PROBLEMA ALGEBRAICVM. %s 



bus conditionibus fatisfiiU : tum Tero tertia dabit 

 cor ^ cof. 'vj -f fm. ^. fin. >) — cof. (^ — 'vi):i: o , ex quo 

 erit ^ — >j.zr9o°, ideoque -v} — ^— 90° , ac propterca 

 cof y\ — fin. ^ et fin. >3 zr — cof. <^. Vnde patet H 

 capiatur : 



Xzi^xcoL^-VyCu-^,^ et Y=iA-fin.(^— ^cof.<? 



XIV. Hoc remmatc praemiffo ex propofitls 

 tribus> \ariabilibus XyjjZ prima alias tres x'^ j', z! 

 ita definio vt fit 



,t'z=:vcof,^+7fin.<?; yrzrfin.^-^^cof.^ ; et z!~z^ 



lioc enim modo certo erit 



x' x' -byy + z' z'zz X X +jy -hzz. 



Deinde ex his fimiii modo alias tres x'',y\ 2" 

 deduco , vt fit 



x"=zx''^ >/'z=^^cof •vi4-2'fin.>5; js^^rrj^fin.-vi— s'cof -vi 



atqiie hinc tandem quaefitns X, Y, Z, ita definio: 



X — z"cofA-^x"Cnr^i Yzzy'^ Zzizz^CinJ-x^coC.^ 



fic enim vtiquc fiet : 



X'+ Y'+ 2"-x" x" +y'j"'+ z'^ z"z:x'x' i-yY^z' z'-xx 



XV. Ex hac autem triplici pofitione fequi- 

 tur forc : 



^"-j^^cof.^-i^^/fin.^jj^^rAfin.i^cof •vj-^ycof.^^cofvi-i-^sfin.'^; z'*' 

 -z. X fin. i^ fiu. vj — j col. ^ fin. .'vi — s cof -^ 



L 3 tum 



