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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xml:space
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">_Probl_. IV.</
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<
s
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<
s
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<
s
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">& </
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<
s
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xml:space
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">_aſymptotis_
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xml:space
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">Fig. 187.</
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DB, DH per F deſcripta ſit _hyperbola_ FXG; </
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<
s
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xml:space
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">item centro Ddeſcrip-
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tus ſit circulus KZL; </
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<
s
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xml:space
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">ſit denuò
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curva AMB talis, ut in hac ſumpto
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quocunque puncto M, & </
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<
s
xml:id
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xml:space
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">per hoc trajectâ rectâ DMZ, item ſumptâ
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DI = DM; </
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<
s
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xml:space
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">& </
s
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<
s
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xml:space
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">ductâ IX ad BF parallelâ, ſit _ſpatium hyperbolicum_
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BFXI æquale duplo _circulari ſectori_ ZDK; </
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<
s
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xml:space
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">curvæ AMB tangens
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ad M determinetur.</
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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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">Ducatur DS ad DM perpendicularis; </
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<
s
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xml:space
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">ſitque DB x BF = Rq;
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</
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<
s
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">fiátque DK. </
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<
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">R:</
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<
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">: R. </
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<
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<
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">tum DK. </
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<
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<
s
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<
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">DT; </
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<
s
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xml:space
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">& </
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<
s
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xml:space
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">connecta-
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tur TM; </
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<
s
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">hæc curvam AMB tanget.</
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</
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<
s
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">Adnotetur curvæ AMB hanc eſſe proprietatatem; </
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<
s
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">ut DI ſit inter
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DB, DO (vel DA) eodem ordine _media proportionalis Geometricè_,
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quo arcus KZ inter _o_
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(ſeu nihilum) & </
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<
s
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">arcum KL eſt medius _Arith-_
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_meticè_. </
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<
s
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xml:space
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">hoc eſt, ſi DI ſit numerus in ſerie _Geometricè proprtionalium_
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incipiente à DB, & </
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<
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">terminatâ in DA; </
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<
s
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">ac _o_
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, KL ſint Logarithmi
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ipſarum DB, DA; </
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<
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">erit KZLogarithmus ipſius DI. </
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<
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">Vel
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retrò (prout vulgares _Logarithmi_ procedunt, ſi DI ſit numerus in
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ſerie _Geometrica_ exorſa à DO, & </
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<
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">deſinente in DB ac _o_
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ſit _Logarith-_
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_mus_ ipſius DO, & </
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<
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">arcus LK ipſius DB, erit arcus LZ _Logarithmus_
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ipfius DI.</
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<
s
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">Quod ſi abſolutè conſtruatur curva AMB, ejúſque _tangens Me-_
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_chanicè_ deprehendatur, inde patet _hpperbolici ſpatii Cycliſmum_ dari,
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vel _Circuli hyperboliſmum_.</
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<
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menſionem) luculentè proſecutus eſt præclariſſimus D. </
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<
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">_Walliſſius
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_, in
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Libro dè
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_Cycloide_; </
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<
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<
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">_Probl_. V.</
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<
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<
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<
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comprehenſa) & </
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ſi utcunque à D projiciatur recta DNM, & </
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<
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cularis ſit, & </
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<
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<
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DN.</
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</
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<
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