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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;
11Fig. 213 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.
11Fig. 213 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.
Conſtat hoc, ut in præcedente;
&
quo pacto radices reſpectivè
determinantur. Verùm adnotetur prætereà.
determinantur. Verùm adnotetur prætereà.
Not.
1.
Curvæ CLH, AMH, ANH ad quintam ſeriem pertinent;
re-
liquæ HL λ, HM μ, HN ν ad ſextam.
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._
& 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}).
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}).