X. >15 ) 
4- 1 r f r\ Hinc autcm invcnitiir parabolam femicu- 
bicfim proHcmati fatisfacei-e, quaiii ita dcfcribere opor- 
tet. Data (in Fig. ii.) linca rcda A B, & ineapiui- 
<5lo C, iina cum liiiea red^ C D anguium fub .BCD 
cum linea C B conftituente sequalem angnlo, in quo 
CLirva fe incerfecare requiritur. Ducatur ad libitum 
H G I ad CD parallela, lumaturque in G H =: 
2 C G ; deinde dividatur angulus liib A C D in duas 
partes sequales linea reda CE, & denique ad diamc- 
triim H I & verticem H defcnbatur parabola femicu- 
bica K H L, quse tranleat per pundum C, ita ut C E 
ordinatim applicetur ad diametrum H I. Hxc para- 
bola ad eandem lineam fimiliter applicata, fed fitu in- 
verlb, fe interfecabit in angulo sequali angulo fiib BCD. 
Si placet curvas hac regula inventas theoremate 
prsecedente conflruere, ex iis, quse hie tradita funt, cur- 
va huic negotio apta inveniri poteft ; erit enim curvse 
illius ordinata sequalis areae curvx ;t ^ ad ^ applicatas, 
quando angulus fub M P v redus ell. Verbi causa, 
hujus areae fluxio, nimirum P j/ x i in exemplo fecun- 
m — K 
do prioris partis hujus regulae erit = R R x R « 
xr+^R' + ^’R^ +/RA izi R R^ X r + ^ R^ 
-f- ^ R^. • • • +/R^i ; ideoque curvae hie requifitae or- 
I n n 
dinata erit — — R n x — i — c 4 i d R* 
a w + ^ mF I 
n 
+ — L— • • • + — 
^ m-\~ 5'^ 
In exemplo poflerioris partis hujus regulae erit R 
(=^ax 
a 
' 2 .bcr-\~icdr^~\~ 
bb-\-zb d^cc Xrr-\-ddr‘^ 
Y ideoque 
