coo 



Equation to the curve, when referred to its principal diumei<-.v>, 



A 8 7/2 



55 - T" 



And when the coordinates originate at the vertex, y* -^ (2 a # -f- 



Or #2 -- (^ 2 as), when the origin is at the centre. 

 Equation to the hyperbola, when referred to its asymptotes, is xy 

 ~jj , where y is parallel to the other asymptote. 



2 

 If the hyperbola is equilateral, xy . 



The general equation to an hyperbolic curve \&yx n =. a n + l 



Note. The general Equation to the Conic Sections, referred to their 

 axes is 



y* m x -f- w .r 2 , where in is the latus rectum, and the conic 

 section is a parabola, ellipse, or hyperbola, according as n = o t or is nega- 

 tive, or positive. 



CONTACT of Curves. (Higman.) 



Let there be two curves, whose equations are y / (x] t and y' 

 <p (#'), and suppose them (1) to have a point in common, so that when x 



x' t y y : (2) that x x' t y y>, and -^ +* : (3) that besides 



the preceding conditions -r | ^ 2 and so on ; then will the dis- 



tance between the curves be infinitely greater in the first case, than it is 

 in the second ; infinitely greater in the second than it is in the third j and 

 so on continually. 



CONTINUED Fractions. See Fractions. 



COORDINATES Polar, tnfind the relation between. (Higman.) 



If the relation between the rectangular coordinates A- and y in any 

 curve be given, that between the polar o?ies and ti may be determined j 

 and conversely. 



For x = cos. 8, and y sin. Oj substitute these values la the given 

 equation, and the polar one will be found. 



