2 4* ^ Mifcellanea Curio fa. 



the Square of the middle Term, is equal to 

 the Square of the half difference of the Ex- 

 treams. And confequently CR-|~AR, and 

 CR— AR, are the Numbers HL or GP, 

 agreeing to the given I og. CH or CP. 



COROL III. 



It is plain from the Demon fixation, that 

 as HD the half Sum of the Logarithmicai 

 Ordinates HL, PG, being applied at right 

 Angles to CH, is an Ordinate to the Cate- 

 naria ; fo alfo the half difference of the fame 

 HL, PG, applied at right Angles to CA 

 in B, is an Ordinate to the Equilateral Hy- 

 perbola, whofe Center is C, and its Vertex 

 A; and confequently (by Cor. II. Prop. II.) 



=ts the Catena AD. For y — \fiax- \ -xx ; 

 and fince it was lliewn in the foregoing Ca- 

 rol* that AR is alfo the half difference of 

 HL and PG \ 'tis plain that AR is == the 

 Portion of the Catenaria AD. From whence 

 by the way, we may obferve a Method, how, 

 from the Catena AD given, to find C the 

 Center of the Conterminal Hyperbola, or 

 the point in the Afymptote of the Logarith- 

 micai Curve GL. For taking AR— the Ca- 

 tena AD, and joining the points B, R, from 

 the middle of BR ereft a Line peipendicu- 

 lar to it, which will meet BA the Axis of 

 the Catena produced, in the point C, fought. 

 Which is evident, fince thus CR will sj= CB. 



COROL. 



