Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

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 B [?] F _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.

63. _Probl_. VI.

Sit rurſus ſpatium EDG (ut in præcedente) reperienda eſt curva
AMB, ad quam ſi projiciatur recta DNM, & ſit DT huic perpen-
dicularis, & MT curvam AMB tangat, fuerit DT = DN.

63.1.

Fig. 188.

Adſumatur quæpiam R, & ſit DZ q = {R 3 /DN}; item acceptâ DB
(cui perpendiculares DH, BF = {R 3 /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.

64. _Probl_. VII

Sit figura quævis ADB (cujus _axis_ AD, _baſis_ DB) & utcunque
ductâ PM ad DB parallelâ datum ſit (ſeu expreſſum quomodocunque)
ſpatium APM, oportet hinc ordinatam PM exhibere, vel expri-
mere.

64.1.

Fig. 189.

Acceptâ quâqiam R, ſit R x PZ = APM; hinc emergat linea
AZZK; huic perpendicularis reperiatur ZO; tum erit PZPO
: : R. PM.

_Exemp_. AP vocetur x & ſit APM = √ r x 3 , ergo PZ = √
{x 3 /r}; unde reperietur PO = {3 x x/2 r}. Eſtque √ {x 3 /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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