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Coignet, Michiel (Michaël)


(also Connette, Cognet, Quignet) (b. Antwerp, Brabant [later Belgium], 1549;

d. Antwerp, 24 December 1623), mathematics, winegauging, navigation, instrument making.

Although Coignet was an able mathematician, his prime contribution to science lies in the development and explanation of scientific instruments, such as astrolabes, nocturlabes, sectors, reduction compasses, and various navigational instruments.

Coignet’s father, Gillis, a well-to-do mathematical instrument maker, died in 1562 or 1563 when Michiel was merely 13 years of age. Michiel must have received a good mathematical training at a young age; in 1568, he started a school in which he taught French and mathematics. He was married to Maria vanden Eynde, with whom he had ten children. In 1606, after the death of his first wife, he married Magdalena Marinus, with whom he had another four children.

His first publication (1573) was an adaptation of Valentin Mennher’s Livre d’arithmétique (first published 1561). To this Coignet appended his own Cent questions ingenieuses, in which he deals with algebra and spherical trigonometry. In 1580, he published Nieuwe onderwijsinghe op de principaelste puncten der zeevaert (New instruction on the most important issues of navigation) as an appendix to Merten Everaert’s translation of Pedro de Medina’s Arte de navegar. Both books would be republished three times in Amsterdam (1589, 1593, 1598). In 1581, the French translation Instrvction novvelle was published. Thomas Blundiville plagiarized Instrvction novvelle and published it as part of his Exercises (1594), which was republished eight times. This seems to indicate that Coignet’s book had its greatest influence in England.

In the book Coignet describes the use of the most commonly known instruments, the cross-staff and the mariner’s astrolabe. Coignet’s is the first book in which the description of a cross-staff with more than one transversal, which allowed for smaller angles to be measured, is found. His improved instruments also allowed pilots to read positional data off the instrument instead of calculating.

Early-sixteenth-century ships from the Low Countries did not travel beyond Scandinavia or the Canary Islands, so navigators could get by with only a compass, instruments to determine latitude, and knowledge of the coastline. But Dutch and Flemish merchants would have much wider opportunities if their ships could navigate the oceans to the Americas and Indies. The major challenge was determining longitude. Coignet’s book treated Reiner Gemma Frisius’s solution to find longitude. Theoretically this amounts to knowing the time difference between a fixed point (e.g., the harbor of departure) and the local time, which allows the longitudinal difference to be calculated. Unfortunately, Coignet’s method was based on the use of sand-filled hourglasses, which are notoriously inexact, especially when used on a rolling ship. He described a nautical hemisphere, which is a meteoroscope adapted for use at sea. In principle the problem of longitude could be solved using the hemisphere. The nautical hemisphere is made of a round horizontal plate with a compass inset. Three arcs, two of which can move, are erected on the plate. One arc represents the meridian; the second, which can revolve around the east-west axis, represents the equinoctial; and the third, which revolves around the pole, represents the altitude. The second arc is mounted with a small arc that indicates time between 6:00 a.m. and 6:00 p.m. These movable arcs allow the user to mechanically solve the PZX or position triangle. The instrument was developed further in works by William Barlow (1597) and Edward Wright (1599). As of 2007, the only known surviving hemisphere was made by Charles Whitwell and was kept in Florence in the Museo di storia della Scienza.

In 1595, Coignet became mathematician to the Hapsburg Archduke Albert and Isabella, who were governors of the Spanish Netherlands. His advice was sought during the sieges of Hulst and Ostend. In this period he had some private pupils, among them Federico Saminiati and Marino Ghetaldi.

From 1601 onward Coignet edited the new editions of Epitome Theatri Orbis Terrarum by Abraham Ortelius. He wrote a new introduction and added another thirteen maps. Coignet also wrote an introduction for de Jode’s Speculum Orbis Terrarum (1593). This introduction is the first known description of projection methods used by mapmakers, although Coignet essentially limits himself to stereographic projections.

It is in this period, between 1600 and 1610, that he seems to have written his first manuscripts on the sector. The sector is a development from the reduction compass and the proportional compass, which were used to mechanically perform calculations. The scales on the legs of all three instruments are such that the principles of similar triangles can be used. A sector consists of two pivoting arms on which scales are engraved. With these scales computations can be carried out by which equations of the type in which three parameters are known, can be solved.

The invention of the sector is usually ascribed to Galileo. However, at least one man can, on the basis of published material, claim priority: Thomas Hood. In the very same year that Galileo made his invention public, Hood published The Making and Use of the Geometrical Instrument, Called a Sector (1598), in which he described a sector for use in surveying. The hitherto earliest known sectors are English sectors: James Kynvyn’s of 1595 and Robert Beckit’s and Charles Whitwell's, both from 1597. Hood never claimed priority and even wrote that the instrument was already in use.

Coignet also has a claim to priority. However, one of the many problems here is that Coignet’s manuscripts about the sector were probably written after 1600. These manuscripts show the development of his sector. They can be divided into three categories: (1) the manuscripts in which he describes his reigle platte; (2) the ones with a modified version of Mordente’s reduction compass; (3) those in which he describes a genuine sector. The reigle is a rather small rule on which scales are engraved. The use of the rule is analogous to that of the sector, but the operations are carried out with pen and paper. Originally there were only four scales on the rule; later it was “enrichy de huict diuisions” (enriched with 8 divisions) (La géometrie, 1626, introduction).

In a later stage, Coignet adapted the reduction compass invented by Fabrizio Mordente. In the partially printed manuscript of 1608, Della forma et parti del compasso di Fabritio Mordente, Coignet describes a rule that can be used in conjunction with the compass, in which case, the operations performed with such a rule are actually the same as for a sector. It is likely that this modification dates back to the 1580s. This he developed into a proper sector, which has sighting vanes at the end of the legs. It allows the sector to be used not only for calculations, but also for observations relating to surveying. The first sector of this type was made for Archduke Albert, indicating that it was constructed no later than 1596. Later, possibly after 1610, he developed his instrument into a sector that bears a close resemblance to Galileo's. Coignet had now transferred the twelve scales of the reigle platte to a set of two sectors, each carrying three scales on either side.

Coignet’s sector had thus reached its final stage. The importance of his sector lies less in its final appearance (which is very similar to Galileo's) than in the fact that its development can be easily traced from additions and incorporation of ideas taken from other instruments to its final form. Although less visible, these aspects are also present in other instruments that Coignet describes. Additions, adaptations, and incorporation of different functions led to an instrument that was seen as an improvement. Some of these changes proved to be impractical and were soon forgotten, while others became common. This becomes obvious in Coignet’s instruments and instrument descriptions. Thus Coignet’s work is a prime example of how the mind of an early modern instrument maker worked.



Cent questions ingénieuses et récréatives pour délecter & aguiser l’entendement, de feu Valentin. Mennher Allemand. Souldées & amplifiées par les raisons géométriques requises à icelles par Michiel Coignet. Antwerp: J. van Waesberghe, 1573.

Nieuwe onderwijsinghe op de principaelste puncten der zeevaert. Antwerp: Henry Hendrix, 1580. (Reprints: C. Claesz, 1589, 1593, and 1598).

Instrvction novvelle des poincts plus excellents & nécessaires, touchant l’art de nauiger. Antwerp: Henry Hendrix, 1581.

“De Regulae Pantometrae Fabrica & usu Libri Septem,” (unpublished manuscript). c. 1600–1610. Bodleian Library Oxford, MS, Canon Misc 243.

Ortelius, Abraham, Epitome theatri orbis terrarum Abrahami Ortelij, edited by Michiel Coignet. Antwerp: J. Keerbergen, 1601. (Numerous reprints and translations).

Della forma et parti del compasso di Fabritio Mordente Salernitano. Con gli usi di esso, raccolti da Michele Coignet Mathematico del Serenissimo Archiduca Alberto. Per quali si risolvono molte propositioni, cavate dalla primi sei libri d’Euclide (unpublished manuscript). 1608. Bibliotheca Estense Modena, MS Gamma G.4.34 (Campori, 548).

Usus Duodecim Diuisionum Geometricarum (unpublished manuscript). 1610–1612. Koninklijke Bibliotheek Albert I Brussel, MS II769.

El uso de las doze diuisiones geometricas (unpublished manuscript). 1618. Stadsbibliotheek Antwerpen, B264708.

Tabula Geographica Indicans Iter Novum inter Mediolanum et Antverpiam, Abraham Verhoeven, 1621.

La géomérie réduite en une facile et briefve pratique, par deux excellens instrumens, dont l’un est le pantomètre ou compas de proportion de Michel Connette, et l’ autre est l’usage du compas à huict pointes inventé par Fabrice Mordente composé en italien par M.C.… Traduits enfrançois par P.G.S. mathématicien, edited by P. G. S. Paris: Charles Hulpeau, 1626.

M. Michel Connette, sur les propositions géométriques extraictes des six premiers liures des “Élémens d’Euclide, Paris: C. Hulpeau, 1626.


Barlow, William. The Navigator’s Supply. Amsterdam: Theatrum Orbis Terrarum, 1597 (New York: Da Capo Press, 1972).

Bosmans, Henri. “Le Traité des Sinus de Michel Coignet.” Annales de la Société Scientifique de Bruxelles 25 (1901): 91–170.

———. “Michel Coignet, ami et correspondant de Galilée.” Revue des questions scientifiques, 3rd series, 16 (1909a): 644–647.

Davids Carolus Augustinus. Zeewezen en wetenschap: De wetenschap en de ontwikkeling van de navigatietechniek in Nederland tussen 1585 en 1815, Amsterdam: Bataafsche Leeuw, 1986.

de Jode, Gerard. Speculum Orbis Terrarum. Antwerp: A. Coninx, 1593.

Meskens, Ad. “Michiel Coignet’s Nautical Instruction.” The Mariner’s Mirror 78 (1992): 257–276.

———. “Winegauging in Late 16th- and Early 17th-Century Antwerp.” Historia mathematica 21 (1994): 121–147. In the 1570s through 1590s Coignet was a wine-gauger.

———. Familia universalis: Coignet. Antwerp: Koninklijk Museum voor Schone Kunsten, 1998. Deals with Michiel Coignet and other members of his family; extensive bibliography and inventory of instruments by Michiel Coignet.

Prims, F. “Michiel Coignet.” Antwerpiensia 19 (1948): 103–114.

Rose, P. L. “The Origins of the Proportional Compass from Mordente to Galileo.” Physis 10 (1968): 53–69.

Ad Meskens

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