De Lateribus et Angulis Triangulorum, tum planorum rectilineorum, tum sphaericorum, libellus eruditissimus & utilissimus, cum ad plerasque Ptolemaei demonstrationes intelligendas.Additus est Canon semissium subtensarum rectarum linearum in circulo.

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Title within an elaborate woodcut border & numerous woodcut diagrams in the text. [30] leaves. 4to, fine 18th-cent. French-style green morocco, triple gilt fillets round sides, spine gilt, a.e.g. Wittenberg: J. Lufft, 1542.First edition of Copernicus' first original publication, containing the first appearance of any part of the text of De Revolutionibus and Rheticus' first published trigonometric tables. "When Rheticus returned to Wittenberg for the opening of the winter semester, he was elected dean of the liberal arts faculty on 18 October 1541. In early 1542 he separately published -- under the title De lateribus et angulis triangulorum -- the section on plane and spherical trigonometry in Copernicus' De revolutionibus. To this brief discussion of the Sides and Angles of Triangles [the present work] Rheticus added a table of half-chords subtended in a circle. Such a half-chord is actually a sine, although both Copernicus and Rheticus studiously avoided the use of that term. The table of sines in the Sides and Angles of Triangles differs from the corresponding table in De revolutionibus by increasing the length of the radius from one hundred thousand to ten million and by diminishing the interval of the central angle from 10' to 1'. Furthermore, by indicating the complementary angle at the foot of the columns and at the right-hand side of the page, the 1542 table became the first to give the cosine directly, although that term is not mentioned. Rheticus did not ascribe the authorship of this table to Copernicus nor, presumably out of modesty, to himself. Nevertheless, the table was undoubtedly his doing. His independent place in the history of mathematics is due precisely to his computation of innovative and monumental trigonometrical tables."D.S.B., XI, p. 396. "This is Copernicus' first printed scientific work. Like most of the ephemeral textbooks from this period, De lateribus is quite scarce."Gingerich, Science in the Age of Copernicus, 22. A fine and large copy with several lower margins uncut. Zinner 1795. N° de ref. de la librería JHABES893

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