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 307
... punctum du- plex in the curve , " two of its arcs interfecting each other there ; or , " fome oval that belongs to that kind of curve becoming infinitely little in M , it vanishes into what is called a punctum conjugatum . " If , in the ...
... punctum du- plex in the curve , " two of its arcs interfecting each other there ; or , " fome oval that belongs to that kind of curve becoming infinitely little in M , it vanishes into what is called a punctum conjugatum . " If , in the ...
Página 314
... punctum duplex . This locus is a line of the third order , BK is its afymptote , and it has a nodus betwixt A and D. If you fuppofe to vanish in the equation , fo that cy2xy = x , then will A and D coin- N K M A P R B m cide , and the ...
... punctum duplex . This locus is a line of the third order , BK is its afymptote , and it has a nodus betwixt A and D. If you fuppofe to vanish in the equation , fo that cy2xy = x , then will A and D coin- N K M A P R B m cide , and the ...
Página 315
... punctum conjugatum in A , because when y vanishes , two values of x vanish , and the third becomes equal to Bb or AD . The whole M A DP m curve befides this point A , lies between DQ and BK . These are demonftrated af- ter the fame ...
... punctum conjugatum in A , because when y vanishes , two values of x vanish , and the third becomes equal to Bb or AD . The whole M A DP m curve befides this point A , lies between DQ and BK . These are demonftrated af- ter the fame ...
Página 320
... punctum du- plex . If AP be taken greater than AB , then fhall there be two values of y , as before , having contrary figns , that value which was pofitive before being now become negative , and the ne- gative value being become ...
... punctum du- plex . If AP be taken greater than AB , then fhall there be two values of y , as before , having contrary figns , that value which was pofitive before being now become negative , and the ne- gative value being become ...
Página 376
... punctum A. Quoniam igitur evanefcente y evanefcat quoque x , ul- timus æquationis terminus , in hoc cafu , erit fx3 - gx2 + b hx = fx X xx - gx f - + 3 / از + 7 = fxxx- g + 2f b - gg Aff ( fi fumatur Aa verfus P æqualis , & ad punctum ...
... punctum A. Quoniam igitur evanefcente y evanefcat quoque x , ul- timus æquationis terminus , in hoc cafu , erit fx3 - gx2 + b hx = fx X xx - gx f - + 3 / از + 7 = fxxx- g + 2f b - gg Aff ( fi fumatur Aa verfus P æqualis , & ad punctum ...
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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
Pasajes populares
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.