CIECA SUPERFICIES CURVAS.
251
etc. sive
/ — /°+y> +/>P ~h etc.
9 =9°-\-9P+9"PP- i r etc.
h — /¿°-j-Jip-}-ii'pp-f- etc.
n = i-\-fqq+f'pqq-\-f"ppqq-\- etc.
+^V -\~9P ( f + etc.
-f-/i 0 ^ 4 -J- etc. etc.
24.
Aequationes art. 22 in casu nostro suppeditant
d r ,
ftsin<j> =
d p ’
dr ^ i dcp
-j—, —W COS ([) = m.
djp’
sin ^
dtp
= m.ji
dq
/drK 2 . ,dr N 2
nn = nn[ Tj ) +(^).
d r d<p . dr dcp
nn -dr q 'd¿+dp-ár P — °
Adiumento harum aequationum, quarum quinta et sexta iam in reliquis continen
tur, series evolvi poterunt pro r, cp, <[», m, vel pro quibuslibet functionibus harum
quantitatum, e quibus eas, quae imprimis attentione sunt dignae, hic sistemus.
Quum pro valoribus infinite parvis ipsarum p, q fieri debeat rr = pp-\-qq,
series pro rr incipiet a terminis pp-\-qq: terminos altiorum ordinum obtine
mus per methodum coefficientium indeterminatorum*) adiumento aequationis
1 drr N 2 , /drn 2
(« *'d^) +(d^) ~ ArV
dq
[1] rr = pp + $f 0 ppqq-\-i/yqq +(l/“A/ # /V?? etc -
q*+ j t9'pV
+ №—t*/°/°)PPÏ
Dein habemus, ducente formula r sin ÿ = ^^,
[2] rsinij) =i> — — ifppqq — (+/"+*/°/°)/?i etc.
\9PPT
(+A°-A/ 0 /°W
*) Calculum, qui per nonnulla artificia paullulum contrahi potest, hic adscribere superfluum duximus.
40 *