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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... those curves , in general® II . Of the Conftruction of quadratic equa- tions , and the Properties of the lines 296 of the fecond order 324 III . Of the Conftruction of cubic and biqua- dratic equations 351 APPENDIX .... De Linearum ...
... those curves , in general® II . Of the Conftruction of quadratic equa- tions , and the Properties of the lines 296 of the fecond order 324 III . Of the Conftruction of cubic and biqua- dratic equations 351 APPENDIX .... De Linearum ...
Página 37
... only can be negative when its exponent is an odd number , though the quantity to be involved be negative .. The pow- ers of + a2 , — a3 , + a * , — a3 , -a are -a , D 2 & c . & c . Those whofe exponents are 2 , 4 CHAP . 7 . 37 ALGEBRA .
... only can be negative when its exponent is an odd number , though the quantity to be involved be negative .. The pow- ers of + a2 , — a3 , + a * , — a3 , -a are -a , D 2 & c . & c . Those whofe exponents are 2 , 4 CHAP . 7 . 37 ALGEBRA .
Página 38
... Those whofe exponents are 2 , 4 , 6 , & c . are pofitive ; but thofe whofe exponents are 1 , 3 , 5 , & c . are negative . $ 42 . The involution of compound quantities is a more difficult operation . The powers of any binomial a + b are ...
... Those whofe exponents are 2 , 4 , 6 , & c . are pofitive ; but thofe whofe exponents are 1 , 3 , 5 , & c . are negative . $ 42 . The involution of compound quantities is a more difficult operation . The powers of any binomial a + b are ...
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... those of increase in the contrary order , 0 , 1 , 2 , 3 , 4 , 5 , 6 . And the fum of their exponents in any term is always 6 . $ 45 . To find the coefficient of any term , the coefficient of the preceding term being known ; you are to ...
... those of increase in the contrary order , 0 , 1 , 2 , 3 , 4 , 5 , 6 . And the fum of their exponents in any term is always 6 . $ 45 . To find the coefficient of any term , the coefficient of the preceding term being known ; you are to ...
Página 55
... those quantities are called Arithmetical proportionals ; as the numbers 3 , 7 , 12 , 16. And the quan- tities , a , a + b , e , e + b . But quantities form a feries in arithmetical proportion , when they " increafe or decrease by the ...
... those quantities are called Arithmetical proportionals ; as the numbers 3 , 7 , 12 , 16. And the quan- tities , a , a + b , e , e + b . But quantities form a feries in arithmetical proportion , when they " increafe or decrease by the ...
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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...
Página 43 - The general Theorem vhich we gave for the Involution of binomials will' ferve alfo for their Evolution ;" becaufe to extract any root of a given quantity is the fame thing as to raife that quantity to a power whofe exponent is a fraction that has...
Página 61 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.