( >34o> 
1 Concipietur Quarto Curvam MSN (in altera Fig, 
Fig. parte delin. Effe unam ex Hypcrboloidibus, cujus 
Afymptoti A K , K H . reftamque S R ad Afymptoton 
KHordinatam, S R fit = y, S P =2, KR = x, 
K P = n , qux bic necedario minor erit quam x I 
ut confideranii patet. Equatio curvae propria eft 
yp x^ == r^ sP cujus loco ( propte r & s quantitates 
dcterminatas > fcribi poffit y p = x , adcoque 
2 — . « q — 2 q— p 
y = x p, 8ci2yy = . . hinc cum 
p X X p 
tzi:=^y y-^-xx — 2nx + nn ^'pro extremo habemus 
— 2q— p 
2q. 
^ y y + 2XX— 2ftX=Q, hoc eft — — XX p 
p 
fj- 2 X X = i n X , 8c ii =: X — X p 
P 
^2q-,p 
. q — — 
adeoque fubnormalis PR(=x — n)=-- x p 
Curvam jam A F G ( ultimo loco ) Cyclolden pri- 
mariam concipiamus ; iitque r Radius, c Arcus 8c ^ 
'^rdjtaata Circuli genitdris, cujus Diameter per. AK re- 
^prerentatiMr centrumqy inrer L & K pofitufti. Turn 
vocata F D cycloidis (ardinatS a , caeterifque ut prius ; 
curvse equatio eft a a = yy + 2cy ^ cc, adeoque 
zz ( = aa+nn 2n.x:;tlxx)-=: y y rf-2 c y + 
€C-}-nn — 2nx -f'-xx 8t ( s ad extremum determi- 
■ nata) 
