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rectâ DB, ſit DB.
R:
: R.
BF (ſit autem BF, ut &
DHipſi DB
perpendicularis) tum per F, angulo BDHincluſa, tranſeat _hyperbola_
FXX; ſitque ſpatium BFXI (poſitâ nempe IX ad BF _parallelâ_)
æquale duplo ſpatio ZDL; ſit denuò DM = DG; erit Min cur-
va quæſita; quam utique ſi tangat recta TM, erit TD. DM: : R.
DN.
perpendicularis) tum per F, angulo BDHincluſa, tranſeat _hyperbola_
FXX; ſitque ſpatium BFXI (poſitâ nempe IX ad BF _parallelâ_)
æquale duplo ſpatio ZDL; ſit denuò DM = DG; erit Min cur-
va quæſita; quam utique ſi tangat recta TM, erit TD. DM: : R.
DN.
_Probl_. VI.
Sit rurſus ſpatium EDG (ut in præcedente) reperienda eſt curva
AMB, ad quam ſi projiciatur recta DNM, & ſit DT huic perpen-
11Fig. 188. dicularis, & MT curvam AMB tangat, fuerit DT = DN.
AMB, ad quam ſi projiciatur recta DNM, & ſit DT huic perpen-
11Fig. 188. dicularis, & MT curvam AMB tangat, fuerit DT = DN.
Adſumatur quæpiam R, &
ſit DZ q = {R3/DN};
item acceptâ DB
(cui perpendiculares DH, BF = {R3/DBq}; & per F intra _aſymptotos_
DB, DH deſcribatur _hyperboliformis_ ſecundi generis (in qua nempe
ordinatæ, ceu BF, vel IX, ſint quartæ proportionales in ratione DB
ad R, vel DG ad R) tum capiatur ſpatium BIXF æquale duplo
ZDL; & ſit DM = DI; erit M in curva quæſita; quam ſi tan-
gat MT, erit DT = DN.
(cui perpendiculares DH, BF = {R3/DBq}; & per F intra _aſymptotos_
DB, DH deſcribatur _hyperboliformis_ ſecundi generis (in qua nempe
ordinatæ, ceu BF, vel IX, ſint quartæ proportionales in ratione DB
ad R, vel DG ad R) tum capiatur ſpatium BIXF æquale duplo
ZDL; & ſit DM = DI; erit M in curva quæſita; quam ſi tan-
gat MT, erit DT = DN.
_Probl_. VII
Sit figura quævis ADB (cujus _axis_ AD, _baſis_ DB) &
utcunque
22Fig. 189. ductâ PM ad DB parallelâ datum ſit (ſeu expreſſum quomodocunque)
ſpatium APM, oportet hinc ordinatam PM exhibere, vel expri-
mere.
22Fig. 189. ductâ PM ad DB parallelâ datum ſit (ſeu expreſſum quomodocunque)
ſpatium APM, oportet hinc ordinatam PM exhibere, vel expri-
mere.
Acceptâ quâqiam R, ſit R x PZ = APM;
hinc emergat linea
AZZK; huic perpendicularis reperiatur ZO; tum erit PZPO
: : R. PM.
AZZK; huic perpendicularis reperiatur ZO; tum erit PZPO
: : R. PM.
_Exemp_.
AP vocetur x &
ſit APM = √ r x3, ergo PZ = √
{x3/r}; unde reperietur PO = {3 x x/2 r}. Eſtque √ {x3/r}. {3 x x/2 r}
: : r. {3/2} √ r x = PM. unde AMB eſt _Parabola_, cujus _Pa-_
rameter eſt {9/4} r.
{x3/r}; unde reperietur PO = {3 x x/2 r}. Eſtque √ {x3/r}. {3 x x/2 r}
: : r. {3/2} √ r x = PM. unde AMB eſt _Parabola_, cujus _Pa-_
rameter eſt {9/4} r.
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