{_cc_/3}, ac ordinetur PV ad curvam AMH, erit PV maxima; item ſi
AQ = {3/8}_b_ + √{9/64}_bb_ + {_cc_/2}, & ordinetur QX ad curvam ANH
erit QX maxima.
3. Hinc, ſi in ſecundo harum gradu ſit _n_& gt; √ _cc_ + {_bb_/4}; in ter-
tio ſi (poſito fore f = {_b_/3} + √{_bb_/9} + {_cc_/3}) ſit _n_
3
& gt; _ccf_ + _bff_
- _f_
3
; in quarto, ſi (poſito fore _g_ = {3/8}_b_ + √{9/64}_bb_ + {_cc_/2}) ſit _n_
4
& gt; _ccgg_ + _bg_
3
- _g_
4
; nulla datur radix; nam his ſupp ſitis,
recta EF curvis non occurret, reſpectivè.
4. Si fuerit Aφ = {_b_/4} + √{_bb_/16} + {_cc_/2}, & ordinetur φ Y; erit Y
_Nodus_ curvarum; unde ſi _n_ = Aφ; erit Aφ una radicum in omni-
bus.
5. Curva CLH, eſt _circumferentia Circuli_, cujus _Centrum_ O; reliquæ AMH, ANH ſunt _Cycliformes_.
6. Peculiare eſt in ſecundo gradu, quòd ſi n& lt; c, detur una tan-
tùm radix.
7. In hac radicum maxima (quæ & minima eſt in nona ſerie) eſt
AH = {_b_/2} + √{_bb_/4} + _cc_.
8. Curva HL λ eſt _hyperbola æquilatera_, cujus _ſemiaxis_ OH; re-
liquæ HMμ, HNν ſunt _hyperboliformes_; unde patet in ſerie nona
ſemper unam, & hanc unicam radicem haberi.
93.
Series decima.
Fig. 216.
_a_ + _b_ - {_cc_/_a_} = _n_.
_aa_ + _ba_ - _cc_ = _nn_.
_a_
3
+ _baa_ - _cca_ = _n_
3
.
_a_
4
+ _ba_
3
-_ccaa_ = _n_
4
, & c.
