iS D£ REDrCTlOXE LlNEARrM CrRrjRrM 



N'N" i=:NN'-NN"' 

 N"N"" =:NN"-NN"' 

 N'"N>^ — NN"'-NN'^ 

 et AN' z=AN-NN' 

 prodibitqiic terminis in ordincin rcdiiAis : 

 ^_,.,^^N--|-MN4-2rN'2lI.N"-i2llI.N'"-f2lV.N'- 



t-f yS fin-av+;— Cnn-3-^'-fin.'y)-|-7,'~r(fin-4"^-fi»-2'y>h ctc. 

 Eft vero ^^^ - z cof v ■ ^-p^'- ^^, cof zv ; ^'^^ 

 — 2cof3V ctc.ctNN". cof i'z=N'i ; NN" cof 21; — 



N"2 ; NN'" cof s-y^N'"^ \ ctc. quibus valoribus in- 

 trodiictis crit : 



AM:=:r(AN-l-MN-}-2lH-2ll2-i-2in3-f2lV4-i-ctc. 

 \nde , cum amplitiido fit — w-j , crit radius arcus circuli 

 acqiic ampli ct ucqiuilis ipfi A M zr 



;VS-)-MN-+-^I'-l--H->-'nt-f-;'V* 



xn. ^'^- 



Q. E. D. 



Coroll. r. 



30. Quod fi diuifio hacc arcus AM in p.irtcs nc- 

 que amplas in infinitum continuctur , rum fbrmula inucn- 

 ta , quac in fcricm infinitam abibit , loiiijitudincm ;u- 

 cus AM vcrc cxhibcbit. 



Coroll. 2. 



31. Qimmuis autcni numcrus partium fit finitus, 

 Limcn plurimi dantur cafus , quibus veritas ipla hoc mo- 

 du cnutur. Et nifi hoc cucniat , crror tamcn crit valdc 



par- 



