paper reaches three conclusions: (1) Hipparchus's final adopted value for the longitude of Spica was determined by his wish to keep the latitude of Spica constant at 2 degrees South; (2) Hipparchus carefully selected two eclipses for comparison so that the effects of the lunar parallax would nearly cancel out; and (3) Timocharis's lunar eclipse was one of two possibilities: the eclipse of April 19, 295 BCE or that of April 8, 294 BCE.
Folios 400r–405v of the Pulkovo XIV preserve a set of Martian ephemerides computed by Benjamin Ursinus under Kepler’s direction. They have been read as an incomplete and partly erroneous set of calculations for 1609. This paper shows instead that they form a coherent 3-year sequence, running from 1609 to 1611, whose transitions between years are concealed both by the loss of intermediate sheets and by the fact that the entries are spaced not by the civil calendar but at 10-day intervals from the moment of zero anomaly; the 1611 sequence opens with a fresh determination of the Martian aphelion and a correspondingly new zero of anomaly. A numerical analysis of the 35 surviving entries shows that the solar longitudes were taken from Tycho’s tables reduced to a meridian some 12½ min of time east of Uraniborg, and that the equated anomalies and distances of Mars reproduce, to a few seconds of arc, the values required by the elliptical orbit and the area law with the parameters of the Astronomia Nova. The residual errors of a few arcminutes in heliocentric longitude are traced to the adopted parameters rather than to the model. These sheets are the earliest known ephemerides computed with Kepler’s first two laws.
This article is devoted to Roberval’s little-known work on optics. After listing the optical manuscripts held in the Archives of the Paris Academy of Sciences, the article provides a critical edition of Livre troisiesme de la Dioptrique ou des lunettes (1648–1651), based on Roberval’s autograph and the copy made by his student François Du Verdus. This fairly long unpublished text (90 pages) is mainly devoted to the study of the anaclastic problem and presents the solutions of the elliptical lens, the hyperbolic lens, and optical eggs, for which Roberval details various geometric constructions.
