JMifceUanea Curiofa. 11^ 



which was fhewn but now to be ^fiax-^xx. 



And therefore AF = V \axA c xx\ And 'tis 

 plain, ;hat the Fluxion of the Ordinate BF, 



ax 



or is to x the Fluxion of the 



V f 2ax-\-xx 



Abfcifle AB, as the conftant Quantity <z, to 

 the Curve AF ; which was the Property of 

 the Catenaria found above. Therefore the 

 points of the Catenaria are rightly determin'd 

 by the foregoing Conftru&ion. Q.: E : D. 



COROL I. 



It is manifeft from the Conftru&ion, that 

 BF the Ordinate in the Catenaria^ is equal to 

 the Parabolick Curve AP, taking away BH, 

 the correfpondent Ordinate, of the conter- 

 minal Hyperbola AH. 



COROL. II. 



'Tis plain from the Demonftration, that 

 the Curve of the Catenaria AF, is equal to 

 BH the correfpondent Ordinate of the con- 

 terminal Equilateral Hyperbola. For fince 

 the Fluxions of thefe Lines are equal, and the 

 Lines themfelves do arife together, it is ma- 

 nifeft that they are always, and every where 

 equal. Whence, giving the Catena^ AC or a 

 will be given alfo, as being equal to the Se- 



miaxis 



