This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1877 Excerpt: ...equation in 2 will have one root z zero when its absolute term vanishes, i, e., when fi(/i) = o; it has two roots aero when we have in addition vfjQi) +/i(m) = 0 i anl so on. Again, if two of the roots be infinite, we hare in addition v/, '00 +/.00 = o. (4) Accordingly, when the values of /u and v are determined so as ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1877 Excerpt: ...equation in 2 will have one root z zero when its absolute term vanishes, i, e., when fi(/i) = o; it has two roots aero when we have in addition vfjQi) +/i(m) = 0 i anl so on. Again, if two of the roots be infinite, we hare in addition v/, '00 +/.00 = o. (4) Accordingly, when the values of /u and v are determined so as to satisfy-the two preceding equations, the corresponding line y = fix + v meets the curve in two points in infinity, and consequently is an asymptote. (Salmon's "Conic Sections," Art. 154.) Hence, if he a root of the equation / (ji) = o, the line is in general an asymptote to the curve. If /i(ju) = o and /o(u) = o have a common root (//, suppose), the corresponding asymptote in general through the origin, and is represented by the equation V = jUl In this case un and evidently have a common factor. The exceptional case when fo'(n) vanishes at the same time will be considered in a subsequent Article. To each root of /o(ju) = o corresponds an asymptote, and accordingly, every curve of the nth degree has in general n asymptotes, real or imaginary. From the preceding it follows that every line parallel to an asymptote meets the curve in one point at infinity. This also is immediately apparent from the geometrical property that a system of parallel lines may be considered as meeting in the same point at infinity--a principle introduced by Desargues in the beginning of the seventeenth century, and which must be regarded as one of the first important steps in the progress of modern geometry. Cor. No line parallel to an asymptote can meet a curve of the nth degree in more than (--1) points besides that at infinity. Since every equation of an odd degree has one real root, it follows that a curve of an odd degree has one real Metho...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
