Guillaume des Moustiers' treatise on the armillary instrument (1264) and the practice of astronomical observation in medieval Europe.

This article is devoted to a thirteenth-century Latin text on how to construct, set up, and use a version of the so-called armillary instrument (instrumentum armillarum), which was first described in Ptolemy's Almagest as a tool for measuring ecliptic coordinates. Written in 1264 by Guillaume des Moustiers, bishop of Laon, this hitherto unstudied Tractatus super armillas survives in a single manuscript, where it is accompanied by a copious set of glosses. The text and its glosses jointly offer an unusually detailed account of the instrument's material aspects and methods of assembly. In addition, they reflect a keen awareness of the potential sources of error that may arise in the context of astronomical observation, while making suggestions on how these errors may be minimized or avoided. The Tractatus super armillas accordingly is a valuable source on the observational side of medieval European astronomy, which has often been minimized in modern historical accounts.

Henry Bate's Tabule Machlinenses: the earliest astronomical tables by a Latin author.

The known works of the medieval astronomer/astrologer Henry Bate (1246-after 1310) include a set of planetary mean motion tables for the meridian of his Flemish hometown Mechelen. These tables survive in three manuscripts representing two significantly different recensions, but have never been examined for their principles of construction or underlying parameters. Such analysis reveals that Bate employed an unusual value for the length of the tropical year (c.365 1/4 - 1/112 days), which was probably derived by comparing ancient and contemporary observations of the vernal equinox. In addition, there are clear signs that Bate kept revising his parameters for the mean motions of Venus and the three superior planets, none of which can be traced back to earlier sources. Together with some of Bate's preserved statements, these findings support the conclusion that the Tabule Machlinenses were unique among the astronomical tables produced in medieval Latin Christendom for using independently derived parameters that were the result of new observations. Bate's achievement connects him to a wider milieu of astronomers operating in late-thirteenth-century Paris, who put an increased emphasis on observation and the critical examination of received data.

Zaccaria Lilio and the shape of the earth: A brief response to Allegro's "Flat earth science".

This is a response to James J. Allegro's article "The Bottom of the Universe: Flat Earth Science in the Age of Encounter," published in Volume 55, Number 1, of this journal. Against the solid consensus of modern scholars, Allegro contends that the decades around 1500 saw a resurgence of popular and learned doubts about the existence of a southern hemisphere and the concept of a spherical earth more generally. It can be shown that a substantial part of Allegro's argument rests on an erroneous reading of his main textual witness, Zaccaria Lilio's Contra Antipodes (1496), and on a failure adequately to place this source in the context of the cosmographical debate of the late fifteenth and early sixteenth centuries. Once this context is taken into account, the notion that Lilio was a flat-earther falls flat.

Astronomy and calendar reform at the curia of Pope Clement VI: a new source.

The article introduces a previously unknown fourteenth-century treatise on computus and calendrical astronomy entitled Expositio kalendarii novi, whose author proposed elaborate solutions to the technical flaws inherent in the calendar used by the Roman Church. An analysis of verbal parallels to other contemporary works on the same topic makes it possible to establish that the Expositio was produced in the context of a calendar reform initiative led by Pope Clement VI in 1344/45 and that this anonymous text is probably identical to a 'great and laborious work' on the calendar that the monk Johannes de Termis prepared for the pope around this time. Its author strove to make an original contribution by extracting new astronomical parameters from both ancient and contemporary data, which made him arrive at an estimate of the length of the tropical year that was independent of the then-current Alfonsine Tables. With its suggestion to remove eleven days from the Julian calendar and to correct the calendar through modified leap-year rhythms and periodically adjusted sequences of lunar epacts, the proposal enshrined in the Expositio exhibits some remarkable similarities to the Gregorian reform of the calendar promulgated in 1582. Although its influence on the latter must remain a matter of speculation, the newly discovered text sheds a revealing light on the history of medieval calendar reform debates and on the mathematical sciences practiced at the Avignon court of Clement VI.

Roman vs. Arabic Computistics in Twelfth-Century England: A Newly Discovered Source (Collatio Compoti Romani et Arabici).

A frequently overlooked aspect of the knowledge transfer from Arabic into Latin in the twelfth century is the introduction of the Islamo-Arabic calendar, which confronted Western computists with a radically different scheme of lunar reckoning that was in some ways superior to the 19-year lunar cycle of the Roman Church. One of the earliest sources to properly discuss this new system and compare it to the old one is the anonymous Collatio Compoti Romani et Arabici, found in a manuscript from Tewkesbury Abbey, Gloucestershire. This article contains the first edition and translation of this previously unknown text, preceded by an analysis of its content and sources. As will be argued, the text was written in the second quarter of the twelfth century as a reaction to the astronomical tables of al-Khwaizmi, recently translated by Adelard of Bath, as well as to eclipse observations that had exposed the flaws of the 'Roman' computation.