Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

334141 {_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_.

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.

11Fig. 216.

_a_ + _b_ - {_cc_/_a_} = _n_.

_aa_ + _ba_ - _cc_ = _nn_.

_a_3 + _baa_ - _cca_ = _n_3.

_a_4 + _ba_3-_ccaa_ = _n_4, & c.