Euclid's Data - The Importance of Being Given is a scholarly contribution to an area - the history of Greek geometrical analysis - that is still insufficiently understood. At the time of Zeuthen, and even up to the middle of the last century, it was fashionable to treat the Data algebraically. Taisbak...
has abandoned this approach completely, arguing that it does nothing to help us understand either the development of the work or the reasons for its having been copied, studied, and quoted for more than 2 millennia. We must bear a queer sort of frustration that affects us everywhere in the Data: we get very little information, hardly any 'knowledge' of the givens. And why not? Probably because 'knowing' geometrical objects was problematic in those days when the concept of 'given' came into being, and the consequences of incommensurability were just being understood. Next to nothing is known of these items, and very little that is worth knowing: length, size, distance, - any of the attributes that can be spoken of by means of numbers.
Although there have been two recent translations of the Data, this one is unique in providing, as well, an extensive commentary, which provides the insights gained from three decades of studying the work. The book is meant as a coherent and understandable account of what could have been going on in Euclid's mind, and some reasons for believing that that is what actually was going on in his mind.
Christian Marinus Taisbak recently retired as associate professor in the Department of Greek and Latin at the University of Copenhagen. He is the author of Coloured Quadrangles. A Guide to the Tenth Book of Euclid's Elements (Museum Tusculanum Press, 1982).
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