Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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xml:space
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">IX Adnotabimus tantùm quòd ex _Problematis_ hujuſce natura con-
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ftructioneque propoſita ſatìs attendenti conſtabit (utique ſicut in _H@-_
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_potheſibus_ antehac tractatis uberiùs eſt declaratum) duorum tantùm
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ad eaſdem axis partes incidentium reflexosad unum ſeſe punctum de-
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cuſſare. </
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<
s
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echoid-s4123
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xml:space
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">nam aliorum unius (qui ſubinde poteſt dari) vel alterius re-
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flexi per ejuſmodi punctum tranſeuntes ad alteris partibus incidentes
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pertinebunt.</
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<
s
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xml:space
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">‖ Ex his quadantenus eluceſcit datis puncti radiantis,
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oculíque poſitione deſignari poteſt linea quævis, in qua dicti puncti
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ſpecies apparebit; </
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<
s
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echoid-s4125
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xml:space
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">incumbit proximè punctum in ea præciſum deter-
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minare, ad quo eadem conſiſtit. </
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<
s
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xml:space
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">eo ſpectat hoc Theoremation.</
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<
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<
s
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">X. </
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<
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">Ab eodem quocunque puncto A manantes duo radii AN, AR
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">Fig. 95, 96.</
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in circuli reflectentis peripheria præter illum arcum NR (qui inci-
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dentiæ punctis interjacent) intercipiant arcum PS; </
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<
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">eorum verò re-
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flexi intercipiant arcum π σ; </
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<
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">erit arcus π σ æqualis Summæ vel diffe-
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rentiæ dupli arcûs NR, & </
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<
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<
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">Nam (1) in prima figura;
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</
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<
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xml:space
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">eſt PS + SR + RN = PN = N π = π σ + σ R - RN; </
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<
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gò, pares hinc indè SR, & </
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<
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">σ R ſubducendo, erit PS + RN =
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π σ - RN. </
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<
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">proindéque PS + 2 RN = π σ. </
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<
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">(2). </
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<
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">in altera figura; </
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erit PS + SR - RN = PN = N π = RN + R σ - σ π. </
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<
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rè rurſus æquales auferendo SR, R σ manebit PS - RN = RN
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- σ π unde tranſponendo erit σ π = 2 RN - PS.</
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<
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">Biſecetur recta NP in E;
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</
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<
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<
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">Fig. 94.</
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& </
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<
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">ubivis ſumatur punctum A; </
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">erit EA = {PA ±: </
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<
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">NA.</
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<
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">/2.</
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<
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EA = {P N/2} ±: </
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<
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">AN = {PN ±: </
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<
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">2 AN / 2} = {PA ±: </
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<
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<
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<
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">Exhinc, ut propoſitum citiùs attingamus, Suppoſito radios
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<
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">Fig. 95, 96.</
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A N, AR (quoad caſum præſentem) ſibi quàm proximos incidere,
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punctum deſignabimus ad quod ipſorum reflexi N π, R σ concurrunt;
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</
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<
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">dicimus utique ſi dicti reflexi concurrant ad Z; </
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">bifectis ſubtenſis NP,
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N π in E, & </
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<
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<
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<
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">‖ Nam quoniam
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arcus NR, PS ex hypotheſi ſunt indefinitè parvi (ſeu minimi) ſe ha-
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bebunt ut ſuæ ſubtenſæ; </
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<
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">nec non idem de arcubus NR, π σ dici poteſt. </
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igitur arc. </
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<
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<
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<
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<
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<
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">(hoc eſt ob RA,
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NA nihil, ex eadem hypotheſi, differentes):</
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<
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<
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<
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bis componendo, erit PS + 2 RN. </
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<
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