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

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Series duodecima

Fig. 217
_a_ - _b_ + {_cc_/_a_} = _n_.
_aa_ - _ba_ + _cc_ = _nn_.
_a3_ - _baa_ + _cca_ = _n3_.
_a4_ - _ba3_ + _ccaa_ = _n4_, & c.

Series decima tertia

_b_ - _a_ - {_cc_/_a_} = _n_.
_ba_ - _aa_ - _cc_ = _nn_.
_baa_ - _a3_ - _cca_ = _n3_.
_ba3_ - _a4_ - _ccaa_=_n4_, & c.
Pro his, Sit AB=_b_; & AC = _c_; & angulus. AB S ſemire-
Fig. 217.ctus, &
G ξ ad AB utcunque perpendicularis, & AG . AC : : AC.
ξ K; & KH KI K _byperbola aſymptotis_ SA , SB deſcripta; denuò
curvæ CLHLILλ, AMHMIMμ, ANHNINν tales ſint, ut inter AG,
GK ſit _media_ GL , _bimedia_ GM , _trimedia_ GN .

Not.

1. Curvæ CLH, AMH, ANH, atque curvæ IL λ, IM μ,
IN ν ad ſeriem duodecimam ſpectant, verùm intermediæ curvæ HLI,
HMI, HNI ad decimam tertiam.
2. Curvæ CLH, IL λ ſunt _hyperbolæ æquilateræ_, quarum com-
mune _centrum_ O (rectam AB biſecans) &
_ſemiaxis_ OH (vel OI)
= √ AO q.
- AC q reliquæ tales ſunt, quales figura monſtrat.

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