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Select Bibliography of primary sources
B. Individual works 1. English
Barrow, Isaac: Euclidis Elementorum libri xv breviter demonstrata. Cantabrigiae, 1655.
Barrow, Isaac LM lectiones mathematicae xxiii in quibus principia matheseos generalia exponuntur ... habitae Cantabrigiae 1664–1666, London 1685.
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.
Barrow, Isaac Archimedis opera: Apollonii Pergaei conicorum libri iiii: Theodosii sphaerica: methodo nova illustrata et succincte demonstrata. London, 1675.
Briggs, Henry: AL arithmetica logarithmica, sive logarithmorum chiliades triginta. ... quorum ope multa perficiuntur arithmetica problemata et geometrica, London, 1624.
Briggs, Henry TB trigonometria britannica, sive de doctrina triangulorum libri duo, Gouda, 1633.
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).
Craig, John: methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi, London, 1685.
Craig, John tractatus mathematicus de figurarum curvilineorum quadraturis et locis geometricis, London, 1693.
Craig, John theologiae christianae principia mathematica, London, 1699.
Craig, John de calculo fluentium libri duo, London, 1718.
Duillier, Fatio de: lineae brevissimi descensus investigatio geometrica duplex. cui addita est investigatio geometrica solidi rotundi in quod minima fiat resistentia, London, 1699.
Gregory, David: exercitatio geometrica de dimensione figurarum, sive specimen methodi generalis dimetiendi quasvis figuras, Edinburgh, 1684.
Gregory, James: VCHQ vera circuli et hyperbolae quadratura, in propria sua proportionis specie inventa et demonstrata, Padua, 11667, 21668
Gregory, James GPU geometriae pars universalis, inserviens quantitatum curvarum transmutationi et mensurae, Padua, 1668.
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.
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.
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.
Halley, Edmund: Apollonii Pergaei conicorum libri octo, Oxford, 1710.
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.
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.
Kersey, John: The Elements of that Mathematical Art commonly called Algebra expounded in four Books, London, 1673.
Mercator, Nicolaus: Log logarithmotechnia, sive methodus construendi logarithmos nova, accurata et facilis, London, 1668.
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.
Napier, John: mirifici logarithmorum canonis descriptio ejusque usus ..., Edinburgh 1614.
Napier, John: mirifici logarithmorum canonis constructio et eorum ad naturales ipsorum numeros habitudines, Edinburgh, 1619.
Napier TV Napier Tercentenary Memorial Volume (ed. C. G. Knott), London, 1915.
Newton, Isaac: (A mass of unpublished mathematical manuscript exists in the Cambridge University Library, especially CUL Add. 3958–3964, 4000, 4004.)
Newton, Isaac: To resolve Problems by Motion. (October 1666.) (CUL Add. 3958.3: 48v–63v.)
Newton, Isaac: analysis per aequationes numero terminorum infinitas, London, 1711 (but written 1668/9).
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.)
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).
Newton, Isaac: MD methodus differentialis, London, 1704 (written c. 1675).
Newton, Isaac: tractatus de compositione locorum solidorum (c. 1675). (CUL Add. 3963.8/12/13).
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).
Newton, Isaac: tractatus de quadratura curvarum, London, 1704 (but written in 1691/2 as part of a projected treatise on geometry).
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.)
Newton, Isaac: regula differentiarum (c. 1692). (CUL Add. 3964.5, printed by D. C. Fraser, London, 1927.)
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.
Raphson, John: SR de spatio reali, seu Ente infinito conamen mathematico-metaphysicum (added to 2nd and 3rd editions of his analysis aequationum universalis).
Wallis, John: operum mathematicorum pars prima/altera, Oxford, 1657/6. Part 1 (1657) has
Wallis, John: MU mathesis universalis, seu opus arithmeticum. Part 2 (1656) includes: philogice et mathematice traditum, arithmeticam numerosam et speciosam aliague continens.
Wallis, John: AI arithmetica infinitorum, sive nova methodus inquirendi in curvilineorum quadraturam aliaque difficiliora matheseos problemata, and
Wallis, John: SC de sectionibus conicis nova methodus expositis tractatus.
Wallis, John: CE commercium epistolicum de quaestionibus quibusdam mathematicis habitum, Oxford, 1658.
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.
Wallis, John: mechanica, sive de motu tractatus geometricus. London, 1670/1.
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.
Wallis, John: Op opera omnia mathematica, Oxford, 1 (1695); 2 (1693); 3 (1699).
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.)
2. French
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.
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.)
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.)
Descartes, René: OE Oeuvres de Descartes (ed. Ch. Adam & P. tannery) (12 vols) Paris, 1897–1910.
Fermat, Pierre: OE Oeuvres de Fermat (ed. P. Tannery & Ch. Henry) (4 vols.) Paris, 1891–1912.
Fermat, Pierre: Op varia opera mathematica, Toulouse, 1679.
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.
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.
LaHire, Philippe de: Nouveaux Elémens des Sections Coniques, les Lieux géométriques, la Construction ou Affectation des Equations, Paris, 1679.
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.
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.
LaLouvère, Antoine de (Antonius Lalovera): veterum geometria promotu in septem de cycloide libris ..., Toulouse, 1660.
Pascal, Blaise: Essay pour les Coniques, Paris, 1640 (privately printed and circulated).
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.
Pascal, Blaise: Traité du Triangle arithmétique, avec quelques autres petits traités sur la mesme matière ..., Paris, 1665.
Pascal, Blaise: OE Oeuvres des Blaise Pascal (14 Vols.) (ed. L. Brunschvicg, P. Boutroux & F. Grazier), Paris, 1908–1925.
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.)
Viète, Francois (Franciscus Vieta): Op opera mathematica (ed. F.v. Schooten), Leyden, 1646.
3. Italian
Cavalieri, Bonaventura: GI geometria indivisibilibus continuorum nova quadam ratione promota, Bologna, 11635, 21653. exercitationes geometricae sex, Bologna, 1647.
Mengoli, Pietro: novae quadraturae arithmeticae, seu de additione fractarum, Bologna, 1651.
Mengoli, Pietro: via regia ad mathematicas per arithmeticam, algebram speciosam, planimetriam, Bologna, 1655.
Mengoli, Pietro: GS geometria speciosa, Bologna, 1659.
Mengoli, Pietro: circolo, Bologna, 1672.
Torricelli, Evangelista: opera geometrica, Florence, 1644.
Torricelli, Evangelista: opere (ed. G. Loria & G. Vassura), (4 vols.) Faenza, 1919/1944.
Torricelli, Evangelista: de in/initis spiralibus (manuscript printed by E. Carruccio, Pisa, 1955.)
4. German/Dutch
St. Vincent, Gregory (Gregorius a Sancto Vincentio): OG opus geometricum quadraturae circuli et sectionum coni, Antwerp, 1647.
Huygens, Christiaan: theoremata de quadratura hyperboles, ellipsis et circuli ex dato portionum gravitatis centro, Leyden, 1651.
Huygens, Christiaan: de circuli magnitudine inventa, Leyden, 1654.
Huygens, Christiaan: OE Oeuvres complètes (22 vols.), The Hague, 1888–1950.
Kepler, Johannes: nova stereometria doliorum vinariorum, Linz, 1615.
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.)
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.
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Communicated by C. B. Boyer and I. B. Cohen
To Michael Hoskin, without whom this would probably never have come to exist, with deepest thanks
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Whiteside, D.T. Patterns of mathematical thought in the later seventeenth century. Arch. Rational Mech. 1, 179–388 (1961). https://doi.org/10.1007/BF00327940
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DOI: https://doi.org/10.1007/BF00327940