Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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FG, FH interceptæ pares interceptis ab EB, EC; </
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<
s
xml:id
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xml:space
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">hoc eſt minores
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interceptis à curvis EY, EZ; </
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<
s
xml:id
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xml:space
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">hoc eſt minores interceptis à curva
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FX, & </
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<
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">recta FA; </
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<
s
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xml:space
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">quapropter angulus XFA rectilineo HFG ma-
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jor eſt; </
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<
s
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xml:space
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">unde recta FA curvam FX non tangit, contra _Hy-_
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_potheſin_.</
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<
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</
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<
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<
s
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">IV. </
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<
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xml:space
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">Itidem, Tangat recta FA curvam FX, & </
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<
s
xml:id
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xml:space
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">ſint duæ curvæ
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EY, EZ tales, ut ab aſſignato puncto D utcunque ductâ rectâ IL
<
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<
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xlink:label
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">Fig. 79.</
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( quæ lineas expoſitas ſecet ut vides ) ſit ſemper KL = IG; </
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<
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xml:space
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EY, EZ ſeſe tangent.</
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<
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<
s
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xml:space
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">Nam, ſineges, his interſeratur _angulus rectiline
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us_ BEC; </
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<
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utcunque a D projecta ſecet recta DL; </
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<
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xml:space
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"> poteſt jam ab F recta
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xml:space
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">(_a_) 20 Lect.
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VII.</
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ci _(_puta FH_)_ talis, ut ſint è projectis à D a rectis FG, FH inter-
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ceptæ minores interceptis abipſis EB, EC, hoc eſt multo minores in-
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terceptis à recta E A, curváque FX. </
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<
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xml:space
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">Unde ſequetur angulum AFX
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rectilineo GF H majorem eſſe; </
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<
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xml:space
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">ac idcircò rectam AF non conting ere
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curvam FX, adverſus _Hypotheſin_.</
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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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">Hæ præcedentes duæ Concluſiones veræ ſunt, & </
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<
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monſtrantur, poſito interceptas IG, KL quamvis ad ſe perpetim ha-
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bere proportionem eandem. </
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<
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<
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xml:space
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">Propoſuimus hæc, ut ſequentium nonnulla à ſcrupulis munian-
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tur.</
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<
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<
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">Sit recta VEI, duæque curvæ YFN, ZGO ſic ad ſe relatæ,
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ut ductâ utcunque rectâ EFG ad poſitione datam AB parallelâ, ha-
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beant interceptæ E G, EF ſemper eandem rationem inter ſe; </
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<
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autem recta TG curvarum unam ZGO in G _(_cum recta VE con-
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veniens in T _)_ ducta TF alteram YFN quoque continget.</
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</
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<
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<
s
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xml:space
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">Nam utcun que ducatur recta IL (lineas expoſitas ut vides interſe-
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cans ) Eſtigitur IL. </
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Igitur IN &</
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<
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">ergò punctum K extra curvam YFN jacet; </
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<
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</
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<
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OL. </
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<
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">NK, ergò cùm lineæ GL, GO ſe tangant, etiam
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neæ F N, FK ſeſe tangent.</
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<
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_jus._</
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<
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<
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<
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<
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ut ductâ utcunque rectâ EFG ad poſitione datam parallelâ, ſint ſem-
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per EG, EF in eadem ra ione, concurrant autem duarum XEM,
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ZGO tangentes ET, GT in T; </
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<
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get.</
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