42 OpUSCULA . 
Rui-fus iii triangulo fphaerico obliquangulo MON, ex fphse- 
ricorum doarina , eft fin. M O N : fm. O M N =i fin. M N : fm. 
. . ^ fi»- M N . fin. O M N o ^ p 
NO, adeoque eft fin. N O =^ ihTMON ' cofinus 
arcus M N vocetur -±_ q , atque / fmus inclinationis lunaris 
orbitae ad eclipticam , erit ^i^^- ^ O =: q-- » & cof. 
N O — »/ r I — - — ^il— 1- ) , atque ob exiguam lunaris orbitac 
^ fin. AOD^ 
inclinationem ad planum eclipticae negligendo quadratum finus 
/, fict cofmus arcus NO quam proxime sequalis radio , & 
anguLfris medius nodorum motus evadet = 
3 Q_ . fin. A O D . cof. A O D . p a . 
2 TTt A 
Ex ipfa etiam Trigonometria eft fin. O M P =: fm. N M P. 
cof N M O ~ cof N M P. fin. N M O , & in triangulo fphaerico 
reaanguio MPN elt lin. N M P : cof MN P = fm. 6 M P ; 
cof MOP, ad^oque eft cof M O P = cof. AOD = 
fin^MP.cor.MNP - cof NM O . cof M N P — 
fiu. N xVl P 
fin. NMO.cof. MNP.cofNMP ^ . ^ , . . . « 
ihTNTiP Denique ex fphaericis eft cofi- 
nus arcus M N ad finum totum , ut tangens complementi aii- 
guli PNM, ^^ve ^^^^Y » tangentem anguli NMP, 
^ fin. NMP , „ cofNMP /•■»i-vT fin. MNP 
iive — r- , ■ ^ , adeoque eft -t^ v^-itt-^ — cof M N . - . 
cof. N M P ' ^ fiu. N M P cof. M N P 
Erit igitur cof AOD - cof N M O . cof M N P — fin. 
N M O . fin. M N P . cof M N = C I — ) . ^ C I — /» ) 
I^Itt/^, & negleao rurfus /% erit cof A O D = ^ ( i - tt* ) 
^Itt/^, & fm. AOD z3 ^ ( I — I -4- TT^^b^TT I -T*) 
./^-TT^/'^') — x + /f.^Ci-7r^), ac denique ftn. A O D . 
cof A O D = ^ ( I — )Ii: /^ H;^ /^ ( I — ) _ ^ 
V^(i— TT^) = X ^ (i— T^)±/^.(i — 2T^), & me» 
dius angularis nodorum motus evadet =i 
2 9r Z A 
T- , j. . 3Q_. VCi— 
rormulae modo mventse pars prior — ^^Ta — " " 
ex- 
