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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... these three Objects in view . 1. To give the general Principles and Rules of the Science , in the shorteft , and , at the fame time , the most clear and comprehenfive manner that was poffible . Agreeable to this , though every Rule is ...
... these three Objects in view . 1. To give the general Principles and Rules of the Science , in the shorteft , and , at the fame time , the most clear and comprehenfive manner that was poffible . Agreeable to this , though every Rule is ...
Página 8
... These are called compound quantities : a fimple quantity confifts of one term only , as + a , or + ab , or + abc . The other symbols and definitions neceffary in Algebra fhall be explained in their proper places . CHA P. II . OF ...
... These are called compound quantities : a fimple quantity confifts of one term only , as + a , or + ab , or + abc . The other symbols and definitions neceffary in Algebra fhall be explained in their proper places . CHA P. II . OF ...
Página 9
... be added together , first add the positive together into one fum , and then the negative ( by Cafe I. ) Then add these two fums together ( by Cafe II . ) B 4 EX- EXAMPLE . + 8a - 7a + 10a 120 Sum CHAP . 2 . 9 ALGEBRA .
... be added together , first add the positive together into one fum , and then the negative ( by Cafe I. ) Then add these two fums together ( by Cafe II . ) B 4 EX- EXAMPLE . + 8a - 7a + 10a 120 Sum CHAP . 2 . 9 ALGEBRA .
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... of two , three , or more quantities , as abc , are faid to be of two , three , or more di- menfions ; and thofe quantities are called factors or roots . If all the factors are equal , then these pro- If CHAP . 4 . 35 ALGEBRA .
... of two , three , or more quantities , as abc , are faid to be of two , three , or more di- menfions ; and thofe quantities are called factors or roots . If all the factors are equal , then these pro- If CHAP . 4 . 35 ALGEBRA .
Página 12
... these pro- ducts are called powers ; as aa or aaa are pow- ers of a . Powers are expressed sometimes by placing above the root to the right - hand a figure expreffing the number of factors that produce them . Thus , a aa aaa aaaa ааааа ...
... these pro- ducts are called powers ; as aa or aaa are pow- ers of a . Powers are expressed sometimes by placing above the root to the right - hand a figure expreffing the number of factors that produce them . Thus , a aa aaa aaaa ааааа ...
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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 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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