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Abstract

Before slide rules became widely used in the nineteenth century, European military architects, surveyors, navigators, and other mathematical practitioners performed calculations on sectors. These mathematical instruments have two arms that are joined by a hinge and marked with various proportional, numerical, trigonometric, and logarithmic scales. The user employed a pair of dividers to transfer distances between a sector and a drawing and to measure distances on the scales, effectively creating a series of similar triangles or proportional relationships. Sectors were independently invented on the Italian peninsula and in England at the turn of the seventeenth century; a third version emerged in France by late in the seventeenth century. This paper uses 27 sectors in the Smithsonian’s National Museum of American History mathematics collections to trace the history of the instrument.

Keywords

Seventeenth Century Regular Polygon Italian Peninsula Similar Triangle Instrument Maker 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Ackerberg-Hastings, A. (2013a). Sectors. Object Groups. National Museum of American History, Smithsonian Institution. http://americanhistory.si.edu/collections/object-groups/sectors
  2. Ackerberg-Hastings, A. (2013b). Sets of drawing instruments. National Museum of American History, Smithsonian Institution. http://americanhistory.si.edu/collections/object-groups/drawing-instruments
  3. Bion, N. (1709). Traité de la construction et de principaux usages des instrumens de mathematique. Paris.Google Scholar
  4. Drake, S., Trans. and intro. (1978). Operations of the geometric and military compass, by Galileo Galilei. Washington, DC: Smithsonian Institution Press.Google Scholar
  5. Heather, J. F. (1851). A treatise on mathematical instruments (2nd ed.). London.Google Scholar
  6. Istituto e Museo di Storia Della Scienza. (2004). Galileo’s compass. Florence. http://brunelleschi.imss.fi.it/esplora/compasso/dswmedia/risorse/testi_completi_eng.pdf
  7. Sangwin, C. J. (2003). Edmund Gunter and the sector. University of Birmingham. http://web.mat.bham.ac.uk/C.J.Sangwin/Sliderules/sector.pdf
  8. Stone, E., Trans. (1723). The construction and principal uses of mathematical instruments, by Nicolas Bion. London: John Senex.Google Scholar
  9. Tomash, E., & Williams, M. R. (2003). The sector: Its history, scales, and uses. Annals of the History of Computing, 25(1), 34–47.MathSciNetCrossRefGoogle Scholar
  10. Van Helden, Al. (1995). The sector. The Galileo Project. http://galileo.rice.edu/sci/instruments/sector.html
  11. Webster Signature Database. (2007). Adler Planetarium and Astronomy Museum, Chicago. http://historydb.adlerplanetarium.org/signatures/

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Maryland University CollegeAdelphiUSA

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