Archive for History of Exact Sciences

, Volume 1, Issue 3, pp 179–388 | Cite as

Patterns of mathematical thought in the later seventeenth century

  • Derek Thomas Whiteside
Article

Select Bibliography of primary sources

B. Individual works 1. English

  1. Barrow, Isaac: Euclidis Elementorum libri xv breviter demonstrata. Cantabrigiae, 1655.Google Scholar
  2. Barrow, Isaac LM lectiones mathematicae xxiii in quibus principia matheseos generalia exponuntur ... habitae Cantabrigiae 1664–1666, London 1685.Google Scholar
  3. Barrow, Isaac LG lectiones xviii Cantabrigiae in scholis publicis habitae; in quibus opticorum phaenomenωn genuinae rationes investigantur ac exponuntur. annexae sunt lectiones aliquot geometricae, London, 1670.Google Scholar
  4. Barrow, Isaac Archimedis opera: Apollonii Pergaei conicorum libri iiii: Theodosii sphaerica: methodo nova illustrata et succincte demonstrata. London, 1675.Google Scholar
  5. Briggs, Henry: AL arithmetica logarithmica, sive logarithmorum chiliades triginta. ... quorum ope multa perficiuntur arithmetica problemata et geometrica, London, 1624.Google Scholar
  6. Briggs, Henry TB trigonometria britannica, sive de doctrina triangulorum libri duo, Gouda, 1633.Google Scholar
  7. Viscount Brouncker, William: None of Brouncker's writings exist in separate form. I have published a full list of the scattered fragments of his mathematical work in Notes and Records of the Royal Society, Tercentenery issue, July 1960 (especially p. 157).Google Scholar
  8. Craig, John: methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi, London, 1685.Google Scholar
  9. Craig, John tractatus mathematicus de figurarum curvilineorum quadraturis et locis geometricis, London, 1693.Google Scholar
  10. Craig, John theologiae christianae principia mathematica, London, 1699.Google Scholar
  11. Craig, John de calculo fluentium libri duo, London, 1718.Google Scholar
  12. Duillier, Fatio de: lineae brevissimi descensus investigatio geometrica duplex. cui addita est investigatio geometrica solidi rotundi in quod minima fiat resistentia, London, 1699.Google Scholar
  13. Gregory, David: exercitatio geometrica de dimensione figurarum, sive specimen methodi generalis dimetiendi quasvis figuras, Edinburgh, 1684.Google Scholar
  14. Gregory, James: VCHQ vera circuli et hyperbolae quadratura, in propria sua proportionis specie inventa et demonstrata, Padua, 11667, 21668Google Scholar
  15. Gregory, James GPU geometriae pars universalis, inserviens quantitatum curvarum transmutationi et mensurae, Padua, 1668.Google Scholar
  16. Gregory, James EG exercitationes geometricae. appendicula ad veram circuli et hyperbolae quadraturam. N. Mercatoris quadratura hyperbolae geometrice demonstrata. analogia inter lineam meridianam planisphaerii nautici et tangentes artificiales geometrica demonstrata, seu quod secantium naturalium additio efficiat tangentes artificiales. item, quod tangentium naturalium additio efficiat secantes artificiales. quadratura conchoidis. quadratura cissoidis. methodus facilis et accurata componendi secantes et tangentes artificiales, London, 1668.Google Scholar
  17. Gregory TV James Gregory Tercentenary Memorial Volume, containing his correspondence with John Collins and his hitherto unpublished mathematical manuscripts ... (ed. H.W. Turnbull), London, 1939.Google Scholar
  18. Halley, Edmund: Apollonii Pergaei de sectione rationis libri duo ... accedunt ejusdem de sectione spatii libri duo restituti, opus analyseos geometricae studiosis apprime utile ..., Oxford, 1706.Google Scholar
  19. Halley, Edmund: Apollonii Pergaei conicorum libri octo, Oxford, 1710.Google Scholar
  20. Harris, John: A New short Treatise of Algebra, with the Geometrical Construction of Equations ..., together with a Specimen of the Nature and Algorithm of Fluxions, London, 1703.Google Scholar
  21. Hayes, Charles: A Treatise of Fluxions, or an Introduction to Mathematical Philosophy containing a full explication of that Method by which the most celebrated Geometers of the present age have made such vast advances in Mechanical Philosophy. A Work very useful for those that would know how to apply Mathematicks to Nature, London, 1704.Google Scholar
  22. Kersey, John: The Elements of that Mathematical Art commonly called Algebra expounded in four Books, London, 1673.Google Scholar
  23. Mercator, Nicolaus: Log logarithmotechnia, sive methodus construendi logarithmos nova, accurata et facilis, London, 1668.Google Scholar
  24. Mercator, Nicolaus: Euclidis elementa geometrica, novo ordine ac methodo fere demonstrata, una cum Nicolae Mercatoris in Geometriam introductione brevi, qua magnitudinum ortus ex genuinis principiis et ortarum affectiones ex ipsa genesi derivantur, London, 1678.Google Scholar
  25. Napier, John: mirifici logarithmorum canonis descriptio ejusque usus ..., Edinburgh 1614.Google Scholar
  26. Napier, John: mirifici logarithmorum canonis constructio et eorum ad naturales ipsorum numeros habitudines, Edinburgh, 1619.Google Scholar
  27. Napier TV Napier Tercentenary Memorial Volume (ed. C. G. Knott), London, 1915.Google Scholar
  28. Newton, Isaac: (A mass of unpublished mathematical manuscript exists in the Cambridge University Library, especially CUL Add. 3958–3964, 4000, 4004.)Google Scholar
  29. Newton, Isaac: To resolve Problems by Motion. (October 1666.) (CUL Add. 3958.3: 48v–63v.)Google Scholar
  30. Newton, Isaac: analysis per aequationes numero terminorum infinitas, London, 1711 (but written 1668/9).Google Scholar
  31. Newton, Isaac: methodus fluxionum et serierum infinitarum (1671). (Add. 3960.14: printed by S. Horsley as geometria analytica, sive artis analyticae specimina in his Newtoni opera quae exstant omnia, 1 London, 1779; and in English by J. Colson, London, 1736.)Google Scholar
  32. Newton, Isaac: AU arithmetica universalis, sive de compositione et resolution arithmetica liber, London, 1707 (printed from his Lucasian lectures of 1673–1683·=·CUL Dd. 9.68).Google Scholar
  33. Newton, Isaac: MD methodus differentialis, London, 1704 (written c. 1675).Google Scholar
  34. Newton, Isaac: tractatus de compositione locorum solidorum (c. 1675). (CUL Add. 3963.8/12/13).Google Scholar
  35. Newton, Isaac: PM philosophiae naturalis principia mathematica, London, 11687, 21713, 31726 (based largely on his Lucasian lectures of 1684–1687·=·CUL Dd. Dd. 9.46/.4.18).Google Scholar
  36. Newton, Isaac: tractatus de quadratura curvarum, London, 1704 (but written in 1691/2 as part of a projected treatise on geometry).Google Scholar
  37. Newton, Isaac: enumeratio linearum tertii ordinis, London 1704 (but written c. 1695—fuller manuscript versions are at CUL Add. 3961 and, of the projective classification of cubics, at Add. 4004: 153–159.)Google Scholar
  38. Newton, Isaac: regula differentiarum (c. 1692). (CUL Add. 3964.5, printed by D. C. Fraser, London, 1927.)Google Scholar
  39. Raphson, John: analysis aequationum univeralis, seu ad aequationes algebraicas resolvendas methodus generalis et expedita, ex nova infinitarum serierum methodo deducta t demonstrata, London, 11690, 21697, 31704.Google Scholar
  40. Raphson, John: SR de spatio reali, seu Ente infinito conamen mathematico-metaphysicum (added to 2nd and 3rd editions of his analysis aequationum universalis).Google Scholar
  41. Wallis, John: operum mathematicorum pars prima/altera, Oxford, 1657/6. Part 1 (1657) hasGoogle Scholar
  42. Wallis, John: MU mathesis universalis, seu opus arithmeticum. Part 2 (1656) includes: philogice et mathematice traditum, arithmeticam numerosam et speciosam aliague continens.Google Scholar
  43. Wallis, John: AI arithmetica infinitorum, sive nova methodus inquirendi in curvilineorum quadraturam aliaque difficiliora matheseos problemata, andGoogle Scholar
  44. Wallis, John: SC de sectionibus conicis nova methodus expositis tractatus.Google Scholar
  45. Wallis, John: CE commercium epistolicum de quaestionibus quibusdam mathematicis habitum, Oxford, 1658.Google Scholar
  46. Wallis, John: tractatus duo, prior de cycloide et corporibus inde genitis; posterior epistolaris in qua agitur de cissoide et corporibus inde genitis: et de curvarum tum linearum ɛvϑύνσɛι, tum superficierum πλατυσμw. Oxford, 1659.Google Scholar
  47. Wallis, John: mechanica, sive de motu tractatus geometricus. London, 1670/1.Google Scholar
  48. Wallis, John: A Treatise of Algebra both historical and practical, showing the original, progress and advancement thereof from time to time, and by what steps it hath attained to the heighth at which it now is ..., London, 1685.Google Scholar
  49. Wallis, John: Op opera omnia mathematica, Oxford, 1 (1695); 2 (1693); 3 (1699).Google Scholar
  50. Wren, Christopher: (As with Brouncker none of Wren's writings exist in separate printed form, and the issue of Notes and Records of the Royal Society there mentioned (on p. 111) contains a list of the mathematical fragments as I know them.)Google Scholar

2. French

  1. Arnaud, Antoine: Nouveaux élémens de géométrie; contenant, outre un ordre tout nouveau et de nouvelles démonstrations des propositions les plus communes, de nouveaux moyens de faire voir quelles lignes sont incommensurables, de nouvelles mesures des angles dont on ne s'estoit point encore avisé, et de nouvelles manières de trouver et de demontrer la proportion des lignes. Paris, 1667.Google Scholar
  2. Desarges, Girard: Brouillon Proiect d'une Atteinte aux Evenemens des Rencontres du Cône avec un Plan, Paris, 1639. (The only copy now known is in the Bibliothèque Nationale at Rés. V. 1209—cf. R. Taton: L'Oeuvre mathématique de G. Desargues, Paris, 1951.)Google Scholar
  3. Descartes, René: La Géométrie (3rd) appendix, pp. 297–413, of his Discours de la Methode pour bien conduire sa Raisonet chercher la Vérité dans les Sciences, Leyden, 1637. geometria... anno 1637 Gallice edita, una cum notis Florimondi de Beaune ..., Leyden, 1649. (A further augmented edition appeared at Amsterdam, 1659/61,21683.)Google Scholar
  4. Descartes, René: OE Oeuvres de Descartes (ed. Ch. Adam & P. tannery) (12 vols) Paris, 1897–1910.Google Scholar
  5. Fermat, Pierre: OE Oeuvres de Fermat (ed. P. Tannery & Ch. Henry) (4 vols.) Paris, 1891–1912.Google Scholar
  6. Fermat, Pierre: Op varia opera mathematica, Toulouse, 1679.Google Scholar
  7. LaHire, Philippe de: Observations ... sur les Points d'Attouchement de trois lignes droites qui touchent la Section d'un Cône sur quelques-uns des Diamètres, et sur le Centre de la mesme Section, mises en lumière par A. Bosse. Paris 1672. (See R. Taton: La première œuvre géométrique de Philippe de La Hire. Révue d'Histoire des Sciences 6 (1953): 73–111.Google Scholar
  8. LaHire, Philippe de: Nouvelle Méthode en Géométrie pour les Sections des Superficies Cylindriques qui ont pour bases des Cercles ou des Paraboles, des Ellipses et des Hyperboles. Plus les Planiconiques, Paris, 1673.Google Scholar
  9. LaHire, Philippe de: Nouveaux Elémens des Sections Coniques, les Lieux géométriques, la Construction ou Affectation des Equations, Paris, 1679.Google Scholar
  10. LaHire, Philippe de: sectiones conicae in novem libros distributae, in quibus quidquid hactenus observatione dignum cum a veteribus, tum a recentioribus geometrie traditum est, novis contractisque demonstrationibus explicatur ..., Paris, 1685.Google Scholar
  11. LaLouvère, Antoine de (Antonius Lalovera): Quadratura circuli et hyperbclae segmentorum, ex dato eorum centro gravitatis, una cum inventione proportionis et centri gravitatis in portionibus sphaerae plurimorumque periphericorum, nec non tetragonismo absoluto certa cujusdam cylindri partis et aliorum ..., Toulouse, 1651.Google Scholar
  12. LaLouvère, Antoine de (Antonius Lalovera): veterum geometria promotu in septem de cycloide libris ..., Toulouse, 1660.Google Scholar
  13. Pascal, Blaise: Essay pour les Coniques, Paris, 1640 (privately printed and circulated).Google Scholar
  14. Pascal, Blaise: Lettres de A. Dettonville, contenant quelques unes de ses Inventions en Géométrie ... L'Egalité entre les lignes Spirale et Parabolique demonstrée a la manière des Anciens ..., Paris, 1659.Google Scholar
  15. Pascal, Blaise: Traité du Triangle arithmétique, avec quelques autres petits traités sur la mesme matière ..., Paris, 1665.Google Scholar
  16. Pascal, Blaise: OE Oeuvres des Blaise Pascal (14 Vols.) (ed. L. Brunschvicg, P. Boutroux & F. Grazier), Paris, 1908–1925.Google Scholar
  17. Roberval, Gilles Persone de: (All Roberval's mathematical work as it then existed was collected after his death and printed in vol. 6 of the Mémoires de l'Académie royale des sciences (1666–1699), Paris, 1693, = (2nd ed.) 1730:pp. 1–478. That still remains our only source, apart from minor correspondence with contemporaries.)Google Scholar
  18. Viète, Francois (Franciscus Vieta): Op opera mathematica (ed. F.v. Schooten), Leyden, 1646.Google Scholar

3. Italian

  1. Cavalieri, Bonaventura: GI geometria indivisibilibus continuorum nova quadam ratione promota, Bologna, 11635, 21653. exercitationes geometricae sex, Bologna, 1647.Google Scholar
  2. Mengoli, Pietro: novae quadraturae arithmeticae, seu de additione fractarum, Bologna, 1651.Google Scholar
  3. Mengoli, Pietro: via regia ad mathematicas per arithmeticam, algebram speciosam, planimetriam, Bologna, 1655.Google Scholar
  4. Mengoli, Pietro: GS geometria speciosa, Bologna, 1659.Google Scholar
  5. Mengoli, Pietro: circolo, Bologna, 1672.Google Scholar
  6. Torricelli, Evangelista: opera geometrica, Florence, 1644.Google Scholar
  7. Torricelli, Evangelista: opere (ed. G. Loria & G. Vassura), (4 vols.) Faenza, 1919/1944.Google Scholar
  8. Torricelli, Evangelista: de in/initis spiralibus (manuscript printed by E. Carruccio, Pisa, 1955.)Google Scholar

4. German/Dutch

  1. St. Vincent, Gregory (Gregorius a Sancto Vincentio): OG opus geometricum quadraturae circuli et sectionum coni, Antwerp, 1647.Google Scholar
  2. Huygens, Christiaan: theoremata de quadratura hyperboles, ellipsis et circuli ex dato portionum gravitatis centro, Leyden, 1651.Google Scholar
  3. Huygens, Christiaan: de circuli magnitudine inventa, Leyden, 1654.Google Scholar
  4. Huygens, Christiaan: OE Oeuvres complètes (22 vols.), The Hague, 1888–1950.Google Scholar
  5. Kepler, Johannes: nova stereometria doliorum vinariorum, Linz, 1615.Google Scholar
  6. Leibniz, Gottfried Wilhelm: Many of Leibniz's mathematical manuscripts, now in the Royal Library at Hanover, remain to be published. A few were printed by C.J. Gerhardt at the end of the 19th century—of which J.M. Child's The early mathematical manuscripts of Leibniz, Chicago, 1916 is a convenient collection (in English translation)—but for the rest we have to rely on the description given by J.E. Hofmann in his Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthaltes in Paris (1672/76), München, 1949. (All Leibniz's important mathematical ideas were given to his contemporaries—if at all—in periodical articles which are far too numerous to list here.)Google Scholar
  7. Sarasa, Alphons Antoine de: solutio problematis a R.P. Marino mersenno minimo propositi: datis tribus quibuscunque magnitudinibus rationalibus vel irrationalibus, datisque duarum ex illis logarithmis, tertiae logarithmum geometrice invenire, Antwerp, 1649.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Derek Thomas Whiteside
    • 1
  1. 1.St. Catharine's CollegeCambridgeEngland

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