29299&
gt;
NO.
quare liquent ea, quæ Propoſita ſunt.
Si _Circulo_ ſubſtituatur _Ellipſis_, eadem concluſio valet idem diſcur-
ſus probat; pofitâ AH _Ellipſis parametro_.
ſus probat; pofitâ AH _Ellipſis parametro_.
XVIII Habeant _hyperbola_ AEB (cujus axis AZ, parameter AH)
& _parabola_ AFB axin eundem AD, & baſin DB, _parabola_ ſupra
DB tota extra _hyperbolam_ cadet, extra verò, ſi infra DB protraha-
11Fig. 143.tur.
& _parabola_ AFB axin eundem AD, & baſin DB, _parabola_ ſupra
DB tota extra _hyperbolam_ cadet, extra verò, ſi infra DB protraha-
11Fig. 143.tur.
Nam connexæ ZH occurrat BD in I;
ergò DI eſt _parabolæ pa-_
_rameter_. Quòd ſi ſupra BD utcunque ducatur recta FEGK ad BD
parallela, ſecans hyperbolam in E, parabolam in F, rectas AD, ZH
punctis G, K, erit FGq = AG x DI & gt; AG x GK = EGq. qua-
re FG & gt; EG. Quòd ſiinfra BD, utcunque ducatur recta MNOL
ſecans hyperbolam in N, parabolam in M, rectas AD, ZH in O, &
L, erit NO q = AO x OL & gt; AO x DI = MOq. & indè NO
& gt; MO. unde conſtant ea quæ propoſita ſunt.
_rameter_. Quòd ſi ſupra BD utcunque ducatur recta FEGK ad BD
parallela, ſecans hyperbolam in E, parabolam in F, rectas AD, ZH
punctis G, K, erit FGq = AG x DI & gt; AG x GK = EGq. qua-
re FG & gt; EG. Quòd ſiinfra BD, utcunque ducatur recta MNOL
ſecans hyperbolam in N, parabolam in M, rectas AD, ZH in O, &
L, erit NO q = AO x OL & gt; AO x DI = MOq. & indè NO
& gt; MO. unde conſtant ea quæ propoſita ſunt.
XIX.
E dictis eliciuntur hæ _ad Circuli dimenſionem pertinentes regu-_
_la._ Sit BAE circuli portio, cujus axis AD, baſis BE; ſitque C
22Fig. 144. centrum circuli, & EH ſinus rectus arcus BAE; item, ſit AD =
{_s_/_t_} CA; erit 1. {2 _t_ - _s_/3 _t_ - 2 _s_} AD x BE & gt; port. BAE.
_la._ Sit BAE circuli portio, cujus axis AD, baſis BE; ſitque C
22Fig. 144. centrum circuli, & EH ſinus rectus arcus BAE; item, ſit AD =
{_s_/_t_} CA; erit 1. {2 _t_ - _s_/3 _t_ - 2 _s_} AD x BE & gt; port. BAE.
2.
EH + {4 _t_ - 2 _s_/3 _t_ - 2 _s_} BH &
gt;
arc.
BAE.
3.
{2/3} AD x BE &
lt;
port.
BAE.
4.
EH + {4/3} BH &
lt;
arc.
BAE.
XX.
Itidem hæ deducuntur ad _hyperbolæ dimenſionem ſpectantes re-_
_gulæ_. Sit _hyperbolæ_ (cujus centrum C) ſegmentum ADB, habens
33Fig. 145. axin AD = {_s_/_t_} CA; & baſin DB;
_gulæ_. Sit _hyperbolæ_ (cujus centrum C) ſegmentum ADB, habens
33Fig. 145. axin AD = {_s_/_t_} CA; & baſin DB;
erit 1.
{2 _t_ + _s_/3 _t_ + 2 _s_} AD x DB &
lt;
ſegm.
ADB.
&
2.
{2/3} AD x DB &
gt;
ſegm.
ADB.