 | Charles Davies - 1836 - 296 σελίδες
...a line of the second order is tx ( '' and the equation of the normal Of Asymptotes of Curves. 125. An asymptote of a curve is a line which continually...infinite distance from the origin of co-ordinates. Let AX and AY be E the co-ordinate axes, and ///B the equation of any tangent line, as TP. • If in... | |
 | Charles Davies - 1838 - 300 σελίδες
...a line of the second order is ,, yy'= and the equation of the normal Of Asymptotes of Curves. 125. An asymptote of a curve is a line which continually...infinite distance from the origin of co-ordinates. Let AX and AY be the co-ordinate axes, and the equation of any tangent line, as TP. If in the equation... | |
 | Elias Loomis - 1851 - 296 σελίδες
...this ratio when the increment is equal to zero, and representing the segment by s, we have or , ds= , which is the differential of the area of a segment...becomes infinite, this distance is infinite. In other ourves, even when the abscissa becomes infinite, the tangent cuts the axes at a finite distance from... | |
 | Elias Loomis - 1851 - 300 σελίδες
...have or r'dt '' 2 ' which is the differential of the area of a segment of a polar curve. ASYMPTOTES OP CURVES. (259.) An asymptote of a curve is a line which...infinite distance from the origin of co-ordinates. In some curves the distance between the origin of the coordinates and the point in which the tangent... | |
 | Albert Ensign Church - 1851 - 318 σελίδες
...are called asymptotes of the hyperbola ; and in general, an asymptote of a curve is a line, ivhich continually approaches the curve and becomes tangent to it at an infinite distance. By an inspection of the figure, it is readily seen that the asymptotes of the hyperbola are the diagonals... | |
 | Albert Ensign Church - 1854 - 322 σελίδες
...enjoys the same property. These two lines are called asymptotes of the hyperbola ; and in general, an asymptote of a curve is a line, which continually...and becomes tangent to it at an infinite distance. By an inspection of the figure, it is readily seen that the asymptotes of the hyperbola are the diagonals... | |
 | Charles Davies - 1855 - 330 σελίδες
...tangent to a line of the second order is yy= and the equation of the normal Of Asymptotes of Curves. 125. An asymptote of a curve is a line which continually...approaches the curve, and becomes tangent to it at art infinite distance from the origin of co-ordinates. Let AX and AY be the co-ordinate axes, and the... | |
 | Elias Loomis - 1856 - 300 σελίδες
...equal tn /.ero. representing the segment by s, and the measuring arc by t, we have or. ds= r'dt 2 ' which is the differential of the area of a segment...infinite distance from the origin of co-ordinates. In some curves the distance between the origin of the.coordinates and the point in which the tangent... | |
 | Albert Ensign Church - 1857 - 324 σελίδες
...enjoys the same property. These two lines are called asymptotes of the hyperbola ; and in general, an asymptote of a curve is a line, which continually...and becomes tangent to it at an infinite distance. By an inspection of the figure, it is readily seen that the asymptotes of the hyperbola are the diagonals... | |
 | William Guy Peck - 1875 - 226 σελίδες
...parallelogram on the axes are asymptotes to both curves. 67. An asymptote to a curve is a line that continually approaches the curve, and becomes tangent to it at an infinite distance. The equations of the diagonals CP and CQ may be written, y=± b -x... (1) Squaring both members, we... | |
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CURVES. (259.) An asymptote of a curve is a line which continually approaches the curve, and becomes tangent to it at an infinite distance from the origin of co-ordinates. 
