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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<
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<
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xml:space
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<
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<
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<
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xml:space
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EBE ſeſe interſecantes in B, ac ita verſus ſe relatæ, ut ductâ utcunque
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rectâ DH ad poſitione datam DB parallelâ (in linea nempe DD D
<
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<
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69.</
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terminatâ) vel à deſignato puncto D projectâ DH; </
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<
s
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inter DH, DE eodem ordine media proportionalis Arithmeticè, quo
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DF inter eaſdem media Geometricè; </
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<
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tuò contingunt.</
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<
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<
s
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xml:space
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">Enimverò linea GBH extra lineam FBF totam cadere manifeſtum
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è præcedente.</
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<
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<
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">Ex iſthinc etiam (quod ſtrictim tranſcurrens moneo) di-
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verſis innumeris _Hyperbolarum_, aut _Hyperboliformium_ generibus con-
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venientes rectæ ασνμπωτοι definiuntur. </
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<
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poſitione datæ; </
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<
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berè rectâ PG ad DB parallela, ſit P φ conſtantèr inter PG, PE eo-
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dem ordine media proportionalis Arithmeticè, quo PF inter eaſdem
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media Geometricè; </
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<
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xml:space
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tinent rationem, eſt linea φ φ φ recta; </
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<
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">verùm linea VFF eſt _hyperbo-_
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_la,_ vel _hyperboliformis_ aliqua (communis quidem vel _Apolloniana_
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_hyperbola_, ſi PF ſit inter ipſas PG, PE ſimpliciter media, ſed alia
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diverſi generis quædam _hyperboliformis_, ſi PE ſit alterius cujuſpiam
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ordinis media) atqui patet è penultima præmiſſa lineam φ φ φ eodem
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ordine reſpondenti lineæ VFF _aſymptoton_ eſſe. </
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<
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neſcio, nobis certè πáρε@γον fuit, hic adnotâſſe.</
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<
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ſint restæ tres BA, BC, BQ; </
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<
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quodpiam D; </
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us BQ partes) tali@, ut à D projectâ quâcunque rectâ, ceu DN; </
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hujus à rectis B Q, BR intercepta pars (F E) minor ejuſdem à rectis
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BA, BC interceptâ parte (N M).</
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<
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D; </
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<
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DE, rectas ſecans, ut vides; </
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<
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VI.</
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ſtratis fore, FE &</
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<
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Vi. 8 Lect.</
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BH talis, ut à BQ, B H interceptæ minores ſint interceptis à BQ,
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BA; </
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<
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utcunque ductâ DN, quæ rectas interſecet, ut exhibet Schema; </
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