1^2 OpUSCULA . 
,d X — — , li ve e -\- s ^ X . d s^- — C"- d d x =: 
d s"- ' zip 
. d d X . Pono e -\- s -\- X ~ z , undc d s d x — d z- , &c d d x 
~ d d : igitur provenit xquatio z d s' := d d z . 
Duplici modo a;quatio inventa integratur, fed juvat fe- 
parare hypothefes . Prima fit , quum £• — o , & initio mo- 
tus corpus, & centrum fint in eodem pundo . Prima me- 
thodus dat integrationem z — A.Ch.s-^B.Sh.s. Si tam 
s , quam x = o , etiam z'r==. o ; ergo , quia S h . j- — o , C h . j 
r=r, remanebit z> — r ^ , hoc efl: A — o: igitur xquatio 
z =: B . b h . s. Si X , s fmt minimae , & nafcentes erit s : x : : 
C : c , & componendo s : s x — z : : C : C -\- c. Jam vero 
z : S h . s zz: s : : B : 1 j ergo B : i : : C -{- c : C , feu B ~ 
: ergo aequatio rite integrata dabit z — . 
Secunda methodus poftulat , ut multiplicetur xquatio 
inventa per d z , ut oriatur z d z d s^- — r'- d z d d z : ergo in- 
tegrando z^ -{- A . d s^ ~ r"- d z"- . Atqui pofita z=: o , debet 
elle ds^:dz^::C^:C-\' c ; ergo : ^ : ; : C -i- / ; ergo 
A—^^JLI . Quare aequatio provenit — ■ ■ —ds, 
five ~-^~=z=:~ds. unde integrando —— - z = S h . 
/C^ z,^ ^-^^ 
^ C+f 
£^:i- . S h . J-. Nulla addita in integratione eft con- 
ftans, cuia x , S h . . , ^ debent fimul evanefcere . 
aut z ■=. ^ 
Ad velocitatem corporis inveniendam , quum 
fit z - 
^^;,^£±_^Sh.., erit X = ^^Sh.s — s, & differen- 
dx =z ^-^dSh . s-d s ^ 
C + r ds. Ch. 
tiis acceptis a x z= — - ^ ' ^ 
1 '^'^ ^' — .£±1 r h s — C. 
— a s : ergo // ~ -j-j" — — ;^ — u . j . 
Ex formulis inventis conftruaio clarc defcendit . Ad 
abfciiTam A S ( Fig. ic. ) defcribatur non curva ^^nuum hy- 
perbolicorum , fed ea , cujus ordinatx hnt ad ^n'^^ l^>P^f 
bolicos AS::C^-r:C. EafitAZ. Agatur reda AT fa^ 
