Publications


Books

Descriptive catalogue, mechanical instruments in the Utrecht University Museum, Utrecht, The Utrecht University Museum, 1968.

Lectures in the history of mathematics, (corrected reprint of edition 1993), History of mathematics 7, Providence R.I., American Mathematical Society, 1997.

Redefining Geometrical Exactness : Descartes' Transformation of the Early Modern Concept of Construction, New York etc. (Springer), 2001.


Books (co-edited)

(as editor, together with M.J.S. Rudwick, H.A.M. Snelders and R.P.W. Visser) Studies on Christiaan Huygens : Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, August 22-25, 1979, Lisse, Swets and Zeitlinger, 1980.

(as editor, together with Herbert Mehrtens and Ivo Schneider) Social history of nineteenth century mathematics, Boston, Birkhäuser, 1981.


Principal research articles

``Christiaan Huygens'', in Dictionary of Scientific Biography (ed. C. C. Gillispie, New York, Scribners, 6, 1972), pp. 597-613.

``Differentials, higher-order differentials and the derivative in the Leibnizian calculus'', Archive for history of exact sciences, 14, 1974, pp. 1-90.

``Huygens and mathematics'', in Studies on Christiaan Huygens, Invited Papers from the Symposium on the Life and Work of Christiaan Huygens, Amsterdam, 22-25 August 1979, (ed. Henk J. M. Bos e.a., Lisse, Swetz and Zeitlinger, 1980), pp. 126-146.

``Mathematics and rational mechanics'', in The ferment of knowledge: studies in the historiography of eighteenth-century science, (ed.George Sebastian Rousseau & Roy Porter, Cambridge, Cambridge University Press, 1980), pp.327-355.

``On the representation of curves in Descartes' Géométrie'', Archive for history of exact sciences, 24, 1981, pp.295-338.

``Arguments on motivation in the rise and decline of a mathematical theory; the `construction of equations', 1637 - ca. 1750'', Archive for history of exact sciences, 30, 1984, pp. 331-380.

``Fundamental concepts of the Leibnizian calculus'', Studia Leibnitiana, Sonderheft 14, 300 Jahre `Nova Methodus' von G.W. Leibniz (1684-1984), (Wiesbaden, Franz Steiner, 1986), pp. 103-118. Reprinted in Lectures (see under `books'), pp. 83-99.

``Introduction'', Christiaan Huygens, The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to Clocks (tr. annot. Richard J. Blackwell, int. Henk J.M. Bos), (Ames, Iowa state university press, 1986), pp. XI-XXIX.

``The concept of construction and the representation of curves in seventeenth-century mathematics'', in Proceedings of the International Congress of Mathematicians, August 3-11, 1986 Berkeley, California, USA, (ed. A. Gleason, Providence, American Mathematical Society, 1987), pp. 1629-1641. Reprinted in Lectures (see under `books'), pp. 23-36.

(together with C. Kers, F. Oort and D.W. Raven) ``Poncelet's closure theorem'', Expositiones mathematicae, 5, 1987, pp. 289-364.

``Tractional motion and the legitimation of transcendental curves'', Centaurus, 31, 1988, pp. 9-62.

``The structure of Descartes' Géométrie'', in Descartes: il metodo e i saggi; Atti del convegno per il 350o anniversario della publicazione del Discours de la Méthode e degli Essais, (ed. Giulia Belgioioso e.a., Florence, Armando Paoletti, 2, 1990), pp. 349-369. Reprinted in Lectures (see under `books'), pp. 37-57.

(togeter with Karin Reich) ``Der doppelte Auftakt zur frühneuzeitlichen Algebra: Viète und Descartes'', in Geschichte der Algebra: eine Einführung, (ed. Erhard Scholz, Mannheim etc., Wissenschaftsverlag, 1990), ch. 7, pp. 183-234.

``Descartes, Pappus' Problem and the Cartesian Parabola: a conjecture'', in An investigation of difficult things - Essays on Newton and the History of the Exact Sciences, (ed. P. M. Harman & Alan E. Shapiro, Cambridge, Cambridge University Press, 1992), pp. 71-96.

``On the interpretation of exactness'', in Philosophy of mathematics : Proceedings of the 15th International Wittgenstein-Symposium, 16th to 23d August 1992, Kirchberg am Wechsel (Austria), vol I, (ed. Johannes Czermak, Vienna, Hölder-Pichler-Tempsky, 1993), pp. 23-44.

``Tradition and modernity in early modern mathematics : Viète, Descartes and Fermat'', in L'Europe mathématique, histoires, mythes, identités : Mathematical Europe, history, myth, identity, (ed. Catherine Goldstein e.a., Paris, Maison des sciences de l'homme - Bibliothèque, 1996), pp. 183-204.

``Johann Bernoulli on exponential curves, ca. 1695 : innovation and habituation in the transition from explicit constructions to implicit functions'', Nieuw Archief voor Wiskunde, 14, 1996, pp. 1-19.

``La structure de la Géométrie de Descartes'' Revue d'Histoire des Sciences 51, 1998, pp. 291-317.

Further research articles

``The influence of Huygens on the formation of Leibniz' ideas,'' in Leibniz à Paris (Studia Leibnitiana supplementa 17), Wiesbaden, 1978, pp. 59-68.


``L'élaboration du calcul infinitésimal, Huygens entre Pascal et Leibniz,'' in Huygens et la France (Taton, R., ed., Paris, 1982), pp. 115-121.

``The significance of Sluse's Mesolabum within seventeenth-century geometry and algebra,,, in Actes du Colloque International "René-François de Sluse" Amay-Liège-Visé, 20-22 Mars 1985 (Bull. Soc. Roy. Sci. Liège, 55, fasc. 1, 1986; Introd. R. Halleux), 1985, pp. 145-163.

``Tractional motion 1692-1767; the journey of a mathematical theme from Holland to Italy,'' in Italian scientists in the low countries in the XVIIth and XVIIIth centuries (Maffioli, C. S., Palm, L. C., eds, Amsterdam, Rodopi, 1989), pp. 207-229.

``Johann Molther's `Problema Deliacum', 1619,'' Vestigia Mathematica : Studies in medieval and early modern mathematics in honour of H.L.L. Busard (Folkerts, M., Hogendijk, J. P., eds, Amsterdam, Rodopi, 1993), pp. 29-46.

Expository articles

``The lemniscate of Bernoulli'', For Dirk Struik, (R. S. Cohen, e.a., eds, Dordrecht, Reidel, 1974), pp. 3-14. Reprinted in Lectures (see under `books'), pp. 101-111.

(Together with Herbert Mehrtens) ``Explorierende Bemerkungen ueber die Wechselwirkungen zwischen Mathematik und Gesellschaft in der Geschichte,'' Zentralblatt für Didaktik der Mathematik, 1977 (4), pp. 186-195.

(Together with Herbert Mehrtens) ``The interactions of mathematics and society in history : Some exploratory remarks'', Historia Mathematica, 4, 1977, pp. 7-30.

``Calculus in the eighteenth century : the rôle of applications'', Bulletin of the Institute of Mathematics and its Applications, 13, 1977, pp. 221-227. Reprinted in Lectures (see under `books'), pp. 113-127.

``Was lehren uns historische Beispiele über Mathematik und Gesellschaft?'', Zentralblatt für Didaktik der Mathematik, 1978, pp. 69-75.

``E.J. Dijksterhuis on Eudoxos' theory of ratio'' (translation of Ch. 8, sections 1,2, of Dijksterhuis' De elementen van Euclides, with commentary), in: Two decades of mathematics in the Netherlands (Bertin, E., e.a., eds, Amsterdam, Mathematisch Centrum, 1978), vol. 1, pp. 177-193.

``David Bierens de Haan 1822-1895,'' Nieuw Archief voor Wiskunde, 1978, p. 65-73.

``Newton, Leibniz and the Leibnizian tradition'', in From calculus to set theory, an introductory history, (ed. Ivor Grattan Guinnes, London, Duckworth, 1980), ch. 2, pp. 49-93. [Spanish translation in: Del càlculo a la teoría de conjuntos, 1630-1910, una introducíon historíca, (Grattan-Guinness, Ivor, ed., Madrid, 1984), ch. 2, pp. 69-124.

``L'oeuvre et la personnalité de Christiaan Huygens'', in Huygens et la France, (ed. R. Taton, Paris, 1982), pp. 1-15.

``Mathematics and its social context: a dialogue in the staff room, with historical episodes'', For the learning of mathematics, 4 (3), 1984 (Nov), pp. 2-9. Reprinted in Lectures (see under `books'), pp. 181-196.

``The closure theorem of Poncelet'', Rendiconti del seminario matematico e fisico di Milano, 54, 1984, pp. 145-158. Reprinted in Lectures (see under `books'), pp. 129-140.

``Matematikken og dens sociale sammenhaenge. En samtale fra et laerervaerelse - med historiske episoder'', Nordisk matematisk tidskrift, 32, 1984, pp. 149-166.

``Poncelet's proof of the closure theorem'' (in Japanese, tr. K. Ueno), Sugaku seminar, 25 (7), 1986, pp. 81-87.

``Recognition and wonder; Huygens, tractional motion and some thoughts on history of mathematics'', Tractrix, yearbook for the history of science, medicine, technology and mathematics, 1, 1989, pp. 3-20. Reprinted in Lectures (see under `books'), pp. 1-21.

``In memoriam Hans Freudenthal (1905-1990),'' Historia Mathematica, 19, 1992, pp. 106-108.

```The bond with reality is cut' - Freudenthal on the foundations of geometry around 1900'', Educational Studies in Mathematics, 25, 1993, pp. 51-58.

``Elements of mathematics : they are no longer what they used to be'', Lectures in history of mathematics, (Providence, American Mathematical Society, 1993), pp. 141-163.

```Queen and Servant' : the role of matematics in the development of the sciences'', Lectures in history of mathematics, (Providence, American Mathematcal Society, 1993), pp. 165-180.

``Christiaan Huygens'', in Célébrations nationales 1995, (ed. Elisabeth Pauly, Paris, Direction des archives de France, 1995), pp. 18-21.


Publikaties in het Nederlands

``Mathematisering en maatschappij, of, hoe loopt een success-story af?'', Euclides, 52, 1976, pp. 82-91.

``Carl Friedrich Gauss; een biografische notitie'', Nieuw Tijdschrift voor Wiskunde, 64, 1977, pp. 234-240.

``Gauss 1777-1855'', Wiskunde en Onderwijs, 3, 1977 (12), pp. 6-16.

``Christiaan Huygens'', De Gids, 142, 1979, pp. 306-319.

``Wiskunde en maatschappij I ; Wiskunde en maatschappij II, voorbeelden van interaktie ; Wiskunde en maatschappelijke verantwoordelijkheid'', Wiskunde en Onderwijs, 6, 1980, pp. 57-67 231-238 367-374.

``De `constructie van vergelijkingen', een vergeten voorouder van de algebraïsche meetkunde'', Nieuw Tijdschrift voor Wiskunde, 68, 1981, pp. 154-165.

``Algebraïsche vergelijkingen en Galois-theorie, een historisch overzicht'', Nieuw tijdschrift voor wiskunde, 69, 1982, pp. 143-165.

``Elementen van de wiskunde, ze zijn niet meer wat ze vroeger waren'', (voordracht tijdens een symposium van het Wiskundig genootschap over `Elementen van de Wiskunde', 8 Januari 1983), Nieuw archief voor wiskunde, (4) 1, 1983, pp. 101-132.

``Johan Frederik Hennert, wiskundige en filosoof te Utrecht aan het eind van de achttiende eeuw'', Tijdschrift voor de Geschiedenis der geneeskunde, natuurwetenschappen en techniek, 7, 1984, pp. 19-31.

``Over de rekenkunde by de Romeinen'', De Gids (special issue `Het pak van Sjaalman'), 147, 1984, pp. 639-640.

Vanuit Herkenning en Verbazing (inaugurele rede, Universiteit Utrecht, 20 Marart 1987), Utrecht, Universiteit Utrecht (OMI), 1987.

``Vanuit herkenning en verbazing'', Euclides, 63, 1987 - 1988, pp. 65-76.

``Wiskunde en maatschappij - Een Discussie in de leraarskamer, met historische episodes'', Euclides, 65, 1990, pp. 255-267.

``Descartes en het begin van de analytische meetkunde'', Wiskunde en Onderwijs, 22, 1996, pp. 276-293.

``De cirkel gedeeld, de omtrek becijferd en pi gebeiteld : Ludolph van Ceulen en de uitdaging van de wiskunde'', Nieuw Archief voor Wiskunde (5) 1, 2000, pp. 259-262.

`` Uit de ivoren toren'' (over Dirk Struik als historicus van de wiskunde), Nieuw Archief voor Wiskunde (5) 2, 2001, pp. 244-247.

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