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" In the one, a system of points being given on a right line, 

 in the other we shall have as many planes, cutting in the 

 same right line. 



"■ In the one, a system of points being given on a plane, in 

 the other we shall have as many planes, passing through the 

 same fixed point. 



" In the one, the points of intersection of a plane curve with 

 a right Hue being given, in the other we shall have as many 

 tangent planes to the same conic surface, all meeting in a 

 right Hue passing through the vertex. 



" In the one, a number of points being common to two or 

 more plane curves, situate in the same plane ; in the other we 

 shall have as many tangent planes to two or more cones having 

 the same vertex. 



" In the one, a system of points being given on the same 

 curved surface ; in the other we shall have an equal number 

 of tangent planes to its reciprocal surface. 



" In the one, the intersection of a surface with a plane being- 

 given ; in the other we shall have a cone circumscribing the 

 reciprocal surface. 



" In the one, the points where a curved surface is met by a 

 right line being given ; in the other, we shall have as many 

 tangent planes to the reciprocal surface, cutting in the same 

 right line. 



" In the one, points being common to three or more curved 

 surfaces, we shall have as many tangent planes in the other, 

 common to as many reciprocal surfaces. 



" In the one, a system of points being given on a curve of 

 double curvature, so many planes will be in the other, tangents 

 to the same developable surface. 



" In the one, the points of intersection of a plane with a 

 curve of double curvature being given ; in the other, so many 

 tangent planes to the same developable surface pass through 

 the same point. 



