ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.

ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann. < >
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  • Another image of ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.
  • Another image of ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.
  • Another image of ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.
  • Another image of ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.
  • Another image of ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, by BILBERG, Johann.
Mathematical teaching at the end of the 16th century

ELEMENTA GEOMETRIÆ PLANÆ AC SOLIDÆ, una cum sphæricorum doctrina atq; praxi trigonometrica. Ad ductum veterum juxta ac recentium mathematicorum. In usum juventutis patriæ peculiari methodo conscripta, necessariisq, demonstrationibus illustrata. Editio altera multo auctior. Cum figuris æneis, & cum privilegio regio. Stockholmiæ, Literis B. Wankijfwii, Ol. Typ. Reg. sumtibus Joh. Siwertz, Bibliop. Upsal.

1691. 8vo, pp. [viii], 191, [1] errata, [102] additional blank pages, of which [53] have been filled with manuscript notes, seemingly in two hands; with woodcut printer’s device, initial, tail-piece, text figures, and four folding engraved plates (fore-edges of plates II-IV slightly furled and nicked in places, with small stain at upper margin of plate IV); title-page a little dust-soiled, some light soiling throughout, with faint dampstain affecting tail of pp. 109-28, old paper repairs to fore-edge of pp. 185 and 191 touching a few letters and with slight loss but not interrupting meaning; inscribed on the title-page Laurentius Brems and dated 25 March 1692, with further signature of ”negat Ph. Oterdal”, and the signature of ”Kjerrulf” on somewhat loose front flyleaf; in contemporary vellum, with red sprinkled edges, covers somewhat soiled and stained, head of spine and upper corner of rear cover abraded, and with loss of 7cms of vellum at fore-edge of upper board; an appealing working copy. Second considerably expanded edition, second issue of this mathematical textbook on the elements of plane and solid geometry, the doctrine of spheres, and trigonometry, the work of Johan Bilberg, Professor of Mathematics at Uppsala from 1679-1690. The rare first edition was published in 1687, and ran to only 32 pages. The first issue of this second edition appeared in 1690. The Swedish Biographical Lexikon consider this to be one of his most enduring work, which went on to be widely used in schools. Bilberg draws upon the work and theories of a number of ancient and contemporary mathematicians, including Euclid, Aristotle, Van Schooten, Blondel, Briggs, Collins, Napier, and Newton, paying especial tribute in the preface to Johann Christopher Sturm’s ‘Mathesis Enucleata (1689), which may have inspired this expanded edition.
The present copy is of note for the evident signs of contemporary and later use and readership. The title-page bears the signature of Laurentius Brems and is dated March 25th 1692, Brems having then had bound at the end of the volume an additional blank notebook. The first leaf of this is signed by him once again and dated May 25th 1692. with a further signature and date of May 25 1692. Whilst most of the notes concern theological matters, there is a section on ‘Computatio cyclica. The copy later came into the possession of ‘Ph. Oterdal’, possibly the master shoemaker Philip Otterdahl (d. 1731), or his son Philip, a Gothenburg merchant. Otterdahl’s name is found both on the title page and on p. (21) in the manuscript, where it is dated 1712. It seems likely that it is he who has drawn up the calendar which makes up part of the manuscript.
One of the most staunch Cartesians in Sweden, Bilberg was the author of a number of works, including on observational astronomy (1695), and a reform of the calendar in 1699. He is considered to have been instrumental in having introduced proper algebraic notation, and above all the study of logarithms into Swedish schools. ‘Bilberg ended his days as the Bishop of Strangnas. Although Queen Christina had decreed that theologians could not hold appointments in the philosophy faculty, this did not prevent Bilberg from seeking clerical office. Nor did it discourage him from holding the radical views, in religion as well as science. His thesis attacking the use of scholastic terminology in theology was banned the year before he was ordained (see Kallinen who cites A. Nilsson, ‘Johan Bilberg’ in Svenska Biografiskt Lexicon (1924, iv, p. 310)’ (Gaskell, 40: 15 offering ‘Refaction solis in occidui, 1695).

Bibliography: Collijn Sveriges bibliografi 1600-talet I, 79; OCLC locates copies of the 1687 first edition at the Swedenborgian Bryn Athyn College and the Royal Swedish Library, which is also the only recorded holder of the 1690 issue, with the present second issue at the Royal Swedish Library, Bryn Athyn and University College London.

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