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 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.

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

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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Scan	Original
71	53
72	54
73	55
74	56
75	57
76	58
77	59
78	60
79	61
80	62
81	63
82	64
83	65
84	66
85	67
86	68
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90	72
91	73
92	74
93	75
94	76
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96	78
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99	81
100	82