Elementa geometriae. [Translated from the Arabic by Adelard of Bath (c. 1080-c. 1152). Edited by Giovanni Campano da Novara (1220-96).]

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Published by Erhard Ratdolt, Venice, 1482

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PMM 25 - the oldest textbook in the history of science. First edition of the "oldest mathematical textbook still in common use today" (PMM), This book "has exercised an influence upon the human mind greater than that of any other work except the Bible" (DSB). Euclid s Elements is the only work of classical antiquity to have remained continuously in print, and to be used continuously as a textbook from the pre-Christian era to the 20th century. It is the foundation work not only for geometry but also for number theory. Euclid s Elements of Geometry is a compilation of early Greek mathematical knowledge, synthesized and systematically presented by Euclid in ca. 300 BC. Books I-IV are devoted to plane geometry, Book V deals with the theory of proportions, and Book VI with the similarity of plane figures. Books VII-IX are on number theory, Book X on commensurability and incommensurability, Books XI-XII explore three dimensional geometric objects, and Book XIII deals with the construction of the five regular solids. The text is the standard late-medieval recension of Campanus of Novara, based principally on the 12th-century translation from the Arabic by Adelard of Bath. In fact, Adelard left three Latin versions of Euclid. Campanus s text is a free reworking of earlier Latin translations, mainly Adelard s second version (an abbreviated paraphrase), with additional proofs that make it "the most adequate Arabic-Latin Euclid of all … With an eye to making the Elements as self-contained as possible, he devoted considerable care to the elucidation and discussion of what he felt to be obscure and debatable points" (DSB). This text was printed more than a dozen times in the late-15th and 16th century. The "decisive influence of Euclid s geometrical conception of mathematics is reflected in two of the supreme works in the history of thought, Newton s Principia and Kant s Kritik der reinen Vernunft" (DSB). Ratdolt s edition is one of the most beautifully printed of early scientific books, and is the first dated book with diagrams (Stillwell). His method of printing diagrams in the margins to illustrate a mathematical text became a model for much subsequent scientific publishing. The method used to is still a matter of scholarly debate: although traditionally described as woodcuts, it is probable that printer s "rules" were used, i.e., thin strips of metal, type high, which were bent and cut and adjusted and set into a substance that would hold them (and pieces of type) in place. Born ca. 300 BC in Alexandria, Egypt, "Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 BC), not to be confused with the physician Hippocrates of Cos (c. 460 375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384 322 BC). The older elements were at once superseded by Euclid s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own … "Euclid understood that building a logical and rigorous geometry depends on the foundation a foundation that Euclid began in Book I with 23 definitions (such as "a point is that which has no part" and "a line is a length without breadth"), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem … "The subject of Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of "the section," the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the gol. Seller Inventory # 6135

Bibliographic Details

Title: Elementa geometriae. [Translated from the ...

Publisher: Erhard Ratdolt, Venice

Publication Date: 1482

Edition: First edition.