Astronomical tables abound in medieval manuscripts and early modern printed texts. Moreover, many of these documents, commonly found in libraries around the world, are restricted to tables, normally containing few words other than those in the titles and the headings of the tables. And it is not unusual to find manuscripts and printed texts with hundreds of pages composed of vast quantities of numbers, in the thousands, or even in the hundreds of thousands. Of course, the sizes of the tables vary substantially from short tables consisting of just two columns and a few rows, to monumental tables requiring tens of pages to reproduce them. Not only were certain sets of astronomical tables copied again and again by patient scribes or typesetters in the early days of printing, or by the astronomers themselves, but many of their users found ingenious ways to ameliorate them, generating new tables based on new approaches, new parameters, or that were just more user-friendly. The number of different sets of astronomical tables extant in manuscripts, produced in the Middle Ages and the early modern period, has never been evaluated but it would not be surprising that it is well beyond a thousand. Clearly, during this long period of time astronomical tables were a major way to convey astronomical ideas.

The authors of the present monograph have invested much time and effort in understanding and explaining astronomical tables that were produced in many countries, written in a variety of languages, and dealing with a great number of different astronomical issues. We are convinced that "cracking" an astronomical table, by bringing to the surface the model on which it is based and the parameters on which it relies, is a way to gain deep insight into how astronomy was conceived and practiced at the time and how it was transmitted to subsequent generations.

In examining hundreds of astronomical tables we have found some that greatly impressed us for the cleverness of their authors in grasping a problem that had been addressed by many previous astronomers and giving innovative solutions. We have also found tables that limited themselves to reproducing the astronomical tradition of their time with little innovation, and others where the main contribution consisted in facilitating the work of astronomical practitioners. And yet in many cases the innovation was not in the models or the parameters underlying them, but in the approach to the various astronomical problems to be solved.

The tables of Giovanni Bianchini (d. after 1469) are certainly voluminous; indeed, they are the largest set of astronomical tables produced in the West before modern times, as far as we know. For many years we cherished the idea of "cracking" these tables, but the task seemed daunting, given their volume. Today we have reached our goal, and our respect for Bianchini has shifted from volume to value. Although not innovative in their building blocks, his tables reflect a well defined approach to astronomy, a practical way to present it, and a solid computing ability. Now we can understand why the wealthy and powerful d'Este family in 15th-century Ferrara engaged him to keep track of their finances.

We thank the Biblioteca Comunale Ariostea of Ferrara for giving us permission to reproduce an image in MS I.147, and all other libraries that have made available to us the manuscripts and printed editions mentioned in this monograph.

José Chabas - Bernard R. Goldstein Rome - Pittsburgh May 2008

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