H I S T O I R E. 



P7 



Conft:ins adiiciend;i inde dcterminatur, quod , fi Xrrra, efle 

 oporteat v|y~o, iinde crit 



C irr — tang. (^ log. tang. (4.5° -1- $ a), atqiie 



vl. — tang. (p [ log. tang. {4-5^ -^IK) — ^og- ^^"g- (45^-^1^) ]. 



Qno hinc cruatur valor ipiius , animadvcrtamus , pofito 



X — ^, fore >4^ — y. Erit itaquc 



tang. (p ~ 1^ . 



log. tang. (+5^^ ^ : |3) — log. tang. (45" -^ i a) 



Quodfi igitur a > (3 , fict Cp > po°, quod pcr fe patet. Si 

 P~a, crit (P — 90°. Eodcm vcro cafu effc quoquc debct 

 X ::iz a rz: p. Produclum cnim 



tang. (p [log. tang. (45^ -+- 1 A) — log. tang. (45" h- | a)], 

 cuius altcr fidor, tang. (p zz: c>o , ncquit efle zz:v{^, vcl aequa- 

 lis quantitati finitac, nifi altcr fador fimul cvancfcat; unde 

 fequitur X — a. Quare fi bina punda A ct B fub codcm 

 fita fucrint Parallclo, Loxodromia in ipfum hunc Parallclum 

 tranfit. Si dcniquc ambo loca fub eodcm conftituta fint Me- 

 ridiano, feu y — o, fit quoquc — o , h. c. via navis eft 

 ipfc Mcridianus. 



§. 3. Infpiciamus iam , qualis proditura fit aequatio 

 inter tres coordinatas redangulas , pro ipfi curva. Sit M Q 

 ad planum Aequatoris pcrpcndicularis , QP in codcm plano 

 ad radium C D normalis , appcllctur C P — .v , P Q ~y , 

 QMi=c;i atque pofito radio (phacrac C M == i , crit cx na- 

 tura fphacrac , i — .v jc -{~J.Y -f- - ~. Habcmus practcrca z zz 

 fin. X; j' — C Q fin. \]^ — coC X fm. \J/ ; x ~ cof X cof \]/. Vn- 

 de fiet d z ~ cof X ^ X ; 



dj — cof X cof vjy c) vp — fm. X fin. v|y 5 X j 

 5 x~ — cof X fin. vjy D v|; — fin. X cof vjy c) X. 

 hijfoire de i-;^6. n Supra 



