( i8i ; ' 
; : T A : T 0 cuinque fit T A S A, eric T O =rr 
A ‘ ' • 
- \ 
Sit jam (i A O. Qudibet 
curva, CLijus arcus minimus fit 
A O, tangentes in pundis A & 
O, AP, O^. Radius Cuiva- 
tur» A R, Perpendiculares in 
tangentes fine S P, S P. erit 
S AkTA ‘ ' 
— T^is = A R. Nam ob 
equiangula triangula eft 
/P ; AO ; : P A : R A 
&AO;TA::SA :PA; 
unde ex ^quo erit / P : T A 
ycl S A : : S A : R A, eft ve- 
» 
ro / P = S P, quare erit R A = 
i 
S A X S A 
S P 
Hinc.fi diftantia S A, in fuam Fluxionem ducatur, 5c 
dividatur per Fluxionem perpendicularis, habebicur ra- 
dius Curvaturx ; Qiio Theoremate facile determinatur 
Curvatura in Radialibus curvis. Exempli Gratia. 
Sit A,Qj Spiralis Nautica ; quoniam angulus SAP 
datur,' ratio quoque S A ad S P dabitur ; fit ilia ratio 
4ad^, eritSP =*M8cSP =i^8rAR = -— 
■? . 4 . S P 
• • j S A - ~ 
= — 7 — , unde facile conftabit, Spiralis Nauticge Evo- 
• U I . • - r _ ' ^ 
lutam efleeandem Spiralem, in»alia pofitione. 
V* \ ^ SASA . SA** SP 
Q.uoniam A R = 
.S P ’ ^‘^‘’^SPiKAR SP5.SA 
Atquehinc rurfus, Vx data relatione'S A ad S P, facile 
invenietuf lex vis centripetJc. ! - - - 
' G c Exem- 
V 
