A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules and Operations. II. The Composition and Resolution of Equations of All Degrees; and the Different Affections of Their Roots. III. The Application of Algebra and Geometry to Each Other. To which is Added, an Appendix, Concerning the General Properties of Geometrical LinesF. Wingrave; T. Longman; W. Richardson; G. G. and J. Robinson; F. and C. Rivington; W. Lowndes; and Cadell and Davies., 1796 - 504 páginas |
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Página 368
... ; and the Different Affections of Their Roots. III. The Application of Algebra and Geometry to Each Other. To which is Added, Colin MacLaurin. J DE LINEARUM GEOMETRICARUM PROPRIETATIBUS GENERALIBUS . E lineis fecundi ordinis.
... ; and the Different Affections of Their Roots. III. The Application of Algebra and Geometry to Each Other. To which is Added, Colin MacLaurin. J DE LINEARUM GEOMETRICARUM PROPRIETATIBUS GENERALIBUS . E lineis fecundi ordinis.
Página 369
... ordinis , five fectionibus , conicis , Defcripferunt uberrime geometræ veteres & recen- tiores ; de figuris quæ ad fuperiores linearum ordines referuntur pauca & exilia tantum ante NEWTONUM tradiderunt . Vir illuftriffimus , in Tractatu ...
... ordinis , five fectionibus , conicis , Defcripferunt uberrime geometræ veteres & recen- tiores ; de figuris quæ ad fuperiores linearum ordines referuntur pauca & exilia tantum ante NEWTONUM tradiderunt . Vir illuftriffimus , in Tractatu ...
Página 370
... ordinis proprietates generales a New- tono traditæ parallelarum fegmenta & afymptotos ple- ræque fpectant . Alias harum affectiones quafdam di- verfi generis breviter indicavimus in tractatu de fluxi- onibus nuper edito , Art , 324 ...
... ordinis proprietates generales a New- tono traditæ parallelarum fegmenta & afymptotos ple- ræque fpectant . Alias harum affectiones quafdam di- verfi generis breviter indicavimus in tractatu de fluxi- onibus nuper edito , Art , 324 ...
Página 371
... ordinis & defignat lineam five locum primi ordinis , quæ quidem femper recta eft . Sumatur enim Fig . 2 . in ordinata PM recta PN ita ut PN fit ad AP ut + a ad unitatem ; conftituatur AD parallela ordinatæ PM æqualis ipfib , & ducta DM ...
... ordinis & defignat lineam five locum primi ordinis , quæ quidem femper recta eft . Sumatur enim Fig . 2 . in ordinata PM recta PN ita ut PN fit ad AP ut + a ad unitatem ; conftituatur AD parallela ordinatæ PM æqualis ipfib , & ducta DM ...
Página 372
... ordinis ex . gr . oc- currit abfciffæ AP cum fx3 - gx2 + bx - ko , cujus æquationis fi tres radices fint reales abfciffa fecabit cur- vam in tribus punctis . Similiter in æquatione generali cujufcunque ordinis index altiffimus abfciffæ ...
... ordinis ex . gr . oc- currit abfciffæ AP cum fx3 - gx2 + bx - ko , cujus æquationis fi tres radices fint reales abfciffa fecabit cur- vam in tribus punctis . Similiter in æquatione generali cujufcunque ordinis index altiffimus abfciffæ ...
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adeoque affumed afymptote alfo alſo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently conic fection contactus Corol cube cubic equation curvæ curvam curvature demonftrated dimenfions divided divifor drawn ducantur ducta enim equa equal erit expreffed fame manner fame right line fecond term feries fhall fide figns fimple equations fince firft firſt flexus fome fquare root fubftitute fubtract fuch fuppofe furd greateſt harmonical mean impoffible interfections laft term laſt leaft lefs lineæ locus meet the curve metical multiplied muſt negative occurrat parallel pofitive PROP propofed equation puncto punctum px² quadratic equation quæ quævis quotient recta rectæ refolved refult Rule ſhall ſuppoſe tangents tertii ordinis thefe theſe third order thofe tion touching the curve unknown quantity vaniſh whence whoſe
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Página 88 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Página 431 - APM, cut a geometrical line of any order in as many points as it has dimensions, the product of the segments of the first terminated by P and the curve, will always be to the product of the segments of the latter, terminated by the same point and the curve, in an invariable ratio.
Página 426 - And by iimilar equations geometrical lines of fuperior orders are defined. § 2. A geometrical line may meet a right line in as many points as there are units in the number which denotes the order of the equation or line, and never in more. The number of times that any curve will meet its...
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