337144
3.
Curva HLLI eſt _ſemicirculus_;
reliquas itidem oſtentat
Schema.
Schema.
4.
Si A ζ = {_cc_/_b_};
A Ψ = {_b_/4} - √ {_bb_/16} - {_cc_/2};
&
A φ = {_b_/4} +
√ {_bb_/16} - {_cc_/2}; ordinentúrque rectæ ζ V, ψ X, φ Y; erunt puncta V,
X, Y _nodi_ curvarum (ſi _b_ & lt; √ 8 _c c_, deerunt _nodi_ X, Y; ſi _b_ = √
8 _c c_; ii coaleſcent).
√ {_bb_/16} - {_cc_/2}; ordinentúrque rectæ ζ V, ψ X, φ Y; erunt puncta V,
X, Y _nodi_ curvarum (ſi _b_ & lt; √ 8 _c c_, deerunt _nodi_ X, Y; ſi _b_ = √
8 _c c_; ii coaleſcent).
5.
Ordinatarum ad curvam CL H _maxima_ eſt ipſa AC ;
ſin AP
= {_b_/3} - √ {_bb_/9} - {_cc_/3}, & ordinetur P γ ad curvam AM H; erit
P γ _maxima_; item ſi AQ = {3/8} _b_ - √ {@9/64} _b b_ - {_cc_/2}; & ordinetur
Q δ ad curvam AN H, erit Q δ _maxima_.
= {_b_/3} - √ {_bb_/9} - {_cc_/3}, & ordinetur P γ ad curvam AM H; erit
P γ _maxima_; item ſi AQ = {3/8} _b_ - √ {@9/64} _b b_ - {_cc_/2}; & ordinetur
Q δ ad curvam AN H, erit Q δ _maxima_.
6.
Ordinatarum ad curvam HLLI _maxima_ eſt ipſa OT ;
ſin AP
= {_b_/3} + √ {_bb_/9} - {_cc_/3}, & ad curvam HM I ordinetur _p g_, erit _p g_
_maxima_; item ſi A q = {3/8} _b_ + √ {9/64} _b b_ - {_cc_/2}; & ordinetur _q d_
ad curvam HN I, erit _q d maxima_.
= {_b_/3} + √ {_bb_/9} - {_cc_/3}, & ad curvam HM I ordinetur _p g_, erit _p g_
_maxima_; item ſi A q = {3/8} _b_ + √ {9/64} _b b_ - {_cc_/2}; & ordinetur _q d_
ad curvam HN I, erit _q d maxima_.
7.
Hinc radicum limites dignoſcentur, ut innuitur in iis, quæ ad
octavam ſeriem animadverſa ſunt.
octavam ſeriem animadverſa ſunt.
8.
Patet in Serie duodecima nunc tres, modo duas, ſemper unam
radicem haberi; in decima tertia verò ſubinde duas, aliquando tantùm
unam, interdum nullam haberi.
radicem haberi; in decima tertia verò ſubinde duas, aliquando tantùm
unam, interdum nullam haberi.
9.
Et hæc quidem conſtant poſito fore {_b_/2}&
gt;
_c_;
at ſi {_b_/2} = β;
evaneſcet Series decima tertia; coaleſcent puncta H, O, I; recta AB
_byperbolam_ KK K tanget; curvæque CL H, IL λ in rectas lineas
degenerabunt.
evaneſcet Series decima tertia; coaleſcent puncta H, O, I; recta AB
_byperbolam_ KK K tanget; curvæque CL H, IL λ in rectas lineas
degenerabunt.
10.
Sin {_b_/2} &
lt;
_c_;
etiam evaneſcit Series decima tertia;
_byperbola_ KKK
tota infra rectam AB jacente; quo caſu curva CL L erit hyperbola
æquilatera, habens centrum O, ſemiaxem (ipſi AB perpendicula-
rem) OT = √ AC q - AO q; tunc & curvæ AM M, AN N
11Fig. 218. ad infinitum procurrent, ſic ut æquationes, quæ in Serie duodecima,
unam ſemper, & unicam radicem obtineant. Hæc ſuffecerit inſinu-
âſſe; quin & rem totam hactenus particulatim attigiſſe. Subnecte-
mus autem notas quaſdam magìs generales.
tota infra rectam AB jacente; quo caſu curva CL L erit hyperbola
æquilatera, habens centrum O, ſemiaxem (ipſi AB perpendicula-
rem) OT = √ AC q - AO q; tunc & curvæ AM M, AN N
11Fig. 218. ad infinitum procurrent, ſic ut æquationes, quæ in Serie duodecima,
unam ſemper, & unicam radicem obtineant. Hæc ſuffecerit inſinu-
âſſe; quin & rem totam hactenus particulatim attigiſſe. Subnecte-
mus autem notas quaſdam magìs generales.
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