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

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in quarto _a_ + {_cc_/4_a_}& gt;_ n_; quæ tamen inæqualitas eo minor eſt, quò
AE (vel _n_) major exiſtit.
_a_ + {_cc_/_a_} = _n_.
_a_ + {_cc_/_a_} = {_nn_/_a_}.
_a_ + {_cc_/_a_} = {_n_3/_aa_}.
_a_ + {_cc_/_a_} = {_n_4/_a_3}.
Poſſit hæc ſeries explicari juxta præcedentium modum ſecundum,
Fig. 212.&
eaſdem adhibendo curvas LXL, MXM, NXN; quarum nimi-
rum proprietas eſt, ut rectâ GK ductâ ad AH utcunque perpendicu-
lari, ſit GL = {_nn_/AG};
& GM = {_n_3/AGq}; & GN = {_n_4/AGcub}.
Nam ſi fiat angulus HAR ſemirectus, & & ſit GE. _c_: :_c_. EO; & per O intra a-
ſymptotos AD, AR deſcribatur _hyperbola_ OO;
hujuſce cum expo-
ſitis lineis LXL, MXM, NXN interſectiones, radices _a_ reſpectivas
determinabunt;
ductis utique LG, MG, NG ad AH perpendicu-
laribus;
erunt interceptæ AG ipſis _a_ æquales reſpectivè.

Fig. 213.
{_cc_/_a_} - _a_ = _n_.
_cc_ - _aa_ = _nn_.
_cca_ - _a_3 = _n_3.
_ccaa_ - _a_4 = _n_4.