9^ PROBLEMA fX OBSERUATIS TRIBUS 



B¥=a , AM— AE-BFrrZ; , et BN=BF-CG— t', 



ct producantiir chordac AB ct BC vsque ad occur- 

 fus H et K fedionis planonim horizontis et paralleli 

 US, ct triangula fimilia MAB, FBH , pracbebunt 

 AM(/7) : AB(2/;u-)3rBF(^):BH(~^> Nec nou 

 triangulii fimilia NBC et FBK, analogiam NB(f), 

 BC(2/n)::FB. (<7;BKi^). 



II. His omnibus jam pofitis, in triangulo rcdi- 

 lineo HBK , cx data ratione laterum BH(---f^) et 

 BK(^Y^), quaecft, \t cm ad bn , et angulo inter- 

 cepto , HBK cujns menfura efi: femiffis arcus AC , in' 

 uenientur anguli BHK , BKH, \el BKI, et KBl po- 

 fita BI normali ad HK , faciendo analogiam , cm 

 -^bn ■.cm—b?i — tang- ang. z red. -^^AOC: tangent. 

 anguli cujusdam .v. Erit enim BKHzrared.— q^AOC 

 ■^x y atque adeo datus, fit finus ejus ~p. 



III. Porro in triangulo redangulo BKI, ha- 

 betnr finus tot. ( i.) finus ang. BKI (^.)::BKv^), 

 35I(2f^). DudaquelF, erit anguhis BIF menfuri 

 inclinationis paralleli ACP ad honzontem, feu ele- 

 uationis acquatoris cujus finus dicatur —y. In tri- 

 angulo vero BFI ad F rec-tungiilo fit BL^). BF. 

 (^)::fin tot. (i). fin. ang. BIF(j')' Adeoque dudi» 

 cxtremis et mediis habetur aequatio znpxjzzc. Ex 

 hac aeqnatione judicaui antea problema indetermi« 

 natum effe ideo , quod nuUae conditiones fuperes- 

 feut , ad quas non refpexerim , et quarum ope alte- 

 yutra jadetermiuati cxterminari posfit ex inuenta 



aequa-- 



