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

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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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