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

[61.] _Probl_. IV.

Page: 317 (124)

[62.] _Probl_. V.

[63.] _Probl_. VI.

[64.] _Probl_. VII

[65.] _Probl_. VIII.

[66.] _Probl_. IX.

[67.] _Probl_. X.

[68.] _Corol. Theor_. I.

[69.] _Theor_. II.

[70.] _Theor_. III.

[71.] _Theor_. IV.

[72.] _Theor_. V.

[73.] _Theor_. VI.

[74.] _Theor_. VII.

[75.] Lect. XIII.

[76.] Æquationum Series prima.

Page: 324 (131)

[77.] _Notetur autem_,

Page: 325 (132)

[78.] Series ſecunda.

[79.] Not.

[80.] Series tertia.

[81.] Not.

[82.] Not.

[83.] Series quarta.

[84.] Not.

[85.] Series quinta.

[86.] Series ſexta.

[87.] Not.

[88.] Series ſeptima.

Page: 332 (139)

[89.] Not.

Page: 332 (139)

[90.] Series octava.

Page: 333 (140)

333140

2. Hinc conſtat in ſecundo gradu ſi fuerit _n_& lt; C, nullam veram
radicem dari; alioquin in omnibus una ſemper habetur, & unica;
quoniam recta EF curvas ſemel interſecabit, nec pluries,

Series octava.

{_cc_/_a_} + _b_ - _a_ = _n_.

11Fig. 215.

_cc_ + _ba_ - _aa_ = _nn._

_cca_ + _baa_ - _a_3 = _n_3.

_ccaa_ + _ba_3 - _a_4 = _n_4, & c.

Series nona.

_a_ - _b_ - {_cc_/_a_} = _n._

_aa_ - _ba_ - _cc_ = _nn._

_a_3 - _baa_ - _cca_ = _n_3.

_a_4 - _ba_3 - _ccaa_ = _n_4. & c.

In recta AI ſumatur AB = _b_; & in AD ad ipſam AI perpen-
22Fig. 215. diculari ſit AC = _c_; fiant autem anguli IAR, ABS ſemirecti;
ducatúrque recta ZGK ad AI utcunque perpendicularis, ipſam BS
ſecans ad ξ; & ſit AG. AC: : AC. ξ K; tum per K intra angu-
lum DSB deſcribatur _byperbola_ KYHK; ſint denuò curvæ CLHLλ,
AMHMμ, ANHNν tales, ut inter AG, GK ſint _media_ GL, _bime-_-
_dia_ GM, _trimedia_ GN; hæ curvæ propoſito ſatisfacient; conſtat
autem hoc ut in præcedente.

Not.

1. Curvæ CLH, AMH, ANH ad octavam ſeriem pertinent, re-
liquæ verò HLλ, HMμ, HN@, ad nonam.

2. Quoad octavam ſeriem, ſi biſecetur AB in O, & ordinetur OT
ad curvam CLH eſt OT maxima; ſin ſiat AP = {_b_/3} + √{_bb_/9}

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