■EVOLVTAE IPSAE SE GENERAKT. 219 



ct -7r==i^r — — - — . Cum igitiir in Ytroque cafu idera 

 valor arcus BF emergat , patet vnam eandemque cur- 

 uam \trique cadii latisfacere. 



Corollarium i. Vt vero conftruatur arcus inuen- 

 tus BF , ponatur conftans C=iI!^^A , in quo vaiorc 

 noua conflans indetcrminata k affumitur •, et radius ofcu- 

 li Rr:^^— , cui valori iam noua variabilis u ineft, ha- 

 bebiturBF=^..^c^l^"I),quemdico effe arcumEpi- 



cycloidis Fig. 2. in qua radius circuli immobilis OEzna^ 

 diameter circuli mobilis ABiz:^. Sit enim chordaquae- 

 uisBErr?^, radio OE, centro O , defcriptus arcus cir- 

 culi EM, et MC conueniens radius ofculi : Erit ex natu- 

 raEpicycloidis(\\ loi. Analyi. Infiaitor.) arcus AM 

 ad chordam AE(ykk-uii\ vti eft fumma diametrorum 

 <^a^k ad radium bafeos OB (^) , itaque AM=: 

 2^xvU:^)-BF. Fig. I. Ob aflumtumvero Rn: 

 ?±^^ , elicitur Z^rzil^^; in Epicycloide autem 



eH:, OA : OBmMG : GC , ergo inuertendo et com- 

 ponendo OB-f-OA : OA=: GC + MG : MGhoc efl : 

 Q.a-\-k : OAzrR : MG(?/), ob MGi^EB, per §, loo. 

 1. c. n. 3. ergo OA=^J±l^=:Z'. Vnde patet, ratio- 

 nem datam problematis a : b ^ effe ipfius OB ad OA. 

 CoroUarium 2. Quodfi ratio data rt : Z» fit aequaH- 

 tatis , habebitur BF=VCC-RR , et fi ftatuatur C=:2f, 

 Rzi2M , erit BF^^ay^^-wz^ , qui eft arcus Cycloidis or- 

 E e £ din:i* 



