286 L EULERI OPERA POSTHUMA. Astron.mtch. 



4. Excentricitas q increraentum dq capiel, ut sit 

 dq = nv^dcp (=^*h- j (^^ — ^) ({i-*-q coss) slns cos^^)— »9^) — (^cos^n-g-t-gcos^^) sin^^^—,^))). 



5. Longitudo absidis a capiet augmcntum dce, ut sit 



dcc =!^ (5"*" 7 (;^""T3) ((^ "*" '^ ^^^*) ^^^* ^®^ (9' — «^) -^ (2 -H g C0S5) sin* sin ((p — .^))). 

 Ex binis postremis formulis coUigur fore 



dq cos s -+- qdcc sin 5 = — 2imvvdq)(—^ ^) sin (g) — &) = — et 



dqsins — qda coss = m^d(p( j--*-— •(— i i) ((^ -*-gcos5) cos (cp — »9^) — q sinisin {(f — ^)))^ 



quarum illa ex differentiatione aequalitatis — _ -»-gco8< ggq^jjyj.^ ^jj — — ^ ^ et d^p — ds = da^ 

 fit enim dg cos 5 -♦- qda sin 5 = — • 



199. Coroll. 1. Ob actionem ergo corporis N singulis momentis elementa sectionis conicae 

 immutantur, ac si id subito annihiiaretur, corpus M secundum ea elementa, quae ultimo momento 



locum habuerint, moveri perg-et molu reeulari. 



'^ ?.■.■.' .. aji.Vjtnii,.: ii!jaioai ojJi;. 



200. Coroll. a. Parameter nullam patitur mutationem , si fucrit vel sin (tp — &) = 0^ vel 

 w = u. Illo casu corpus N cum corporibus L et M in directum est situm , ideoque ex L cum M, 

 vel in oppositione vel conjunctione conspicitur; hic vero casus locum habet, ubi fuerit cos^^j — j^)=3-.^ 



' ' 201. Coroll. 3. Si fuerit 95 — ^ = et u>c, erit w=^H — ^ c, el perturbationes momen- 

 taneae praeter dp = invcniuntur: 



dr = 2nrrvvdq)'t — ( ), dq =^mvd(p s\ns( ]t dct^ — — -( ). 



^ P \WW UU/ ' ' \WV) UUJ q \tDXB uuj 



■:,,:u;u,;i:. 



202. CoroII. 4. Eodem porro casu, quo g) — ^ =,.0, si sit tt.<.f, ac propterea w=v — a, 

 erunt perturbationes momentaneae: 



1, n j osina/l 1\ , ,./1 1\ , nwd® cos«/l 1 "\ 



«'' = — 2nrrvvdg)'- — .( 1 — ), dq = — nvi^dcpsmsi 1 — )> da = (_h--). 



■^ p \ww uuj * ^ \ww uuj q \ww uuj 



lOG ^\ '>C{i ho T. 



203. CoroII. 5« Sin autem sit (p — 19^ = 180", erit cos (^p — ^) = — -^ ^t w = v-¥-u, unde 

 praeter dp = reliquae perturbationes erunt 



jr« ' o». J qnns / 1 1\, ,./1 l\i —nwdcpcoss/ 1 i\ 



dr = 2nrrvvd(p'- — ( h-), dq = nQvdq>s\ns( --!-—)> du = — — ( 1 — )• 



* P \ ww uu/ * -^ \ ww uuj q \ ww uuj 



20*. CoroU* 6. Casu vero, quo fit w = Ut ubi etiam dp=Oy reliquae perturbationcs momcn- 

 taneae sunt: - 



