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_,

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[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.

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[90.] Series octava.

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324131

Lect. XIII.

Æ _Quationum_ naturam è terminorum _analogia_ expoſuit _Vieta_;
illam ex eorum in ſe ductu dilucidiùs explicuit _Carteſius_. Eam
ego jam è linearum ſingulis appropriatarum deſcriptione conabor ali-
quatenus enucleatam dare; qui ſanè modus rem præſertim elucidare
videtur, ac ob oculos ponere, agedum.

_Notetur_, In ſequentibus perpetim ad eaſdem ſeries redigi æquatio-
nes, quæ _coefficientes_ habent eaſdem.

Æquationum Series prima.

_a_ + _b_ = _n_.

_aa_ + _ba_ = _nn_.

_a_3 + _baa_ = _n_3.

_a_4 + _ba_3 = _n_4, & c.

Sumatur recta BA æqualis coefficienti _b_, & hæc verſus H indefini-
11Fig. 206. tè protendatur; ſint anguli RAH, SBH ſemirecti, ſintque lineæ
ALL, AMM, ANN tales, ut rectâ GK ductâ ad AH utcunque
perpendiculari (quæ dictas lineas ordine ſecet punctis L, M, N; re-
ctaſque BS, AR punctis K, Z) ſit inter GZ, GK _media_ GL , 22Vid. pag. 90. _media_ GM, _trimedia_ GM; hæ lineæ propoſitarum æquationum
naturæ explicandæ inſervient. Nam ſi AG (vel GZ) dicatur _a_; erit
BG (vel GK) = _b_ + _a_; atque GLq = _aa_ + _ba_; & GM cub.
= _a_3 + _baa_; & GN_qq_ = _a_4 + _ba_3.

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