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the Philofopliical Tranfaftions tlie confti-u(!lioii of cubic and 

 biquadratic equations, by a parabola and circle, with im- 

 provements of the methods of Des Cartes, Baker, &c. ; and 

 alfo a memoir on the nvunbcr of the roots of equations, 

 with their limits and figns. M. RoTle, in 1690, publilhed 

 in 4to, " Traitc d'AIgebre ;" in 1699, " Une methode 

 pour refoudre les queilions iiidetermine'es ;" and in 1 704, 

 " Memoirs fur I'inverfe des Tangents," and fome other 

 pieces. Jofeph Raphfon, in 1690 publifhed his " Ana- 

 lyfis ^quationum Univerfalis," which is a general me- 

 thod of approximating to tlic roots of equations in num- 

 bers. His " Hillory of Fluxions" was publilhed in Eng- 

 lilh and Latin in 1715. Dechales publilhed his " Curlus 

 feu Mundus Mathematicus," in 4 vols, folio, in 1690. 

 About the year 1691, &c. De Laguy publiHied many 

 pieces on the refolution of equations in numbers ; and in 

 1693 appeared a little volume, entitled, " Synopfis Alge- 

 braica, opus poilhumum Joluuinis Alexar.dri." An inge- 

 nious tratt on the numeral extraction of all roots, without 

 any previous reduction, was communicated in the Philofo- 

 yhical TraufaClion, by Dr. Halley in 1694. This traCt is 

 annexed to fome editions of Newton's Univerfal Arith- 

 metic. Craig publifhed, in 1694, in 410, his treatile, " Dc 

 fig. curvil. quadraturis et loeis gcometricis," in which he 

 propofed new tormulse for the conlhuttion of equations : 

 and this method was improved by Herman in 1737, in 

 Mem. of Peterlburgh. Mr. John Ward of Chcfter, pub- 

 hflied in 1C95, " A Compendium of Algebra ;" and in 

 1 706, the tirft edition of " The Young Mathematician's 

 Guide," which has been much ufed. In 1696 the " Ana- 

 lyfe des Infmimcnt Petits," of the Marquis de I'Hopital, 

 was pubhihed, and a poilhumous treatife by the fame au- 

 thor, entitled, " Traitc Analytique des SeClions Coniques, 

 ct le Conllruftion des lieux Geometriques," was publiflied 

 in 1707. Mr. Ab. DcmoivTe, in 1697, and fueceeding 

 years, furnillied the Philofophical Tranfaftions with various 

 papers, containing improvements in algebra: in 1697, a 

 method of raifmg an infinite multinomial to any power, or 

 extratting any root of the fame; in 1698, the extraftion 

 of the root of an infinite equation; in 1707, an analvtical 

 fohition of certain equations of the 3d, 5th, 7th, &c. de- 

 grees ; in 1722, of algebraic fraftions, and recurring leries ; 

 in 173B, the reduftion of radicals into more fimple forms ; 

 and in 1730 he publilhed " Mifcellanea Analyticade Serie- 

 bus et Qviadraturis," containing great improvements in 

 feries, &e. Mr. Richard Sank publilhed, in 4to, " A new 

 Treatife of Algebra, applied to numei'al queftions, and 

 geometry ; with a converging feries for all manner of ad- 

 fe£led equations," which feries is Raphfon's method of 

 approximation, which had been lately publilhed. In 1698 

 Hugo d'Omer publiflied his " Analyfis Geometrica, &c." 

 in which, by combining the algebraic analyfis of the mo- 

 derns with that of the ancients, he ixfolved in an elegant and 

 fimple manner may' curious problems. In 1699 Hyac.ChriliO- 

 pher pubhihed at Naples, in 4I0. a tract, entitled, " De 

 Conftruftione Equationum." Ozanam's algebra, contain- 

 ing the Diopbantine analyfis, was publifhed in 1702, his 

 mathematical didtlonary in 1691, and his courfe of niathe- 

 tics, in 5 vols. 8vo, in 1693. In 1705, Dr. Harris, the 

 author of the " Lexicon Technicum," publifhed a fmall 

 piece on algebra and fluxions. M. Guitnec publiflied, in 

 1705, his " Apphcation de I'Algcbre a la Gconietiie," in 

 4to. In 1706, Mr. Jones publiflied his " Synopfis Pal- 

 mariorum Mathcfeos," which is an ufeful compendium of 

 the m.athcmatical feiences ; and in 171 1, he publillied in 

 4to, a coUeftion of Sir Ifaac Newton's papers, entitled, 

 " AnAlyfis per quantitatum feries, fiuxioncs, ac differcn- 



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tias ; cum cnumerationc lincarum tertii ordinis." Tlie firfl 

 edition of Newton's " Aritlimetiea Univerfalis, five de 

 Compofitione et Refolutione Ariihmctica llbcr," was I'ub- 

 lifluxi by Wlullon in 1707; and many editions have been 

 publilhed fince. It is of courfe included in Horfley'u 

 edition of Newton's works. This treatife was the text 

 book of the author at Cambridge ; and though not de- 

 figned for publication, it contains many vei")' confidcrabic 

 improvements in analytics ; particularly in the nature and 

 tranfmutation of equations ; the limits of their roots ; the 

 number of impofTible roots ; the invention of divifors, both 

 furd and rational ; the relolution of problems, arithmetical 

 and geometrical ; the linear confirudtion of equations ; llic 

 approximation to the roots of all equations, S:c. Com- 

 mentaries have been publilhed on this work for the aihll- 

 ancc of beginners, by S'Gnivefande, Callilion, Wilder, &c. 

 ']"he " Analyfe Deniontree" of Reyneau, was publillied In 

 4to. in 1708, and in 1 71.1, "La Science du Caleiil," 

 and reprinted with additions in 1736, under the title of 

 " Ufagc de I'Analyfe," &c. In 1709 an Englifh tranfia- 

 tion of Alexander's algebra was publiflied, with an appen- 

 dix, by Humphry Ditton. in I 7 15, Dr. Brooke Taylor 

 publillied his valuable work, entitled, " Methodus Incre- 

 mentorum ;" and in the Philofophical Traufaclions for 1718- 

 an improvement of the method of approximating to the 

 roots of equations in numbers. M. Nicole, in 1717, com.- 

 mur.icated, in the Memoirs of the Academy of Sciences, a 

 traft on the calculation of finite differences, and in fol- 

 lowing years various other trafts on the fame fubjeft, and 

 alfo on the refolution of equations of the third degree, and 

 on the irreducible cafe in cubic equations. Ronay nc, in 1717, 

 publillied a treatife on algebra ; and in the fame year Mr. 

 James Stirling publilhed a work of improvement on analy- 

 tics, entitled, " Lineas tertii Ordinis;" and in 1730, "Me- 

 thodus Difierentialis ; five traiStatus de funimatione et inter- 

 polatione ferierum infinitarum ;" witli great improvements 

 on infinite feries. Maclaurin, in 1726 and 1729, gave, in 

 the Philofophical Tnmfadtions, trafts on the imaginary roots 

 of equations, and afterwards hi'i " Algebra," was publilhed 

 from his poilhumous papers, with its application to curve- 

 lines. S'Ciravefande's algebra, with a commentary on 

 Newton's Un. Aritlim. appeared in 1727 ; and in 1728 

 Mr. Campbell communicated, in the Philofophical Tranf. 

 an ingenious paper on the number of impolSble roots of 

 equations, and tiie papers of Maclaurin and Campbell v. ere 

 annexed to Gravefande's edition of the " Arithm. Univ." at 

 Lcyden in 1732. Lecchi, a Jefuit, publitlKd the "Arithm. 

 Un." with an imperfeft commentai-)-, in 3 vols. 8vo. iii 

 1752. Wolfius's algebra was publifhed in 1732, in his 

 " Elementa Mathefeos Univerfs." in 5 vols. 4to. Mr. 

 John Kirkby's arithmetic and algebra were pubhflied iiv 

 1735, and in 1 748 his doClrine of ultlm.ators. Several im- 

 provements in feries, and other parts of algebra, are con- 

 tained in Mr. Thomas Simpfon's " EfTays," publiflied in 

 1740, in his " Diflertations," 1743, ^"'^ '" '''^ trafts, 1757; 

 and alfo in his " Algebra," firll printed in 1745, '""^ '" 

 his " Seleft Exercifes," in 17J2. In 1740, Saunderfon's 

 " Elements of Algebra," were publiflied in 2 vols. 4to. 

 M. de la Caillc, publiflied in 1741, " Lemons de Matlieii.a- 

 tiques ; 011 Elemens d'AIgebre et Geometric ;" and in the 

 fame year M. de Gua, in the Memoirs of the Academy of 

 Sciences, communicated two articles on the number of po- 

 fitive, negative, and iniaglnaiy roots of equations, witii an 

 hillorical account of the improvements in algebra, in wliich 

 he feverely cenfures Wallis for his partiality, whilH he 

 himfelfis, at leaft, equally faulty. M. Clairaut publifhed 

 liis " Elemens d'AIgebre," in 1746, in which he has many 



improvements, 



