Astronomta mechanica, 253 



ubi quantitates ^T, 33, 6, D, E, F et S ut valde parvae sunt spectandae. Ponamus brevitatis gratia 



^^H-3( = ^, 2-1-03 = ^, et — /•-i-5'H-g = C, 

 ut formula irrationalis sit 



l// j B c D E F\ 



VlA-i ¥ H-5--t- — -H-r)» 



\ V iv V' V* v^ J 



quae posito ^ — \ — ita comparata esse debet, ut factorem obtineat sin*, seu ut evanescat 



posito tam * = quam 5=180*'. Quocirca efficiendum est, ut fiat 



^-.B(ifi)-HC('f^)VD(i^y-.etc. = 0. 



fiant ergo necesse est et "~^ binae radices hujus aequationis 



A-^Bz-^-Czz-^ Dz^H" Ei^-i- Vz^-^ etc. = 0, 



quae rejectis terminis minimis habebit hanc forraam — - — i-2z — /zz = 0, unde fit z— — —^ ita 

 ut sit proxime p-^f^X ^ = ^. Ponatur jam in terminis minimis p = fetq = kt et habebimus 



kk-l of 2(izt<j) fd(l±k) fHdzq)^ (S-H(S)(l±ft)* Z)(lr±:Jfc)3 £(i±*)* F(ldtft)S__ 



,,/ . ... > ,* , ; f , PP ff f^ f* P 



qnae ob signa ambigua resolvitur in has duas 



tt-l ^f 2 » Al-*-W) (5-*- e) (!-♦-**) Z)(l-*-3M) JE(l-i-6M-+-*4) F(l-HlOfcft-«-5^*) ^ 



f p f pp ff f^ r* f^ 



2? »* 2/^ 2(5-4- (S)A D(3Jfc-*-t») £(4fc-H4Jk3) F(5Jfc-*-10fc«-*-ft°) __ q 



n . 1 l-t-a; . . ,. . , iaKdiq/» 



Ponamus jam — = —-—, et prior aequatio abit m hanc 



^ I 91 ■ ^ rgg , (5--(£)(l-i-^*) i)(l-i-3M) _ 



^-f-^-H ^ — -H ^ H- ^, -f-etc.-u, 



oode deducimus 



?? W 51 35 (5-^(S)(l-*-ibfc) D(l-4-3AA) £(l-^6**-f-iH) ^(1 -^ 10**-*-5A*) ^ . . 



vp ff f ff r» r* r* a« 



altera autem per q multiplicata , qui factor in terminis minimis abit in ^, praebet 



2aj » 2 (@ -H 5) Z) (3 -+- kk) £(4-^4Jbt) F(5-t-10*it-t-**) 



_____H _ , _ , _ H ^3 



unde deducimus 



1 1 25 (i-+-S Z)(3-f-A*) EiA-t-Akk) F(5-*-10A*-H**) 



P r 'if /f ^f^ ^ 'if* V^ 



rf t 95 (S-5 D(3-4-*A) £(4-t-4**) F(5-*- 10 ** -»-*«) . N 



