Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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lineámque VIF tangat recta FT; </
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<
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xml:space
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xml:space
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IX.</
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FS. </
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<
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<
s
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xml:space
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<
s
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xml:space
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"> ergò DE x SD = (2 VDEZ = ) FDq. </
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<
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xml:space
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">unde conſtat angulum
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<
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(_b_) it
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xml:space
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">Cor. præc.</
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QFS rectum eſſe. </
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<
s
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">quod Propoſitum erat.</
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<
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<
s
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xml:space
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">Adjungam & </
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<
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<
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<
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">Sit curva quævis AGEZ, punctúmque quoddam D (à quo
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projectæ DA, DG, DE, & </
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<
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<
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">ab initio DA continuò decreſcant)
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tum altera ſit curva DKE, priorem interſecans in E, naturâque ta-
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lis, ut à D utcunque projectâ rectâ DKG (quæ curvam AEZ ſecet
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in G, curvam DKE in K) ſit perpetuò rectangulum ex DK, & </
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<
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ſignatâ quâdam lineâ R æquale ſpatio ADG; </
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<
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DE perpendiculari, ſit DT = 2 R; </
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<
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xml:space
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">& </
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<
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">connectatur TE; </
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<
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curvam DKE continget.</
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<
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">Nam ſumpto quovis in curva DKE puncto K, ducatur recta DKG;
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</
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">ſumptâ DL = DK, ducatur LR ad DT parallela ( ſecans ipſam
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DG in Y). </
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<
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">tum per E ducatur EX ad DE perpendicularis (hæc
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verò extra curvam AEZ, ad partes Z cadet, quia decreſcunt proje-
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ctæ verſus Z; </
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<
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<
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nus ſaltem, quatenus huic Propoſito ſatisfaciet). </
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ctum G ſupra E, verſus initium A, & </
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<
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</
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adeóque RL x DE = TD x LE (a) = 2 R x LE (a) = 2 GDE
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&</
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punctum Y extra curvam, quia DY &</
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<
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<
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punctum R eſt extra curvam.</
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<
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utì priùs, RL x DE = 2 GDE &</
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</
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<
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<
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tota, (nam etiam extra arcum LK curvæ KE circumductum tota ja-
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cet) ergò punctum R rurſus extra curvam exiſtit. </
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<
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tur rectam TER curvam DKE tangere.</
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</
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<
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<
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quod ducta ſit DKG; </
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<
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DT = 2 P; </
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<
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la; </
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<
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">Nam concipiatur curva DOG, per G tranſiens, talis, ut rectâ
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quâcunque DON à D projectâ (quæ curvam DOG ſecet in O,
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curvam DNE in M, curvam AGE in N) ſit ſemper DO x P æ-
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qualis ſpatio ADN; </
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<
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DM. </
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<
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neæ DKE, DOG analogæ erunt. </
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