ij6 JMifcellanea Curiofa. 



COROL L 



AC: CB:: BH : BH : FR. For this is 

 the Property of the right Line FR, that was* 

 found }uft flow. 



COROL. II. 



The right Line CB is == the right Line 

 BI or UR. For each is — a\x. 



COROL. III. * 



The Evoluent Line UF is a third Propor- 

 tional to AC and CB. For becaufe of the 



fimilar Triangles f F s, UFR, it is s F : F f 



• « 



ax-\~xx 



: s FR : UF or x : : : 



V ' 2ax-\-xx 



jt~\-x x V * iax~\-xx 



, , . jjf, which is therefore 



a 



a~\-x 



=3= . Whence a : a-\-x : a-\-x : UF, 



a 



which is the Radius of the Circle that has 

 the fame Curvature with the Catenaria at the 

 point F. 



COROL. 



