Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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xml:space
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">Si à puncto E in _axe A m coni recti_ ABC _p_ recta infinita EC
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tranſeat per _coni ſuperficiem_, & </
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<
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">Fig. 178.</
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recta ECdonec redeat ad locum à quo coepit moveri, ita ut femper
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aliqua pars ejus ſecet _coni ſuperficiem_ (puta per H) _perbolam_ CFD & </
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<
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rectas DAA Cin ſuperficie coni ſitas) _ſolidum comprebenſum à ſuper-_
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_ficie vel ſuperficiebus genitis à linea_ EC ſic mota & </
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<
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">à _portione ſuperft-_
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_ciei_ ejuſdem coni terminatæ à linea vel lineis CFD, DA, ACquas
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recta ECcircumlata deſcribit in _ſuperficie conica_, erit æquale _Pyra-_
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_midi_ cujus _Altitudo_ eſt æ qualis _perpendiculari_ E _n_ à puncto E ad latus
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_Coni_ deductæ _b@ſis_ verò æqualis eidem _ſuperficiei conicœ terminat œ à_
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linea vel lineis CFD, DA, ACgeneratis à motu lineæ EC.</
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<
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">_Solidum_ enim ECF, DAC conſtat ex _infinitis pyramidibus_ EC _o_ A
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E _o o_ A, &</
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<
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">æquialtis perpendiculari E n, quarum baſes omnes
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ſimul ſumptæ, exhauriunt _ſuperficiem conicam_ CFD, DA, AC.</
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<
s
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">Datus ſit _Conus rectus_ ABC _p_ ſecetur à plano CFD axi A _m_ pa-
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rallelo ducantur rectæ AC, ADà vertice _coni_ ad _lineam byperbolicam_
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CFD, & </
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_verticem_ E in _axe coni_; </
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E _n_ lateri coni.</
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<
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ctis DA, ACita ſe habet ad ACD _baſem pyramidis_ EACD ut
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_altitudo_ E δ _pyramidis_ EACD ad perpendiculum E _n._ </
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enim Conici ACF D, ECFD habent vertices A & </
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CFD (quæ eſt utrique Conico communis) parallelo ergo ſunt æ-
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quales. </
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">Si ergò à ſolido quod componitur à conico ACFDaddito
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pyramide ECADauferatur conicus ECFDreliquum erit ſolidum
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ECFDACquale in propoſitione prima deſcribitur motu rectæ EC
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æquale pyramidi EAC D. </
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<
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ciprocæ ſunt _baſes al@itudinibus_, ut _altitudo_ E δ _pyramidis_ EACD
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ad perpendiculum E _n_ ita erit _ſuperſicies conica_ terminata à _linea by-_
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_perbolica_ CFD & </
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