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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<
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xml:space
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<
s
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xml:space
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Schema.</
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</
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<
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<
s
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xml:space
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">4. </
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<
s
xml:id
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xml:space
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">Si A ζ = {_cc_/_b_}; </
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<
s
xml:id
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echoid-s15909
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xml:space
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">A Ψ = {_b_/4} - √ {_bb_/16} - {_cc_/2}; </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
="
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">A φ = {_b_/4} +
<
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√ {_bb_/16} - {_cc_/2}; </
s
>
<
s
xml:id
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xml:space
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">ordinentúrque rectæ ζ V, ψ X, φ Y; </
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<
s
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xml:space
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">erunt puncta V,
<
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X, Y _nodi_ curvarum (ſi _b_ &</
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<
s
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xml:space
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">lt; </
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<
s
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">√ 8 _c c_, deerunt _nodi_ X, Y; </
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<
s
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xml:space
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<
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8 _c c_; </
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<
s
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xml:space
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">ii coaleſcent).</
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<
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</
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<
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<
s
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">5. </
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<
s
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xml:space
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">Ordinatarum ad curvam CL H _maxima_ eſt ipſa AC ; </
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<
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xml:space
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= {_b_/3} - √ {_bb_/9} - {_cc_/3}, & </
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<
s
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="
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xml:space
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">ordinetur P γ ad curvam AM H; </
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<
s
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xml:space
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">erit
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P γ _maxima_; </
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<
s
xml:id
="
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xml:space
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preserve
">item ſi AQ = {3/8} _b_ - √ {@9/64} _b b_ - {_cc_/2}; </
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<
s
xml:id
="
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xml:space
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">& </
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<
s
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xml:space
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">ordinetur
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Q δ ad curvam AN H, erit Q δ _maxima_.</
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<
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</
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<
s
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">6. </
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<
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xml:space
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">Ordinatarum ad curvam HLLI _maxima_ eſt ipſa OT ; </
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<
s
xml:id
="
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xml:space
="
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">ſin AP
<
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/>
= {_b_/3} + √ {_bb_/9} - {_cc_/3}, & </
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>
<
s
xml:id
="
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xml:space
="
preserve
">ad curvam HM I ordinetur _p g_, erit _p g_
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_maxima_; </
s
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<
s
xml:id
="
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xml:space
="
preserve
">item ſi A q = {3/8} _b_ + √ {9/64} _b b_ - {_cc_/2}; </
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<
s
xml:id
="
echoid-s15933
"
xml:space
="
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">& </
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<
s
xml:id
="
echoid-s15934
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xml:space
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">ordinetur _q d_
<
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/>
ad curvam HN I, erit _q d maxima_.</
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<
s
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="
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xml:space
="
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"/>
</
p
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<
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<
s
xml:id
="
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xml:space
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">7. </
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<
s
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xml:space
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">Hinc radicum limites dignoſcentur, ut innuitur in iis, quæ ad
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octavam ſeriem animadverſa ſunt.</
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<
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</
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<
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<
s
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">8. </
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<
s
xml:id
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xml:space
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">Patet in Serie duodecima nunc tres, modo duas, ſemper unam
<
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radicem haberi; </
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>
<
s
xml:id
="
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xml:space
="
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">in decima tertia verò ſubinde duas, aliquando tantùm
<
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unam, interdum nullam haberi.</
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<
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</
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<
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<
s
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">9. </
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<
s
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xml:space
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">Et hæc quidem conſtant poſito fore {_b_/2}&</
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<
s
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">gt; </
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<
s
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">_c_; </
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<
s
xml:id
="
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xml:space
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">at ſi {_b_/2} = β;
<
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</
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<
s
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xml:space
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">evaneſcet Series decima tertia; </
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>
<
s
xml:id
="
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xml:space
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">coaleſcent puncta H, O, I; </
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>
<
s
xml:id
="
echoid-s15950
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xml:space
="
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">recta AB
<
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_byperbolam_ KK K tanget; </
s
>
<
s
xml:id
="
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xml:space
="
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">curvæque CL H, IL λ in rectas lineas
<
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degenerabunt.</
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<
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</
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<
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<
s
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">10. </
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<
s
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">Sin {_b_/2} &</
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<
s
xml:id
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<
s
xml:id
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">_c_; </
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<
s
xml:id
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">etiam evaneſcit Series decima tertia; </
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<
s
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xml:space
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">_byperbola_ KKK
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tota infra rectam AB jacente; </
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<
s
xml:id
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xml:space
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">quo caſu curva CL L erit hyperbola
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æquilatera, habens centrum O, ſemiaxem (ipſi AB perpendicula-
<
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rem) OT = √ AC q - AO q; </
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<
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<
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<
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<
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">Fig. 218.</
note
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ad infinitum procurrent, ſic ut æquationes, quæ in Serie duodecima,
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unam ſemper, & </
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<
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">unicam radicem obtineant. </
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<
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xml:space
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âſſe; </
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<
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<
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<
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mus autem notas quaſdam magìs generales.</
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