81.
Not.
1. Si in AD (ad ipſam AB perpendiculari) deſumatur AE = _n_;
& ducatur EF ad AB parallela, hujuſce cum lineis expoſitis interſe-
ctiones exhibebunt radices _a_ reſpectivè.
2. Cum ad haſce curvas ordinatæ ſemper terminatæ ſint, & inter
ipſas maxima quædam detur, hujus _ſeriei æquationes_, pro modulo aſ-
ſignatæ AE (vel _n_) ſubinde duas radices veras habent (cùm utique
fuerit AE curvæ maximâ ordinatâ minor reſpectivè, hoc eſt cùm EF
curvæ bis occurrerit) nonnunquam duntaxat unam (cum AE nempe
maximam adæquet, adeóque EF curvam contingat) aliquando nullam
(cum ſcilicet AE maximam excedat, adeoque nec EF curvæ unquam
occurrat).
3. In ſecundo gradu ſi AO = OB, & ordinetur OT, erit OT
maxima; (adeóque radicum una major quàm {AB/2}, altera minor) in
tertio, ſi AP = 2 PB, & ordinetur PV, erit PV maxima (unde
radicum una major erit quàm {1/3} AB, altera minor) demùm in quar-
to gradu ſi AQ = 3 QB, & ordinetur QX, erit QX _maxima_
(& hinc una radicum ſemper major, quàm {1/4} AB, & altera minor).
4. Hinc conſectatur, ſi fuerit, in ſecundo gradu n & gt; {_b_/2}; in tertio
_n_
2
& gt; {4_b_
3
/9} - {8_b_
3
/27
[?]
} = {4 _b_
3
/27}; in quarto _n_
4
& gt; {27/64}_b_
4
- {81/256}_b_
4
=
{27_b_
4
/256}; nullam dari radicem.
5. Omnium radicum _maxima_ eſt ipſa AB, vel _b_.
6. Omnium curvarum communis _interſectio_ (ſeu _nodus_) eſt pun-
ctum T; & ſi fuerit _n_ = {_b_/2}; ſemper AO (vel {_b_/2}) eſt una radix.
7. Curva ALB eſt _Circulus_, reliquæ AMB, ANB eum quo-
dammodo referunt.
1. # 2. # 3.
_a_ + _b_ = _n_ \\ _a_ + _b_ = {_nn_/_a_} \\ _a_ + _b_ = {_n_
3
/_aa_} \\ _a_ + _b_ = {_n_4
4
/_a_
3
} # _a_ - _b_ = _n_. \\ _a_ - _b_ = {_nn_/_a_} \\ _a_ - _b_ = {_n_
3
/_aa_} \\ _a_ - _b_ = {_n_
4
/_a_
3
3} # {_b_ - _a_ = _n_. \\ _b_ - _a_ = {_nn_/_a_} \\ _b_ - _a_ = {_n_
3
/aa} \\ _b_ - _a_ = {_n_
4
/_a_
3
}
