= (8+) = 



d X zrz n d (^ fin. >. (P -]- k d <P coC. (^ cof. X et 

 dv — n d (l) coC. \ <P — kd(pcoC(P i\n. X (p) , 

 vndc ambo valorcs prodibiint alijebraici, dum ne fit X~h-i. 



§- 27. Rcduclionc igitur folita in vfum vocata nan- 

 cifccmur has formulas : 



Lf*m 2«fin.X(J)-f-/: cof.(X-+-i)(P^ k cor(X— i) et 

 ^^ = 2»cor.XCp— /:fin.(X-»-i)(I) — )tnn.(X— 0, 

 yadc intCvi^aa4o dcduclmus : 



2.r =— ^" conX(p-H Jl_ fin.(X-(-i)(|)-+-_L_fin.(X — i)(I)et 

 2^ =:-»- ':^ fin. X(I)-^- ^cof (X-f-i)(I)-H j-A_ cof (X— i)(I), 

 quae curunc icidcm mnximc difcrcpant a pracccdcntc folutionc. 



Scholion. 



§. 2 8. Quamuis autcm liac folutioncs infinitics infini- 

 tas fuppcditcnt liiicas curiias algcbraicas problemati nodro fa- 

 tiNfacicnt«s, taiiKn vix aflirmari polfc vidctnr, in his formulis 

 omncs planc iolutioncs couiincri: tam pariim cnim adhuc ifhid 

 argumentum e(l claboratum , vt vix quicquam ccrri in hoc 

 ncgotio ftatui poHe videatur ; fed potius qnacflio gencralis , 

 qua curuac algcbraicnc dcfidcrantur , quarum iongitudo pcr 

 datam formulam intcgralcm / V c) v cxprimatur, vbi V dcno- 

 tct finKTtioncm qiiaincunquc ipfiiis v , tantopcrc ctiamnuiic tc- 

 ncbris obuoluta dcprchcnditnr , vt folutioiicni pauciiJimi». tan- 

 tura' ctWibus euoliicrc liccar , qucmadmodiim nobis loliiiio fuc- 

 ccllit pro arcubus Paiabolici.^ ct Ellipiicis. Si onim talis 

 quacflio circa arcus llypcrboliros proponatiir , fatcri cogor , 

 nullo adtiuc modo mc >cl viiicam falttm curuam algcbraicam 

 erucre potuifll-, cuius fiuguii arcus pcr formulam : 



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