SFI SIMILES FRODFCVNT 9 



conftriiAio dednci queat , eliciamus ex aequatione inuenta 

 rzzins aequationem inter coordinatas orthogonaks AP 

 nzx et P M zzj pro eadem curua quacfita AMB. Quum 

 vero pofitus (it arcus AMmj, erit dx -^dy^ — ds \ 

 atque fi fiat dxzz.pds et djz=:ds V (i—pp) cnt curuae 

 radius osculi rzz^^-f^. Hac itaque fubftitutione fadla 

 ifta emergit aequatio — ^~^::=zns feu y^^^p^,) =: t 

 cuius integrale eft wA fin. p — /^, feu />3=fin. A^/a , 

 vnde fit y ( I ~/jp) =1 cof A ^ /^ . Quapropter nan- 

 cifcimur dxnzds fin. A^ /f Gt djzz.ds cof. A J- /|-. 



§. 10. Ad has aequationes denuo integrandas fequens, 



notandum eft lemma , quod in folutionibus fequentium 



problematum maximum afferet fubfidium. Eft fcilicet: 



rjr r^ A r ^i P^ r» a r ii V(«-4 -P^*) 



jaS lin. A .7v(a-t-i3s^) — 7:^ ""• -^ •7v(a-h(3«; x-H-^ 



COf. A •Jy(a^(3«> 



atque 

 /^. cof. A ./^V^ = .-^ cof. A ./^$p^ 4- '-^fi 



fin. A ./v(^q:p7;) 

 quae formulae vfiim habent folo excepto cafu , quo eft 

 P =: — I . Hoc autem cafu , quia eft J^j^zrn) — ^ fin. y^, 

 erit fin. A ./7^^^=: y^; liincque Jds fin. A .J-^^iz:rsf= 



ss ^ c j r K r ds rds _/ / \ sV(a-sr) 



,y^, et fds cof A .yv(«z:n)=Jy^ y(a-ii) zn -^y^ 

 -f-^ A cof.y^- 



§. II. Qiiia nunc in noftro cafii eft ^ /^ =/^ erit 

 lemmate ad hunc cafum accommodando , a iz: o , (3 =: 

 «w, quibus valoribus fubftitutis fit x:zzjds iin. A./^= 



Fig. 4h 



Tom, XIL B 





