Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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ta recta BD; </
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<
s
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<
s
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particula indefinitè parva; </
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<
s
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xml:space
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">ducatúrque recta POad DTparallela,
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<
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curvam ſecans ad N; </
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<
s
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xml:space
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">dico PNad NOrationem habere majorem quâ-
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vis deſignabili, puta quàm R ad S.</
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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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<
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<
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xml:space
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">: RS; </
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<
s
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xml:space
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">connexaque recta BEcurvam ſecet in
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G, rectam POin K; </
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<
s
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xml:space
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">per G verò ducatur FHad DAparallela.
<
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</
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<
s
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xml:space
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">quoniam igitur BP ponitur indefinitè parva, eſt BP &</
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<
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<
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<
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">adeóq; </
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PK &</
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<
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">lt; </
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<
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">PN (nam ſubtenſa BGintra curvam tota cadit). </
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<
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">ergo PN. </
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NO &</
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">: DE. </
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<
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<
s
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xml:space
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<
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</
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<
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">Hinc, ſi baſis DBin partes ſecetur indeſinitè multas ad puncta
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Z; </
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<
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">& </
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<
s
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xml:space
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">per hæc ducantur rectæ ad DAparallelæ curvam ſecantes pun-
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ctis E, F, G; </
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<
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">per hæc verò ducantur _Tangentes_ BQ, ER, FS, GT
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parallelis ZE, ZF, ZG, DA occurrentes punctis Q, R, S, T;
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</
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<
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">habebit recta ADad omnes interceptas EQ, FR, GS, AT(ſi-
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mul ſumptas) rationem quàvis aſſignabili majorem.</
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</
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<
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<
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xml:space
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">Nam ducantur rectæ EY, FX, GV ad BD parallelæ. </
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igitur rectæ ZE, YF, XG, VA ad rectas EQ, FR, GS, AT (ſin-
<
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">Fig. 175.</
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gulæ ad ſingulas ſibi in directum poſitas reſpectivè) rationem deſigna-
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bili quâcunque majorem. </
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<
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_rationem_ habent deſignabili quâvis _majorem;_ </
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+ FR + GS + AT ejuſmodi rationem habet.</
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<
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">Hinc inter computandum, omnes EQ, FR, GS, AT ſimul ac-
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ceptæ nihilo æquivalent; </
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quantur; </
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portiunculis BE, EF, &</
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<
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</
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<
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<
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<
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">Fig. 176.</
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applicata DB; </
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<
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">æquiſecetur autem DB in partes indefinitè multas ad
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puncta Z, per quæ ducantur rectæ ad AD parallelæ, curvam AB
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interſecantes punctis X; </
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<
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parallelæ rectæ ME, NF, OG, PH; </
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<
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(rectis AD, DB, & </
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<
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">curvâ AB comprehenſo) _circumſcripta ſigura_
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ADBMXNXOXPXRA major _ſpatio_ quodam S; </
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<
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ADB non eſſe minus quàm S.</
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</
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<
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ADLKadæquante, & </
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<
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minor quàm AK, liquet rectangulum ADZRminus eſſe </
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