ex Proprietatibtis Variationis Curvature, 
465 
THEOREMA III. 
• ddz 
T dp 
Manentibus iifdem ac in theoremate primo.erit , — 
1 fa Vi-tf- 
t • ddz T da 
vcl etiam • 
V I_ - 2 
dx 
Eft enlm dzzz -■/ — ; et dx = dz*S 1 ~p\ quare R(- - tl ) 
_ fay/ 
1 P 
dp 
, cujus fluxiones — 
_ dd \ / 
1 -P 
dp 
dp. 
pofita arcus 
MP fluxione conftante, per dz divifae dant T ( = 
ddz. 
T dp 
= — * dz ^ l d — > quafequitur — --^=. Et quum fluxio 
arcus circuli asqualis fit negative fluxioni complimenti, erit etiam 
ddz T dq 
d% y/ 1 — <f 
Cor . Si Tint ut antea tangens anguli BCD, r et fecans s , ha- 
ds 
, „ ddz dr 
betur — = 5= « 
dz 1 + r Sy/f - 1 
Schol. 1. Si alterutra aequationum formas dx = 2 ,dz et dy ~ 
'Zdz, inter fluxiones abfciflae vel ordinatas et curvas, relatio 
detur, per formulam T = - — -- V^ 1 vel T = — - — - , 
7 r dzdp dzdq 
riatiocurvaturasin^, - , in q — L, et in z 
va- 
zv^nr* 
dp 
con- 
eodem ac antea habetur, pofita fluxione quantitatis 
J / 1 
ftante. 
£V/W. 2. Ope hujus theorematis invenire licet indolem curvas, 
fi inter T etp, T et q, &c. relatio detur. Sjf T = P, fun&ioni 
P p p 2 finus 
