518 people, of whom no memorial remains but some of their attainments in science T Writers on Algebra. Diophantus, Arithmctico- rum Libri sex, about A.D. 360 (First edition of his writ ings, 1575 ; the best, 1670.) Leonardo Bonacci (his works described in Cossali) 1202 Lucas Paciolus, or De Burgo, Summa de Arithmetica, &c 1494 Rudolff, Algebra 1522 Stifelius, Arithmetica In tegra, &c 1544 Cardan, Ars Magna quam vulgo Gossam vacant 1545 Ferreus 1545 Ferrari (first resolved bi quadratic equations) 1545 Tartalea, Quesiti ed Inven- tioni diverse 1546 Scheubelius, Algebra Com- pendiosa 1551 Recorde, Whetstone of Wii 1557 Peletarius, De Occulta parte Numerorum 1558 Buteo, De Logistica 1559 Uamus, Arithmeticae Libri duo ct totidem Algebrae...l5QO Pedro Nugnez or Nonnius, Libro de Algebra, &c. ...1567 Jossalin, De Occulta parte Mathematicorum 1576 Bonibelli 1579 Clavius 1580 Bernard Solignac, Arith. Libri ii. ct Algcbiae toti dem ..1580 Stevinus, Arithmetique, <kc. aussi V Algebre 1585 Vieta, Opera Mathematica, 1600 Folinus, Algebra, sive Liber de Rebus Occultis 1619 VanCeulen 1619 Bachet, Diophantus cum Commentariis 1621 Albert Girard, Invention Nouvelle en Algebre 1629 Ghetaldus, De Resolutionc et Compositione Mathema tica 1630 Harriot, Artis Analytical Praxis 1631 Oughtreed, Clams Matl<,e- matica 1631 Herigonius, Cursus -i athe- maticus 1634 Cavalerius, Geometria In- divisibilibus Continuo- rum, <Lc 1635 Descartes, Geometria 1637 Franciscus a Schooten, Florimond de Beaune, Erasmus Berthol inus, Joh. Hudde, F. Rabuel, James Bernoulli, John de Witt, &c. Commentators on Descartes. Roberval, De Recognitions Aequationum, &c 164( De Billy, Nova Gcometricae Clavis Algebra 1643 Renaldinus, Opus Algebrai- cum 164< Pascal 1654 Wallis, Arithmetica Infini torum, 1655 ; Algebra, 1685 Slusius, Mesolabum 1659 Rhonius, Algebra (trans lated into English) 1659 Kinckhausen, used as a text book by Sir I. Newton... 1661 Sir Isaac Newton, The Bi nomial Theorem 1666 ^renicle, Various papers in Mem. of French Acad. ...1666 il (translated and im proved Rhonius Algebra) 1668 fames Gregory, Exercita- tiones Geometricae 1668 Hercator, Loganthmotcch- nia 1668 3arrow, in Lcctiones Geo metricae 1669 Jersey, Elements of Algcbral673 Prescot, Nouvcaux EUmens de MaUiAmatiques 1675 Leibnitz, in Leipsic Acts, &c 1677 Furmat, in Varia Opera Mathematica 1679 liulliald, Opus Novum ad Arithmeticam Infinito rum 1682 Tschirnhausen, in the Leip sic Acts 1683 Saker, Geometrical Key, &c. 1684 Dr Halley, in Philosophical Transactions ...1687 and 1694 Rolle, Une Mcthode pour la Resolution dcs Equations Ind&terminees 1690 Raphson, Analysis Aequa tionum Universalis 1690 Dechales, Cursus scu Mun- dus Mathematicus 1690 De Lagny, various pieces on Equations 1692 Alexander, Synopsis Alge- braica 1693 Ward, Compendium of Algebra, 1695 ; Young Mathematician s Guide 1706 De Moivre, various Memoirs in Phil. Trans. ...1697-1730 Sau It, New Treatise of Algebra 169& Christopher, De Construc- tionc Aequationum Ozanam, Nouveaux Elemens d Algebre 1702 Harris, Lexicon Technicum 1704 Guisnee, Application de V Algebre, a la Gemn6trie..l705 Jones, Synopsis Palmari- orum Mathcseos 1706 Newton, Arithmetica Uni versalis 1707 L Hopital, Traite Analy- tique des Sections Coniques 1707 Reyneau, Analyse Dlmontrle~L7Q8 Brooke Taylor, Methodus Incrementorum 1715 Stirling, Lineae Tertii Ordinis, 1717 ; Methodus Differentialis 1730 Nicole, On Cubic Equations, in Mlm. Acad. des Sciences 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 Lemons de Mathematiques 1741 De Gua, On the Roots of Equations, in M6m. Acad. des Sciences ... 1741 Clairaut, EUmcns d Al gebre .......................... 1746 Slaclaurin, Algebra ......... 1747 Fontaine, L Art de Resoudre les Equations ............... 1747 Donna Maria Gaetana Ag- nesi, Instituzioni Anali- tichi ........................... 1748 Boscovich, in Elementa Universae Matheseos ...... 1754 Segner, Berlin Mem .......... 1756 Jastillon, Aritkmetica Uni- ver salts Newtoni cum Commentario ............... 1761 Emerson, Algebra, &c ....... 1763 Landen, Residual Analysis, &c ............................ 1704 Lagrange, Traite de la Rl- solutioii dcs Equations Numeriques, Recucil dcs Mem. de I Acad. de Berlin ........................ 1767 Do. republished with Notes, Paris ......... 1797 Euler, Algebra ............... 1770 Waring, Afeditationss Alge- braicae, &c .......... 1770, 1776 Soladini, Compendia d Ana- lisi ........................... 1775 Paoli, Elementi d Algebra ..1794 Rufiini, Teoria delle Equa- zione Alcjeb ....... ........ 1799 [HISTORY. Budan, Noui-clle Mithode pour la Resolution des Equations Numeriqucs ...1807 Gompertz, Principles and Application of Imaginary Quantities 1817 and 1818 Biot, Gergonne s Annales, vol. vi. Homer, Philos. Trans 1819 Dandelin, Mem. de I Acad. Roy. deBruxelles 1826 Swinburne and Tylecote, oji the Binomial Theorem 1827 Warren, on the Geometric Representation of tlie Square Roots of Negative Quantities 182S Abel, Memoire sur les Equations Algebriqucs, Christiania 1829 and in Crelle, vol. i. 4. Fourier, Analyse des Equa tions Determines (post humous), with preface by Navier 1831 Malfatti, Mem. della Soc. ItaL, vol. xi. Davies Gilbert, Philos. Trans 1831 Sturm, Mem. presentcs par les Savons Strangers 1835 Lockhart, Resolution of Equations 1837 To the preceding list of ivriters, which contains almost ,all of an early date, the following are to be added: Arbogast, Calcul des Dirivations. The Bernoullis, Begnalt, Ber- trand, Bezout (C ours dcs Mathe matiques), Bossuet, Burja, Brunacci, Babbage, Bridges, Bland, Budan, Bounycastle, Bourdon, Barlow (on the Theory of Numbers), Baltzer (on Determinants). Cousin, Cauchy, Coignet, Car- not, Cayley, Cockle. Degraave, Ditton, Dodgson (on Determinants). Frisius, Francoeur, Frend. Gauss, Disquisitiones Arithmc- ticae, 1801. Hemisclrius, Hales, Hirsch, Mutton, Holdred, Horner, Hargreaves. Kuhnius, Kramp, Kaestner. Laloubre, Lorgna, Le Blonde, Lee, Lacroix, Ludlam, Le- gendre (on the Theory of Numbers), L Huillier, Leroy. Mescher, Malebrauche, Manfredi, Maseres, Murphy. Nicholson, Nieuwentijdt, (Ana lysis Infinitorum). Polleti, Poignard (on Magic Squares), Playfair. Ilowning, Reimer. Suremain-Missery (on Impossible Quantities), Schonerus, Salig- nut, Sturm, Serret, Salmon, Sylvester. Trail, Tedenat, Thacker. Vilent, Vandermoude. Warren, Wells, Wilson, Wood, Woodhouse. Young. Elementary Treatises of Bryce, Colenso, De Morgan, Hind, Kclland, Peacock, Todhunter. Writers on the History of Algebra. Wallis, in his Algebra; Maseres, Scriplorcs Logarithm-id, 1791, Moutucla, in Histoire des Mathematiques; Bossuet, Ilis- toire des Mathematiques; 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 Mathematiques en Italic, Paris 1838. Terquem, Bulletin de Biblio graphic. Peacock, Report of British Association, 1833. For the titles of works on Algebra, consult Murhard, Bibliotlieca Mathematics; and for Memoirs on Algebra, in Academical Collections, see Reuss, Repertorium Cowmen- tationum, torn. vii. ; Smith (on the Theory of Numbers), Brit. Assoc. 1859-60, 1862-63. NOTATION AND FIRST PRINCIPLES. 1. In arithmetic there are ten characters, which being variously combined, according to certain rules, serve to denote all numerical magnitudes whatever. But this me
thod of expressing quantities (a phrase used to designate
