470 
'Mithodus Inveniendi Line as Cur v as 
i • rrdh-Ldr >, „ 
Generalrter conftat, quod, quoties J — pp — • non lit par 
reus circulares integrabilis, curva lit tranfeendens. 
Ex. i . Si radius curvaturae evolutae S = 
aT . 9 + T 2 » 
54 
IT , dS dT 
quaeritur 
dp 
curva. Per theorema obtinetur ~ = p- » - 
ct 
integranoney'i^ 5 + C= -/^= 
dp 
. Quinn vero arcuum, 
r_ 3 iL et - C—X. — finus fint . - et \/i -f, fi arcus con- 
J 9 + T- J v'g + T* 
rp ^ ^ 
ftantis C finus fit c , erit = v/i -P~ et refoluta hac 
V p _l rr 2 
9 + T 
^ 7 “ 
aequatione T in p habetur. Si fit c ss o, erit T = ^ ^ et per 
theorema i. y — Vax, curva igitur in hoc cafu eft parabola 
Apolloniana. 
E*. 2. Quaenam eft curva, fi evolutae curvature radius rsr 
aT . 9 1 4'i jh ? Theoremate habetur = - — == et integra* 
2 V 27 9 + 4 T O 
done f + C = - . Arcuum / l 6 ff .et - , 
J 9 + 4 t J c/9 + 4T' i 
2T 
iinus funt ^=^ etv/i -/*, fi arcus conftantis C finus pona- 
tur c, prodit ^^==^2 — ^ x per quam T in p obtine- 
o y'T'irT 5 
tur, quae, in cafu c = o, dat T^ J — ■ 
et theoremate 1, 
2 7 > 
" aequatio ad curvam, quae conftruitur rectifications 
7 *C- 
4 , = 7 t-? 
; ; v .v 4 — 
ellipfeos et hyperbolae aequilaterae conjunCtim. 
2 
THEOREMA 
t 
