Arithmetica Logarithmica sive Logarithmorum Chiliades Centrum, pro numeris naturali serie crescentobus ab Unitate ad 100000. Una cum Canone Triangulorum Seu Tabula Artificialium Sinuum, Tangentium & Secantium.
Folio [21.5 x 33.5 cm], (4) ff., 79 pp.; (282) ff. Bound in contemporary German/Austrian blindstamped pigskin over boards, Jesuit insignia stamped in center of covers, raised bands on spine with author's name stenciled in ink. Ownership inscription of the Jesuit College in Vienna, dated 1720, with shelf-mark and notice that it was entered in the library catalog. Light browning and foxing generally seen in books during the 30 Years War, rather less than usual. Generally very good.
The work's publication history is complicated and probably remains to be described. The only published collation is Bierens de Haan, which appears to require more unnumbered leaves for the tables than are present in this copy. We assume this to be apparent only, as the present copy is physically integral, is in a contemporary binding, and moreover, is identical to one in the collection of Mr Erwin Tomash, to whom we owe thanks for making his as usual scrupulous comparison.
[Bound with:]VLACQ, Adrian. / BRIGGS, Henry Trigonometria Artificialis... Gouda, Petrus Rammasenius, 1633.
(4) ff., including title and half-title, 52 pp., (136) ff.
Rare editions of two works important for bringing the new computational technique of Briggs and Napier to the Continent. The first work is considered the second edition of Briggs exposition of his own as well as Napier's treatment of the logarithm (first 1624):
"[It] included thirty thousand logarithms, those from 1 to 20,000 and those from 90,000 to 100,000. The work contains a dissertation on the nature and use of logarithms and proposes a scheme for dividing among several hands the calculation of the immediate numbers from 20,000 to 90,000...Chapters 12 and 13 of the introduction explain the method of constructing logarithms by interpolation from differences, an interesting forerunner of the Canonotechnia of Roger Cotes,. A second edition of the Arithmetica, completed by Adrian Vlacq (or Flack), contained the intermediate seventy chiliads and appeared in 1628." - G. Huxley in DSB II.462 (s.v. Briggs). Vlacq's contribution consisted in extending the already published series to 10 decimal places, and to adding the Canon triangulorum,, with the decimal logarithms of the trigonometric lines computed from Pitiscus' Trigonometria. The second work, Trigonometria artificialis, in first edition employs the technique of sexagesimal division of angles, with log sine, log cosine, log tangent and log secant for angles increasing by ten seconds.
* *Erwin Tomash, Letter of July 16, 1998; cf. Bierens de Haan 5048 & 5052; on Vlacq, see D.J. Struik in DSB XIV.51-2.
Price: $4,500.00