Incunabula and the Keio University Library Collection

The book Elementa Geometriae is the classic work of geometry written by the Greek mathematician Euclides (c. 330-275 BCE), first printed in Venice in 1482 with more than four hundred geometrical figures. Euclides studied at the Academy, the research and educational organization inaugurated by Plato and located in Athens. At the invitation of the Egyptian king Claudius Ptolemy I, he became head of the Mathematics division of the Mouseion, the grand library and research institute in Alexandria, where he made a significant contribution to the advancement of mathematics. His Elementa Geometriae succeeded in systematizing all the studies of ancient Greek geometry since Pythagoras using one consistent system. In other words, he used some simple axioms and postulates from which he derived some five hundred theorems; in this way he organized geometry into a system. Euclidean geometry was thus accepted as the standard throughout the medieval and early modern periods; later it became the model for modern mathematics. In the 19th century, studies that evolved from doubts about the fifth postulate in the Elementa gave birth to non-Euclidean geometry. This is regarded as different from the Euclidean geometry that had preceded it: Euclidian geometry principally dealt with planar and spatial figures without torsion, while non-Euclidean geometry dealt with curved surfaces and spatial figures with torsion.

The Elementa Geometriae is the first edition printed by Erhard Ratdolt (c. 1443-1528), the German printer from Augsburg, using the text translated from the Arabic into Latin by the 12th-century English scholar Adelard of Bath, and annotated by Campanus of Novara in Italy. As over one hundred copies of this edition, published in 1482, are extant, it is assumed that substantial numbers were actually printed. Ratdolt went to Venice around 1476, and there acquired great sophistication in printing during his two-year operation of the press with Bernhart Maler and Peter Loslein. From around 1480, he started to run his own printing house there.

The British Library copy has the dedication with letters printed in gold, a feature lacking in the Keio copy. In the dedication of the Keio copy(π(pi)1v) Ratdolt emphasizes that he invented a new method. According to him, Ratdolt, at the time he planned to begin printing, realized there were very few printed books on mathematics. He struggled to find a way to reproduce pictorial figures. Once he had discovered a method for printing them, he recounts they were as easy to handle as text. His boast is surely justified by the facts that the geometrical figures are sharply defined, and complicated figures, including curves and words in Gothic types, occupy a large portion of the margins on each page. How Ratdolt managed to print such complicated figures is not known: one theory is that he used woodcuts, while another posits metallic moulds. The borders on the top of A1r are said to demonstrate his technical expertise.

Ratdolt's printing technique – particularly in his figures, woodcut ornamental borders and initials – has been highly acclaimed; nevertheless, some claim that his abilities have been overestimated, since his technology and methods have not yet been determined (BMC, V, xvii). Ratdolt certainly established a reputation for knowing what, when and how to print.

[Bibliography]
  斉藤憲『ユークリッド「原論」の成立』(東京: 東京大学出版会, 1997)
  Heiberg, I. L. 編『ユークリッド原論』中村幸四郎 訳 (東京: 共立出版, 1971)

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