Elliptical Compasses

From Inventions

Revision as of 11:23, 8 September 2010 by Ghada (Talk | contribs)

(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)

Name used since the sixteenth century.

Compass for drawing ellipses. Documented already in Arab mathematical tradition under the name of perfect compasses, the instrument was illustrated in the sixteenth century by Benvenuto della Volpaia (who attributes its invention to Leonardo), Albrecht Dürer, Guidobaldo del Monte and other mathematicians. It generally consists of an inclined fixed leg representing the axis of a cone, and a revolving leg of variable length representing the generatrix. Turning around the inclined leg, the point of the revolving leg traces an elliptical curve on a sheet of paper. A variant designed to trace an ellipse as the oblique section of a cylinder is illustrated in a manuscript by the Venetian Senator Giacomo Contarini, who may have invented it.

Bibliographical Resources

Della Volpaia, Benvenuto, Macchine e strumenti, ms., XVI secolo, Venezia, Biblioteca Marciana, It. IV, 41 (= 5363), c. 18 r: “Seste da far l’ovato”.
Siena, Biblioteca degli Intronati, Ms. L.IV.10, c. 93.
Siena, Biblioteca degli Intronati, Ms. S.IV.6, c. 65v.
Benedetti, Giovanni Battista, Diversarum speculationum mathematicarum et phisicarum liber, Torino, 1585, pp. 325-327.
Besson, Jacques, Theatrum instrumentorum et machinarum, Lione, 1578, Figura V.
Del Monte, Guidobaldo, Planisphaeriorum universalium theorica, Pesaro, 1579, pp. 105, 125.
Barozzi, Francesco, Admirandum Illud Geometricum Problema, Venezia, 1586, pp. 30-31.
Contarini, Jacopo, Figure d'Istromenti Matematici e loro uso, ms., ca. 1590, Oxford, Bodleian Library, Ms. Canon. Ital. 145, cc. 9-13.
Bonino, Marco, ms., ca. 1580, Los Angeles, University of California, Ms 170/358, c. 12v.
Scheiner, Christoph, Exegeses Fundamentorum Gnomonicorum, Ingolstadt, 1615, p. 64.
Oddi, Muzio, Degli Horologi solari, Venezia, 1638, pp. 183 sgg.

Existing Instruments

- Museo Galileo, Institute and Museum of the History of Science, Florence
Firenze, Museo Galileo. Istituto di Storia della Scienza, inv. 597.
Firenze, Museo Galileo. Istituto di Storia della Scienza, inv. 2542.

- Adler Planetarium, Chicago
Chicago, Adler Planetarium, inv. M-101

- Dresden, Mathematisch-Physikalische Salon
Dresden, Mathematisch-Physikalische Salon, inv. A.I.13

- Museum of the History of Science, Oxford
Museum of the History of Science, Oxford, inv. 38132

Norimberga, Germanisches Nationalmuseum, WI 1801, compasso di Christoph Schissler.

Images

Benvenuto della Volpaia, Libro di macchine diverse, ca. 1520, Venezia, Biblioteca Nazionale Marciana, Ms. It. IV, 41 (=5363), c. 18r.	Modello del compasso ovale disegnato da benvenuto della Volpaia, Firenze, Museo galileo-Istituto di Storia della Scienza (2001).	Jacques Besson. Theatre des instrumens mathematiques de Iacques Besson ... / avec l'interpretation des figures d'iceluy par François Beroald. Lyon, 1579, tav.5.
Francesco Barozzi. Admirandum illud geometricum problema tredecim modis demonstratum : quod docet duas lineas in eodem plano designare, quae nunquam inuicem coincidant, etiam si in infinitum protrahantur & quantò longiùs producuntur, tantò sibiinuicem propiores euadant / Francisco Barocio ... autore ; accessit etiam instrumentum quoddam olim ab eodem autore inuentum, quo cuiuslibet coni ortus ac trium conicarum sect, Venetiis, 1586, p.31.	Guidobaldo Del Monte, Planisphaeriorum universalium theorica, Pesaro, 1579, p. 105.	Guidobaldo Del Monte, Planisphaeriorum universalium theorica, Pesaro, 1579, p. 125.
Compasso per ellissi e altre figure curvilinee, da Archimêdous Panta sôzomena = Archimedis Opera quae extant / nouis demonstrationibus commentariisque illustrata per Dauidem Riualtum a Flurantia, Parisiis, 1615, p.234.	Giovanni Battista Benedetti. De gnomonum vmbrarumq[ue] solarium vsu liber ... : nunc primùm publicae vtilitati studiosorumq[ue] commoditati in lucem aeditus. Torino, 1574, p.117r.