(B) HISTORY OF ALGEBRA

(xviii)
Writers on Algebra

Diophantus, Arithmeticarum, Libri sex, .....about A.D. 360
(First edition of his writings; the best, 1670.)

Leonardo Bonacci,
(his works described in Cossali) .....1202

Lucas Paciolus, or de Burgo,
Summa de Arithmetica, etc. .....1494

Rudolf,
Algebra......1522

Stifelius,
Arithmetica Integra, etc. .....1544

Cardan,
Ars Magna quam vulgo Cossam vocant ......1545

Ferreus .....1545

Ferrari (first resolved biquadratic equations) .....1545

Tartalea,
Quesiti ed Inventioni diverse .....1546

Scheubelius,
Algebra Compendiosa .....1551

Recorde,
Whetstone of Wit .....1557

Peletarius,
De Occulta parte Numerorum .....1558

Buteo,
De Logistica .....1559

Ramus,
Arithmeticae Libri duo et totidem Algebrae .....1560

Pedro Nugnez or Nonnius,
Libro de Algebra, etc. .....1567

Josalin,
De Occula parte Mathematicorum .....1576

Bombelli .....1579

Clavius .....1580

Bernard Solignac,
Arith. Libri ii. et Algebrae totidem .....1580

Stevinus,
Arithmétique, etc. aussi l'Algèbre .....1585

Vieta,
Opera Mathematica .....1660

Folinus,
Algebra, sive Liber de Rebus Occultis .....1619

Van Ceulen .....1619

Bachet,
Diophantus cum Commentariis .....1621

Albert Girard,
Invention Nouvelle en Algèbre .....1629

Ghetaldus,
De Resolutione et Compositione Mathematica .....1630

Harriot,
Artis Analyticae Praxis .....1631

Oughtreed,
Clavis Mathematica .....1631

Herigonius,
Cursus Mathematicus .....1634

Cavalerius,
Geometria Indivisibilibus Continuorum, etc. .....1635

Descartes,
Geometria .....1637

Franciscus à Schooten, Florimond de Beaune, Erasmus Bertholinus, Joh. Hudde, F. Rabuel, James Bernoulli, John De Witt, &c. -- Commentators on Descartes.

Roberval,
De Recognitione Aequationum, &c. .....1640

De Billy,
Nova Geometricae Clavis Algebra ....1643

Renaldinus,
Opus Algebraicum .....1644

Pascal .....1654

Wallis,
Arithmetica Infinitorum .....1655;
Algebra .....1685

Slusius,
Mesolabum .....1659

Rhonius,
Algebra (translated into English) .....1659

Kinckhausen,
used as a textbook by Sir I. Newton .....1661

Sir Isaac Newton,
The Binomial Theorem .....1666

Frenicle,
Various papers in Mem. of French Acad. .....1666

Pell
(translated and improved Rhonius' Algebra) .....1668

James Gregory,
Exercitationes Geometricae .....1668

Mercator,
Logarithmotechnia ......1668

Barrow,
in Lectiones Geometricae .....1669

Kersey,
Elements of Algebra .....1673

Prescot,
Nouveaux Elémens de Mathématiques .....1675

Leibnitz,
in Leipsic Acts, etc. .....1677

Fermat,
in Varia Opera Mathematica .....1679

Bulliald,
Opus Novum ad Arithmeticam Infinitorum ......1682

Tschirnhausen,
in the Leipsic Acts .....1683

Baker,
Geometrical Key, &c. .....1684

Dr Halley,
in Philosophical Transactions .....1687 and 1694

Rolle,
Une Méthode pour la Résolution des Equations indéterminees ......1690

Raphson,
Analysis Aequationum Universalis .....1690

Dechales,
Cursus seu Mundus Mathematicus .....1690

De Lagny,
various pieces on Equations .....1692

Alexander,
Synopsis Algebraica .....1693

Ward,
Compendium of Algebra, .....1695;
Young Mathematician's Guide .....1706

De Moivre,
various Memoirs in Phil. Trans. .....1697-1730

Sault,
New Treatise of Algebra .....1698

Christopher,
De Constructione Aequationum .....

Ozanam,
Nouveaux Elémens d'Algèbre .....1702

Harris,
Lexicon Technicum .....1704

Guisnée,
Application de l'Algèbre à la Géométrie .....1705

Jones,
Synopsis Palmariorum Matheseos .....1706

Newton,
Arithmetica Universalis .....1707

L'Hôpital,
Traité Analytique des Sections Coniques .....1707

Reyneau,
Analyse Démontrée .....1708

Brooke Taylor,
Methodus Incrementorum .....1715

Stirling,
Lineae Tertii Ordinis .....1717;
Methodus Differentialis .....1730

Nicole,
On Cubic Equations, in Mém. Acad. Des Sciences .....1727

S'Gravesande,
Algebra .....1727

Wolfius,
Algebra: Cursus Mathematicus .....1732

Kirby,
Arithmetic and Algebra .....1735

James Gregory .....1736

Simpson,
Algebra, and various works .....1740, 1742

Saunderson,
Algebra, 2 vols. 4to .....1740

La Caille,
Algebra in Leçons de Mathématiques .....1741

De Gua,
On the Roots of Equations, in Mem. Acad. Des Sciences .....1741

Clairaut,
Elemens d'Algèbre .....1746

Maclaurin,
Algebra .....1747

Fontaine,
L'Art de Résoudre les Equations .....1747

Donna Maria Caetana Agnesi,
Instituzioni Analitichi .....1748

Boscovich,
in Elementa Universae Matheseos .....1754

Segner,
Berlin Mem. .....1756

Castillon,
Arithmetica Universalis Newtoni cum Commentario .....1761

Emerson,
Algebra, etc. .....1763

Landen,
Residual Analysis, etc. .....1764

Lagrange,
Traité de la Résolution des Equations Numériques, Recueil des Mém. De l'Acad. De Berlin .....1767
Ditto, republished with Notes, Paris .....1797

Euler,
Algebra .....1770

Waring,
Meditationes Algebraicae, etc. .....1770, 1776

Soladini,
Compendio d'Analisi .....1775

Paoli,
Elementi d'Algebra .....1794

Ruffini,
Teoria delle Equazione Algeb. .....1799

Budan,
Nouvelle Méthode pour la Résolution des Equations Numériques .....1807

Gompertz,
Principles and Application of Imaginary Quantities .....1817 and 1818

Biot,
Gergonne's Annales, vol. vi

Horner,
Philos.Trans. .....1819

Dandelin,
Mém. de l'Acad. Roy. De Bruxelles .....1828

Swinburne and Tylecote,
on the Binomial Theorem .....1827

Warren,
on the geometric Representation of the Square Roots of Negative Quantities .....1828

Abel,
Mémoire sur les Equations Algébriques, Christiania .....1828
and in Crelle, vol. i.4.

Fourier,
Analyse des Equations Determinées (posthumous), with preface by Navier .....1831

Malfatti,
Mem. della Soc. Ital., vol. xi

Davies Gilbert,
Philos. Trans. .....1831

Sturm,
Mém. présentés par les Savans Etrangers .....1835

Lockhart,
Resolution of Equations .....1837


To the preceding list of writers, which contains almost all of an early date, the following are to be added:

Arbogast, Calcul des Dérivations.

The Bernoullis, Begnalt, Bertrand, Bezout (Cours des Mathématiques), Bossuet, Burja, Brunacci, Babbage, Bridges, Bland, Budan, Bonnycastle, Bourdon, Barlow (on the Theory of Numbers), Baltzer (on Determinants).

Cousin, Cauchy, Coignet, Carnot, Cayley, Cockle.

Degraave, Ditton Dodgson (on Determinants).

Frisius, Francoeur, Frend.

Gauss, Disquisitiones Arithmeticae, 1801.

Hemischius, Hales, Hirsch, Hutton, Holdred, Horner, Hargreaves.

Kuhnius, Kramp, Kaestner.

Laloubre, Lorgna, Le Blonde, Lee, Lacroix, Ludlam, Legendre (on the Theory of Numbers), L'Huillier, Leroy.

Mescher, Malebranche, Manfredi, Maseres, Murphy.

Nicholson, Nieuwentijdt (Analysis Infinitorum).

Polleti, Poignard (on Magic Squares), Playfair.

Rowning, Reimer.

Suremain-Missery (on Impossible Quantities), Schonerus, Salignut, Sturm, Serret, Salmon Sylvester.

Trail, Tedenat, Thacker.

Vilent, Vandermonde.

Warren, Wells, Wilson, Wood, Woodhouse.

Young.

Elementary Treatises of Bryce, Colenso, De Morgan, Hind, Kelland, Peacock, Todhunter.


Writers on the History of Algebra

Wallis, in his Algebra; Maseres, Scriptores Logarithmici, 1791, Montucla, in Histoire des Mathématiques; Bossuet, Histoire des Mathématiques; Cossali, Origine. Trasporto in Italia, e Primi Progressi in Essa dell' Algebra, 2 vols. printed in 1797; Hutton, in his Dictionary, and more diffusely in his Tracts, vol. ii.; Libri Histoire des Sciences Mathématiques en Italie, Paris 1838.
Terquem, Bulletin de Bibliographie.
Peacock, Report of British Association, 1833.

For the titles of works on Algebra, consult Murhard, Bibliotheca Mathematica; and for Memoirs on Algebra, in Academical Collections, see Reuss, Repertorium Commentationum, tom. vii.; Smith (on the Theory of Numbers), Brit. Assoc. 1859-60, 1862-63. (A. W.)





Read the rest of this article:
Algebra - Table of Contents



The above article was written by: Philip Kelland, M.A., F.R.S., F.R.S.E.; Professor of Mathematics in the University of Edinburgh; author of Algebra: A Complete and Easy Introduction to Analytical Science and Introduction to Quarternions.