326133
GZ, GK media GL, bimedia GM, trimedia GN;
propoſitas æ-
quationes explicabunt hæ lineæ. Nam ſi AG (vel GZ) vocetur _a_;
erit BG (vel GK) = _a_ - _b_; & GLq = _aa_ - _ba_; & GM cub.
= _a_3 - _baa_; & GN _qq_ = _a_4 - _ba_3.
quationes explicabunt hæ lineæ. Nam ſi AG (vel GZ) vocetur _a_;
erit BG (vel GK) = _a_ - _b_; & GLq = _aa_ - _ba_; & GM cub.
= _a_3 - _baa_; & GN _qq_ = _a_4 - _ba_3.
Not.
1.
Ductâ AD ad AI perpendiculari, &
EF ad AI parallelâ, ſi
AE ponatur æqualis ipſi _n_; erunt EK, EL, EM, EN radices æqua-
tionum reſpectivæ, ſeu æquales quæſitis _a_.
AE ponatur æqualis ipſi _n_; erunt EK, EL, EM, EN radices æqua-
tionum reſpectivæ, ſeu æquales quæſitis _a_.
2.
Quoniam ordinatæ GK, GL, GM, GN à termino B verſus I
infinitè excreſcunt, ſemper habetur una vera radix, & unica.
infinitè excreſcunt, ſemper habetur una vera radix, & unica.
3.
Curva BLL eſt _hyperbola æquilatera_, cujus _axis_ AB, reliquæ
curvæ ſunt _hyperboliformes._
curvæ ſunt _hyperboliformes._
4.
Si AB biſecetur in O, triſecetur in P, quadriſecetur in Q, du-
cantúrque ad AR parallelæ OT, PV, QX, erunt hæ curvarum BLL,
BMM, BNN _aſymptoti._
cantúrque ad AR parallelæ OT, PV, QX, erunt hæ curvarum BLL,
BMM, BNN _aſymptoti._
5.
Hinc ſeqiutur in ſecundo gradu fore _a_ &
gt;
_n_ + {_b_/2};
in tertio
_a_ & gt;_ n_ + {_b_/3}; in quarto _a_ & gt; _n_ + {_b_/4}; quòd ſi _n_ ſatis magna ſit,
iſtæ inæqualitates ad æqualitatem proximè accedunt.
_a_ & gt;_ n_ + {_b_/3}; in quarto _a_ & gt; _n_ + {_b_/4}; quòd ſi _n_ ſatis magna ſit,
iſtæ inæqualitates ad æqualitatem proximè accedunt.
6.
Verarum in his radicum habetur _minima;_
ſcilicet ipſa AB, vel _b_.
Series tertia.
_b_ - _a_ = _n_.
_ba_ - _aa_ = _nn_.
_baa_ - _a_3 = _n_3.
_ba_3-_a_4 = _n_4.
&
c.
Sit AB = _b_, &
anguli RAB, SBA ſemirecti;
tum curvæ
11Fig. 280. ALB, AMB, ANB tales, ut ductâ rectâ GK ad AB utcunque
perpendiculari (quæ lineas expoſitas ſecet, ut vides) ſit inter AG
(ſeu GZ) & GK _media_ GL, _bimedia_ GM, _trimedia_ GN; pro-
poſitas æquationes explicatas dabunt hæ lineæ. Nam poſito fore AG
= _a_, erit GK = _b_ - _a_; & GLq = _ba_ - _aa_; & GMq =
_baa_ - _a_3. & GNq = _ba_3 - _a_4.
11Fig. 280. ALB, AMB, ANB tales, ut ductâ rectâ GK ad AB utcunque
perpendiculari (quæ lineas expoſitas ſecet, ut vides) ſit inter AG
(ſeu GZ) & GK _media_ GL, _bimedia_ GM, _trimedia_ GN; pro-
poſitas æquationes explicatas dabunt hæ lineæ. Nam poſito fore AG
= _a_, erit GK = _b_ - _a_; & GLq = _ba_ - _aa_; & GMq =
_baa_ - _a_3. & GNq = _ba_3 - _a_4.