Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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. XIII.</
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<
s
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">Æ _Quationum_ naturam è terminorum _analogia_ expoſuit _Vieta_;
<
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</
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<
s
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xml:space
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">illam ex eorum in ſe ductu dilucidiùs explicuit _Carteſius_. </
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<
s
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xml:space
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">Eam
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ego jam è linearum ſingulis appropriatarum deſcriptione conabor ali-
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quatenus enucleatam dare; </
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<
s
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xml:space
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">qui ſanè modus rem præſertim elucidare
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videtur, ac ob oculos ponere, agedum.</
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<
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">_Notetur_, In ſequentibus perpetim ad eaſdem ſeries redigi æquatio-
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nes, quæ _coefficientes_ habent eaſdem.</
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Series prima.</
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<
s
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xml:space
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">_a_ + _b_ = _n_.</
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<
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</
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<
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<
s
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xml:space
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">_aa_ + _ba_ = _nn_.</
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<
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</
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<
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<
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">_a_
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+ _baa_ = _n_
<
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.</
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<
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</
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<
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<
s
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">_a_
<
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+ _ba_
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= _n_
<
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, &</
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<
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">c.</
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<
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">Sumatur recta BA æqualis coefficienti _b_, & </
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">hæc verſus H indefini-
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">Fig. 206.</
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tè protendatur; </
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">ſint anguli RAH, SBH ſemirecti, ſintque lineæ
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ALL, AMM, ANN tales, ut rectâ GK ductâ ad AH utcunque
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perpendiculari (quæ dictas lineas ordine ſecet punctis L, M, N; </
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<
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ctaſque BS, AR punctis K, Z) ſit inter GZ, GK _media_ GL ,
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xlink:label
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_media_ GM, _trimedia_ GM; </
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">hæ lineæ propoſitarum æquationum
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naturæ explicandæ inſervient. </
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">Nam ſi AG (vel GZ) dicatur _a_; </
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">erit
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BG (vel GK) = _b_ + _a_; </
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<
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xml:space
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">atque GLq = _aa_ + _ba_; </
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xml:space
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">& </
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">GM cub.
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+ _baa_; </
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xml:space
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">& </
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<
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xml:space
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">GN_qq_ = _a_
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+ _ba_
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.</
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