252 
DISQUISITIONES GENERALES 
nec non per formulam rcoscj; = -j— 
[3] rcos<\> = +(f/'— tV/W? etc. 
+ l9 () ppqq-\-\gp i qq 
Hinc simul innotescit angulus <p. Perinde ad computum anguli 9 concinnius 
evolvuntur series pro reos9 atque rsimf, quibus inserviunt aequationes diffe- 
rentiales partiales 
d.rcosep •, • dep 
= n cos 9. sm 9 — r sin 9. ^ 
d.rcosep t • dep 
—= cos 9. cos 9 — rsm9.^- 
d. r sin 9 • • 1 1 d cp 
—= n sin 9 . sm9-|-rcos9. -ÿ 
d. r sin ep • . , d cp 
1 = Sin 9 • COS 9 “r t cos 9 • 
1 dep ... dep 
r sin 9 d. r cos ep , , d. r cos ep 
.—5—--4-rcosd».—3— 1 = reosep 
n ap ' T dq 7 
r sin di d . r sin ep , . d . r sin ep 
1 . 3 -4- r COS . —3 1 = r sm CC 
n dp ' T d q 7 
Hinc facile evolvuntur series pro reos9, rsin9, quarum termini primi manifesto 
esse debent p et q, puta 
[4] r cos 9 = /»-|- if‘p f J'i+A/ppq<l + (A-/"— A/"/° )jf> 3 ? ? etc. 
+ig"v<f +/.-»!"/ 
+ (fA°-*/7>? 4 
[5] »-sinif = i —i/y ? — (iV/"—jV/TV? etc - 
—i/pp qg — i-ng/qq 
E combinatione aequationum [2], [3], [4], [5] derivari posset series pro rrcos(^+9), 
atque hinc, dividendo per seriem [1], series pro cos (cp —9), a qua ad seriem pro 
ipso angulo —{— cp descendere liceret. Elegantius tamen eadem obtinetur se-