Galileo's compass - History of an invention

Dinamic version

HISTORY OF AN INVENTION
Throughout the Renaissance (fig.1) many attempts were made to develop a universal instrument (fig.2) that could be used to perform arithmetical calculation and geometric operations easily. (fig.3) This need was felt especially in the military field, where the technology of firearms called for increasingly precise mathematical knowledge. To satisfy these requisites, the first proportional compasses (fig.4) were developed in the second half of the sixteenth century, among them some singular instruments known as the “radio latino” (fig.5) and the “proteo militare” (fig.6). The geometric and military compass of Galileo belonged to this class of instruments. Invented in Padua in 1597, the instrument is also linked to Galileo’s activity (fig.7) in the Accademia Delia (fig.8), founded in Padua to provide mathematical instruction for young noblemen training for a military career. (fig.9) With the seven proportional lines traced on the legs of the compass and the four scales marked on the quadrant, it was possible to perform with the greatest of ease all sorts of arithmetical and geometric calculations, ranging from calculating interest to extracting square and cube roots, from drawing polygons to calculating areas and volumes, from measuring gauges to surveying a territory. Between 1598 and 1604, Galileo instructed several European sovereigns on the use of his compass, (fig.10) among them Prince John Frederick of Alsace, Archduke Ferdinand of Austria, the Landgrave Philippe of Hesse and the Duke of Mantua.

THE SUCCESS OF THE INSTRUMENT
The success of the instrument encouraged Galileo to divulge his invention still further. In 1606 he published 60 copies of Le operazioni del compasso geometrico e militare (fig.11), each of which he sold privately along with one of the instruments. (fig.12) The production of compasses, from which Galileo earned a substantial profit, was entrusted to an instrument-maker whom the scientist housed for some years in his own home. The publication of the treatise immediately aroused great interest, so intense as to provoke bitter arguments in the academic world over the authorship of the invention. Already in 1607 Baldassarre Capra, one of Galileo’s pupils, tried to claim credit for the invention of the instrument among erudite circles by publishing a treatise in Latin on its operations (fig.13). Other adversaries of Galileo (fig.14) claimed that the instrument had been invented first by the Dutch mathematician Michel Coignet. Many variations in the instrument were made (fig.15) and, with the addition of new proportional lines, its fields of application were later extended. Specific treatises (fig.16) were written by Michel Coignet, who called it “compasso pantometro”, by Muzio Oddi who called it “compasso polimetro” (fig.17), by Ottavio Revesi Bruti who, adding proportional lines for architectural drawing, called it “archisesto” (fig.18), by Girard Desargues and other French mathematicians who, adding proportional lines for perspective drawing, called it the “optical or perspective compass”. Numerous variations (fig.19) were developed throughout the seventeenth and eighteenth centuries, while during the course of the nineteenth, the proportional compass was gradually replaced by the dissemination of highly refined slide rules (fig.20) which survived in the technical studios of engineers, architects and geometers up until the very recent advent of the computer.

Images

  1. Fig.1

    Galileo Galilei, Le operazioni del compasso geometrico e militare. Frontespizio
    Galileo Galilei, Le operazioni del compasso geometrico e militare, ms. 1606

  2. Fig.2

    Regolo pieghevole di Antonio Bianchini (XVI sec.)
    Folding rule of Antonio Bianchini (16th ca.)

  3. Fig.3

    Tavola raffigurante alcuni militari che misurano con un compasso la canna di un cannone
    Plate portraying soldiers using a compass to measure the barrel of a cannon

  4. Fig.4

    Compasso tipo Mordente (1591)
    Mordente’s compass (1591)

  5. Fig.5

    Tavola raffigurante il radio latino
    Plate illustrating the radio latino

  6. Fig.6

    Tavola raffigurante il proteo militare
    Plate illustrating the proteo militare

  7. Fig.7

    Ritratto di Galileo Galilei
    Portrait of Galileo Galilei

  8. Fig.8

    Tavola raffigurante due artiglieri, istruiti da un terzo, alle prese con la misurazione del calibro dei cannoni
    Plate portraying two gunners, instructed by a third, engaged in measuring cannon bores

  9. Fig.9

    Compasso geometrico e militare di Galileo Galilei (c. 1606)
    Geometric and military compass of Galileo Galilei (c. 1606)

  10. Fig.10

    Incisione raffigurante una carta geografica dell'Europa (1569)
    Engraving of a geographic chart of Europe (1569)

  11. Fig.11

    Galileo Galilei, <em>Le Operazioni del compasso geometrico e militare</em>, Frontespizio
    Galileo Galilei, Le Operazioni del compasso geometrico e militare, Frontespiece

  12. Fig.12

    Incisione raffigurante un costruttore di compassi nella sua bottega (1568)
    Engraving portraying a compass-maker in his shop (1568)

  13. Fig.13

    Baldassarre Capra, Usus et fabrica circini cuiusdam proportionis, Frontespizio
    Baldassarre Capra, Usus et fabrica circini cuiusdam proportionis, Frontespiece

  14. Fig.14

    Disegno raffigurante il compasso di Baldassarre Capra
    Drawing of Baldassarre Capra’s compass

  15. Fig.15

    Il compasso
    Michel Coignet’s “pantometro” compasst

  16. Fig.16

    La
    Michel Coignet’s “regula pantometra”

  17. Fig.17

    Muzio Oddi, <em>Fabbrica et uso del compasso polimetro di Mutio Oddi da Urbino</em>, Frontespizio
    Muzio Oddi, Fabbrica et uso del compasso polimetro di Mutio Oddi da Urbino, Frontespiece

  18. Fig.18

    Tavola raffigurante un disegno dell'archisesto
    Plate with drawing of an “archisesto”

  19. Fig.19

    Scatola per strumenti matematici (XVII sec.)
    Box for mathematical instruments (17th ca.)

  20. Fig.20

    Disegno raffigurante un regolo calcolatore che reca incise diverse scale Peter Nicholson
    20. Drawing of slide rule with various scales marked on it, Peter Nicholson

Dinamic version

Click on images to enlarge