t2 3 8 Mifcellanea Curt of a. 



C0R01 



V. 



The Curve KU is a third Proportional to 

 the right Line AC, and the Curve AF or the 

 rieht Line AL. For from the Property of 

 the Evolution, KU = (UK A — KA^VF— < 



S/iaxJnxx : KU. But (by Cor. II. Prop.ll) 



V iax\xx sfc AF. Wherefore AC : AF : : 

 AF • KV. 



COROL VI. 



The right Line KI is double of AB. For 

 fince BI = (BC =) CA+AB, alfo AI fhall 

 — CA-f 2AB. But AK^AC (by Cor. IV. of 

 this Profofition.) Therefore KI~2AB. 



COROL. VII. 



The Reftangle AC* BR is = to double the 

 Hyperbolical Space BAH. For FRxAC — 



KA- 



. And therefore, a : V iax-\-xx t : 



a 



x% vzax-\-xx-\- a % y xax-\-xx = AB x BH 



M;-AC 



