Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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am puncto M, ductíſque rectis MPX ad BD, & </
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parallelis, poſitóque rectam MT tangere curvam AMB, ſit TP.
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note-0307-01
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PM:</
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<
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<
s
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xml:space
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">erunt figuræ ADKE, DBLG ſibimet æqua-
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les.</
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<
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<
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<
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quentur, & </
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<
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<
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<
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xml:space
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">: QY.
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</
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<
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<
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">Omnium hactenus Propoſitorum fœcundiſſimum eſt hoc
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_Tbeorema_; </
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<
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">præcedentium quippe complura vel in eo continentur, aut
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ab eo facilè conſectantur. </
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<
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">Nam poſito lineam AMB indeterminatam
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eſſe naturâ, ſi ipſarum EXK, GYL alterutra pro tuo arbitratu de-
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terminetur, exinde reſultabit Theorema quoddam ejuſmodi, qualia
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ſuperiùs exhibentur aliquammulta. </
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">linea GYL ponatur recta
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cum ipſa BD ſemi-rectum conſtituens angulum (quo caſu concipiun-
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tur puncta D, G coincidere) proveniet indè prima _Lectionis_ XI. </
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<
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GYL ſit recta ad DB parallela, emerget _Lectionis ejuſdem._ </
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<
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ſus ſi PM = PX (vel lineæ AMB, EXK ſint eædem) conſeque-
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tur hinc _decima_ ejuſdem. </
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<
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">Exhinc porrò liquet adſumpto cuilibet ſpa-
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tio _infinita, genere diverſa, ſpatia æqualia_ facilè deſignari veluti ſi _ſpa-_
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_tium_ DGLB ponatur _circuli quadrans_, cujus _centrum_ D; </
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AMB ſit _parabola_, cujus _axis_ AD, emerget curvæ EXK hæc pro-
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prietas, ut (ſi dicatur DB = r; </
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xml:space
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">_k_ (vel
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{DB q/2 AD}) ſit _parabolæ ſemipar ameter_) ſit {_rrk_/2} = _kkx_ + _xyy_. </
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<
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AMB ponatur _hyperbola_, procreabitur alterius generis curva EXK.
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</
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<
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αν meam incuſo, qui non hoc _Theorema_ (ſi-
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cut & </
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<
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">ea quæ ſubſequuntur, quorum ferè ratio conſimilis eſt, & </
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par uſus) primo loco poſuerim, & </
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">ex eo (nec non è reliquis mox
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ſubjiciendis) quod fieri poſſe video, reliqua deduxerim. </
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hujuſmodi _Phrygiam ſapientiam_ juxta mecum pleriſque familiarem au-
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tumo, literas has tractantibus.</
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<
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comprehenſum) ſint item curvæ EXK, GYL ità relatæ, ut ſi in curva
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AMB liberè ſumatur punctum M, ducatur DMX, ſit DQ = DM,
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ducatur QY ad DB perdendicularis, ſit DT ad DM perpendicula-
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ris, recta MT curvam AMB contingat; </
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<
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TD. </
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duplum.</
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