29097
RG.
AG:
: _m.
n_:
: TD.
AD &
gt;
SG.
AG.
quare 112. _hujus._
_app._225. _hujus ap._& gt; SG. unde patet tota AFB extra circulum AEB jacere.
333. _hujus ap.__app._225. _hujus ap._& gt; SG. unde patet tota AFB extra circulum AEB jacere.
X.
Reliquis itidem ſtantibus, ſiad baſin GE (utcunque parallelam
44Fig. 139. ipſi DB) & axem AD conſtituta intelligatur _paraboliformis_ ejuſdem cum
ipſa AFB generis (nempe cujus etiam exponens {_n_/_m_}) illa ad partes A
ſupra GE, extra _circulum_ tota jacebit.
44Fig. 139. ipſi DB) & axem AD conſtituta intelligatur _paraboliformis_ ejuſdem cum
ipſa AFB generis (nempe cujus etiam exponens {_n_/_m_}) illa ad partes A
ſupra GE, extra _circulum_ tota jacebit.
Nam in arcu AE accepto quocunque puncto M, ductâque MP ad
EG parallelâ, & MV circulum tangente; eſt VP. AP & lt; SG.
AG & lt; RG. AG: : _m. n_; itaque rurſus liquet 553. _hujus ap._tum.
EG parallelâ, & MV circulum tangente; eſt VP. AP & lt; SG.
AG & lt; RG. AG: : _m. n_; itaque rurſus liquet 553. _hujus ap._tum.
XI.
Conſectatur etiam dictam (ipſi AFB coordinatam &
ad ba-
ſin GE conſtitutam) _paraboliformem_ infra GE ad DB protractam,
66Fig. 139. eatenus intra _Circulum_ totam cadere,
ſin GE conſtitutam) _paraboliformem_ infra GE ad DB protractam,
66Fig. 139. eatenus intra _Circulum_ totam cadere,
Quòd intra _Circulum_ ſtatim infra EG cadet ex eo patet, quòd ipſam
tangens RE circulum ſecat (quia nempe SE circulum tangit). quòd
alibi _Circulo_ non occurret hinc patet; quoniam poſito quòd occurrat
uſpiam ad N, tota ſupra N extra circulum caderet, contra 773. _hujus ap._ modò dictum ac oſtenſum eſt.
tangens RE circulum ſecat (quia nempe SE circulum tangit). quòd
alibi _Circulo_ non occurret hinc patet; quoniam poſito quòd occurrat
uſpiam ad N, tota ſupra N extra circulum caderet, contra 773. _hujus ap._ modò dictum ac oſtenſum eſt.
XII.
Porrò, _Hyperbolæ_ AEB (cujus centrum C) &
_parabolifor-_
88Fig. 140. _mis_ AFB, cujus exponens {_n_/_m_}, communes ſint axis AD, baſis DB;
ſit autem AD = {2 _n_ - _m_/_m_ - _n_} CA; & BT _hyperbolam_ tangat; hæc
quoque _paraboliformem_ AFB continget.
88Fig. 140. _mis_ AFB, cujus exponens {_n_/_m_}, communes ſint axis AD, baſis DB;
ſit autem AD = {2 _n_ - _m_/_m_ - _n_} CA; & BT _hyperbolam_ tangat; hæc
quoque _paraboliformem_ AFB continget.
Nam eſt CD.
CA:
: CA.
CT.
acindè AD.
TA:
: CD.
CA;
inverſéq;
componendo TD. AD: : CA + CD. CD. Verùm ex hypo-
theſi, eſt _m_ - _n_. 2 _n_ - _m_: : CA. CD; adeoque inversè compo-
nendo CA. CD: : _m_ - _n. n_: & rurſus componendo CA + C D.
CD: : _m. n._ hoc eſt TD. AD: : _m. n_. unde BT _hyperboliformem_
contingit.
componendo TD. AD: : CA + CD. CD. Verùm ex hypo-
theſi, eſt _m_ - _n_. 2 _n_ - _m_: : CA. CD; adeoque inversè compo-
nendo CA. CD: : _m_ - _n. n_: & rurſus componendo CA + C D.
CD: : _m. n._ hoc eſt TD. AD: : _m. n_. unde BT _hyperboliformem_
contingit.
XIII.
Hinc rurſu datà ratione ipſius AD ad CA, _paraboliformis_
ad punctum B _bype bolam_ contingens deſignabitur. nempe ſit AD =
{_s_/_t_} CA; erit {_n_/_m_} = {_t_ + _s_/2 _t_ + _s_}. Nam hoc ſuppoſito erit
ad punctum B _bype bolam_ contingens deſignabitur. nempe ſit AD =
{_s_/_t_} CA; erit {_n_/_m_} = {_t_ + _s_/2 _t_ + _s_}. Nam hoc ſuppoſito erit
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