Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

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,
& 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}.

84.1.

Fig. 212.

Nam ſi fiat angulus HAR ſemirectus, & utcunque ducatur GEO
ad AH perpendicularis; & 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.

Poſſint conſimili modo ſubſequentes omnes æquationes explicari; ſed eas modo duntaxat priore dabimus expoſitas.

85. Series quinta.

Fig. 213.

{_cc_/_a_} - _a_ = _n_.

_cc_ - _aa_ = _nn_.

_cca_ - _a_ 3 = _n_ 3 .

_ccaa_ - _a_ 4 = _n_ 4 .

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