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 250
... parallel with it in the line AB ; fo that the in- dex of x in any fquare may exprefs its distance from the line AB , and the index ofy in any fquare fquare may exprefs its diftance from the lime AC . 250 PART IL A TREATISE of.
... parallel with it in the line AB ; fo that the in- dex of x in any fquare may exprefs its distance from the line AB , and the index ofy in any fquare fquare may exprefs its diftance from the lime AC . 250 PART IL A TREATISE of.
Página 251
... parallels ; but al- fo in the terms taken in any oblique ftraight line whatever ; for in any fuch term it is ma- nifeft that the indices of y and x will be in arith- metical progreffion . The indices of y , because thofe terms will ...
... parallels ; but al- fo in the terms taken in any oblique ftraight line whatever ; for in any fuch term it is ma- nifeft that the indices of y and x will be in arith- metical progreffion . The indices of y , because thofe terms will ...
Página 255
... parallel to itself , all the terms which it will touch at once will be of the fame dimensions of y : for they will bear the fame proportion to one another as the terms in the line ZE themselves . The terms which the Ruler will touch ...
... parallel to itself , all the terms which it will touch at once will be of the fame dimensions of y : for they will bear the fame proportion to one another as the terms in the line ZE themselves . The terms which the Ruler will touch ...
Página 304
... parallel to the or- dinates PM , and equal to through D you ca , draw DF parallel to AN , DF will be the locus . required . Where you are to take AD on the fame fide of the line AE , with PN , if bx and cd have the fame fign , but on ...
... parallel to the or- dinates PM , and equal to through D you ca , draw DF parallel to AN , DF will be the locus . required . Where you are to take AD on the fame fide of the line AE , with PN , if bx and cd have the fame fign , but on ...
Página 305
... parallel to itself come to touch it in the point N ; then the two points of interfection , M and m , go into one point of contact N. If PM ftill move on parallel to itfelf , the points of interfection will , beyond N , become imaginary ...
... parallel to itself come to touch it in the point N ; then the two points of interfection , M and m , go into one point of contact N. If PM ftill move on parallel to itfelf , the points of interfection will , beyond N , become imaginary ...
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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.