Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

86. Series ſexta.

_a_ - {_cc_/_a_} = _x_.

_aa_ - _cc_ = _nn_.

_a_ 3 - _cca_ = _n_ 3 .

_a_ 4 - _ccaa_ = _n_ 4 .

Fiat angulus RAI ſemirectus, & AD ad AI perpendicularis; in qua AC = _c_; tum utcunque ductâ GZ ad AD parallelâ, ſit
AG (vel GZ). AC: : AC. ZK, & per K, intra angulum DAR
deſcribatur _hyperbola_ KYK; tum ſint curvæ CLYHLλ, AMYHMμ,
ANYHN ν [?] tales, ut inter AG (vel GZ) & GK ſit _media_ GL,
_bimedia_ GM, _trimedia_ GN; hæ propofito deſervient.

86.1.

Fig. 213

Conſtat hoc, ut in præcedente; & quo pacto radices reſpectivè
determinantur. Verùm adnotetur prætereà.

87. Not.

1. Curvæ CLH, AMH, ANH ad quintam ſeriem pertinent; re-
liquæ HL λ, HM μ, HN ν ad ſextam.

2. Quoad curvas ad quintam ſeriem pertinentes; ſi A φ = √{ACq/2}; & ordinetur φ Y; erit Y communis linearum interſectio, ſeu _no_-
_dus._

3. In harum primo gradu ordinata AK eſt inſinita in ſecundo AC
eſt maxima; in tertio ſi fuerit AP = √{ACq/3}, & ordinetur PV,
erit PV maxima(unde radicum una ſemper major eſt quam √{ACq/3}
altera minor) in quarto ſi AQ = √{ACq/4} = {AC/2}, & ordinetur QX,
erit QX maxima (unde radicum una major erit, altera minor ipsâ
{AC/2}).

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