Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of contents

< >
[61.] _Probl_. IV.
[62.] _Probl_. V.
[63.] _Probl_. VI.
[64.] _Probl_. VII
[65.] _Probl_. VIII.
[66.] _Probl_. IX.
[67.] _Probl_. X.
[68.] _Corol. Theor_. I.
[69.] _Theor_. II.
[70.] _Theor_. III.
[71.] _Theor_. IV.
[72.] _Theor_. V.
[73.] _Theor_. VI.
[74.] _Theor_. VII.
[75.] Lect. XIII.
[76.] Æquationum Series prima.
[77.] _Notetur autem_,
[78.] Series ſecunda.
[79.] Not.
[80.] Series tertia.
[81.] Not.
[82.] Not.
[83.] Series quarta.
[84.] Not.
[85.] Series quinta.
[86.] Series ſexta.
[87.] Not.
[88.] Series ſeptima.
[89.] Not.
[90.] Series octava.
< >
page |< < (125) of 393 > >|
318125 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.
_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.
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.
_Probl_. VII
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 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.

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index