De motu comefanm in orhitis paraholicis, solem in foco habentibus. 411 



2k. Coroll. Si,iigUur comet^ tempore /f dierum a perihelio movetur per an^ulum f, tompore 

 k-^y dierum movebitur proximp per angulum v -^^iJS^cos^ — ^* ^.^1 si iste anffulus propius desi- 

 deretur, erit is (>-*- 2^V cos* |:P.— '•■iV',^^ cos',-i- p sin^p, atque tertius terminus 



u-i mMllnf.. vA:2V3>t3coslO^(,(7_8cOS^-|-(>) 



cum sequentibus semper tuto negligi poterit, dummodo utroque tempore cometa vel ante vel post 

 perihelium versetur. fon'"»^.--- 



25. J*icliolioii 1. Quo naec approximatio magis conhrmetnr, sumamus exemplum cometae 

 A. i680 visi, pro quo erat N = 2^,lQ%58y qui numerus, cum sit mullo major unitate, terminos 

 seriei illius, valorem ipsius ^ exhibentis,' cresccntes efficere videatur. Cum autem iste cometa uno 

 Jie per angulum pius quam 132° aperihelio circa solem moveatur, quia cometam diu ante vel post 

 perihelium observari ponimus, erit c> 152° ,^et. costJ-p < sin H*' et proinde cos4-<^<0,2^19219, 



boc est < ^ • Hinc erit cos^* -|"^ <^ zie * *1"^ valore terminus 2Nk cos* -^ v valde redditur exiguus. 



Sumamus spatium h esse decem dierum, erit (8) p=167°34'' et lv = 8Vkl'. Si jam hinc 

 luaeramus an&:ulum tempori k-+-x dierum respondeptem. sequens calculus instituatur: •• „;,„„ 



'"■•'- • Tcos!|-^{^=\-4Xoi)fe§§r "'" ^^^'^^^"^ Wilnn ^ii^imi ^'''^^^ 



l sin f t' = (— 1),9974386 ,/2 = 0,3010300 



«fV= 1,^265857 icos^i^-^C— ^),1383300 



- -'" - - er^o-^A^cbs^it^^^MWri '^ ^- '^ '• '• ' '^»««00 iB-JB^ 30.J 



^.-iifojn.f. 'jjviorno') inuili^riiii;;; i;'. :: ; jtliwri ainomon Jia VI oidiUB iaboDO 



'ro secundo termino erit . r,^,)rjntnnf r..->ff^J^.- i 2.853171^,,.^^^ g.,j,j, ggj^Qg ^onrf mu.J ,frm!.sMn 



iA- = . 0,6020600 

 Uos^^-c^^— 7),2?t20775 

 rsin4-f=.(— 1),9974386 , . ^ , ^ .^ , ^ 



\>= 8h >, ibon obMJi^/ioUia -C^^J^^^^-T^^j^rjiL-IO.O = 'A luiBHon ^'jIwr 



ergo 4iV^cos'f 9 sin,f^ = 0,0002^95. ,„,,„„., ,,,,;,,,, 



'ro lermino tertio utrumque membrum seorsim cQmpw.t,?tur, nempe 



IN^=^ ^^,2797571 •n..nr.7, IN'^ =k ff,279757l'fi''- '^f'r>»c n.; 



/f = ''' 0,12^^9387 ^-;= 0,12V9387 



11= 0,8^50980 'ift'''L"^"'''^tt,90^^^^^^ 



•ii'ffO'>oii'>(i ')i,i'MU('t ohuJif... ^^^ 

 icos^oi^^(_,0),3f^58250 r cos"-|- f> = (- i2),MV9900 



(- 5),5956188 :'>'"i (-- 7).7227758 



