Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

75. 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.

76. 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-
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 , _bi-_ _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 .

76.1.

Fig. 206.
Vid. pag. 90.

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