Mifcellanea Curt of a. 2 \ I 



COROLLARIES. 



C O R O L. I. 



As the Catenaria is defcrib'd by the help 

 of the Logarithms, fo on the other hand, 

 by the help of the Catenaria (a Curve pro- 

 duced by Nature it felf) the Logarithm of 

 any given Number, or rather of any given 

 Ratio y may be found. As if, putting CA— t, 

 whofe Log.=o-, the Log. of the Number 

 CQ, or of the Ratio between CA and CQ_, 

 were fought. Let GV be a third Proportional 

 to CQ. and CA, and CB the half Sum of CQ. 

 and CV \ then an Ordinate to the Catenaria, 

 from the point B, viz.. BD, will be the Log. 

 fought. 



COROL II. 



Vice verfa, if giving the Log. CH or CP, 

 the correspondent Number HL or PG, or 

 the Ratio of HL to CA, or PG to GA, be 

 fought. From H or D ered a Perpendicu- 

 lar meeting the Catena in D or F, and in the 

 Horizontal Line AR, take CR— HD or PF, 

 or CB. And then will AR be the half dif- 

 ference of the fought Lines LH, GP, as HD 

 or CR, is (from the above demonftrated Pro- 

 perty of the Catenaria) their half Sum. For 

 in three Quantities Geometrically Propor- 

 tional, fuch as are HL, CA, PG, the Square of 

 the half Sum of the Extreams lefTsn'd by 

 R the 



