Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of contents

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[71.] _Theor_. IV.
Page: 321 (128)
[72.] _Theor_. V.
Page: 322 (129)
[73.] _Theor_. VI.
Page: 323 (130)
[74.] _Theor_. VII.
Page: 323 (130)
[75.] Lect. XIII.
Page: 324 (131)
[76.] Æquationum Series prima.
Page: 324 (131)
[77.] _Notetur autem_,
Page: 325 (132)
[78.] Series ſecunda.
Page: 325 (132)
[79.] Not.
Page: 326 (133)
[80.] Series tertia.
Page: 326 (133)
[81.] Not.
Page: 327 (134)
[82.] Not.
Page: 328 (135)
[83.] Series quarta.
Page: 329 (136)
[84.] Not.
Page: 329 (136)
[85.] Series quinta.
Page: 330 (137)
[86.] Series ſexta.
Page: 331 (138)
[87.] Not.
Page: 331 (138)
[88.] Series ſeptima.
Page: 332 (139)
[89.] Not.
Page: 332 (139)
[90.] Series octava.
Page: 333 (140)
[91.] Series nona.
Page: 333 (140)
[92.] Not.
Page: 333 (140)
[93.] Series decima.
Page: 334 (141)
[94.] Series undecima.
Page: 335 (142)
[95.] Not.
Page: 335 (142)
[96.] Series duodecima
Page: 336 (143)
[97.] Series decima tertia
Page: 336 (143)
[98.] Not.
Page: 336 (143)
[99.] Laus DEOO ptimo Maximo. FINIS.
Page: 340 (147)
[100.] ERRATA
Page: 341
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            <s xml:id="echoid-s3122" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s3123" xml:space="preserve">Item, dico fore NX (rectioris itidem reflexi concursûs
              <lb/>
            incidentiæque punctis interjectam partem) minorem quartâ parte
              <lb/>
            totius N Π. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">Etenim fiat ang. </s>
            <s xml:id="echoid-s3125" xml:space="preserve">HR Π = ang. </s>
            <s xml:id="echoid-s3126" xml:space="preserve">N Π R; </s>
            <s xml:id="echoid-s3127" xml:space="preserve">quapropter
              <lb/>
            erit HR = H Π; </s>
            <s xml:id="echoid-s3128" xml:space="preserve">adeóque 2 H Π = HR + H Π &</s>
            <s xml:id="echoid-s3129" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3130" xml:space="preserve">R Π &</s>
            <s xml:id="echoid-s3131" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3132" xml:space="preserve">N Π.
              <lb/>
            </s>
            <s xml:id="echoid-s3133" xml:space="preserve">item quoniam ang. </s>
            <s xml:id="echoid-s3134" xml:space="preserve">RHN = 2 ang. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">HR Π = ang. </s>
            <s xml:id="echoid-s3136" xml:space="preserve">XRH; </s>
            <s xml:id="echoid-s3137" xml:space="preserve">eſt
              <lb/>
            XH = XR &</s>
            <s xml:id="echoid-s3138" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3139" xml:space="preserve">XN. </s>
            <s xml:id="echoid-s3140" xml:space="preserve">quum itaque ſit H Π major ſemiſſe totius N Π; </s>
            <s xml:id="echoid-s3141" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">XH major ſemiſſe reſidui NH; </s>
            <s xml:id="echoid-s3143" xml:space="preserve">liquet totam X Π majorem eſſe
              <lb/>
            triplâ X N; </s>
            <s xml:id="echoid-s3144" xml:space="preserve">ſeu totam N Π majorem eſſe quadruplâ N X: </s>
            <s xml:id="echoid-s3145" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3146" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3148" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3149" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">Hinc perſpicuum eſt, ſi fuerit NZ reflexi N Π quadrans,
              <lb/>
            quòd nullus alter hujuſmodi reflexus punctum Z permeabit. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">Etenim
              <lb/>
            alterius cujuſvis reflexus permeare dicatur; </s>
            <s xml:id="echoid-s3152" xml:space="preserve">erit igitur, ſi obliquior
              <lb/>
            is fuerit, NZ &</s>
            <s xml:id="echoid-s3153" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3154" xml:space="preserve">{1/4} N Π; </s>
            <s xml:id="echoid-s3155" xml:space="preserve">ſin rectior fuerit, erit NZ &</s>
            <s xml:id="echoid-s3156" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3157" xml:space="preserve">{1/4} N Π (ni-
              <lb/>
            mirum è proximè demonſtratis hæc conſequuntur) quæ repugnant
              <lb/>
            hypotheſi.</s>
            <s xml:id="echoid-s3158" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3159" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s3160" xml:space="preserve">Quinetiam ipſi N Π propiùs adjacentium occurſus puncto Z vi-
              <lb/>
              <note position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">Fig. 77.</note>
            ciniores ſunt, hinc indè. </s>
            <s xml:id="echoid-s3161" xml:space="preserve">Secent. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">inquam, radiorum LM, RS reflexi
              <lb/>
            L μ, R σ ipſam N Π punctis Y, X; </s>
            <s xml:id="echoid-s3163" xml:space="preserve">iſtæ quidem (rectior) in Y, hic
              <lb/>
            (obliquior) in X; </s>
            <s xml:id="echoid-s3164" xml:space="preserve">erit ZY &</s>
            <s xml:id="echoid-s3165" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3166" xml:space="preserve">ZX. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">Nam connectantur R Π,
              <lb/>
            L Π; </s>
            <s xml:id="echoid-s3168" xml:space="preserve">& </s>
            <s xml:id="echoid-s3169" xml:space="preserve">fiat ang. </s>
            <s xml:id="echoid-s3170" xml:space="preserve">Π LH = ang. </s>
            <s xml:id="echoid-s3171" xml:space="preserve">N Π L; </s>
            <s xml:id="echoid-s3172" xml:space="preserve">ducantúrque rectæ RH,
              <lb/>
            RY. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">eſtque RH &</s>
            <s xml:id="echoid-s3174" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3175" xml:space="preserve">LH = H Π; </s>
            <s xml:id="echoid-s3176" xml:space="preserve">adeóque ang. </s>
            <s xml:id="echoid-s3177" xml:space="preserve">H Π; </s>
            <s xml:id="echoid-s3178" xml:space="preserve">R &</s>
            <s xml:id="echoid-s3179" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3180" xml:space="preserve">ang.
              <lb/>
            </s>
            <s xml:id="echoid-s3181" xml:space="preserve">HR Π; </s>
            <s xml:id="echoid-s3182" xml:space="preserve">& </s>
            <s xml:id="echoid-s3183" xml:space="preserve">proinde ang. </s>
            <s xml:id="echoid-s3184" xml:space="preserve">NHR &</s>
            <s xml:id="echoid-s3185" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3186" xml:space="preserve">2 ang. </s>
            <s xml:id="echoid-s3187" xml:space="preserve">H Π R. </s>
            <s xml:id="echoid-s3188" xml:space="preserve">item YR &</s>
            <s xml:id="echoid-s3189" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3190" xml:space="preserve">YL
              <lb/>
            = YH; </s>
            <s xml:id="echoid-s3191" xml:space="preserve">proindéque rurſus ang. </s>
            <s xml:id="echoid-s3192" xml:space="preserve">NYR &</s>
            <s xml:id="echoid-s3193" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3194" xml:space="preserve">2 ang. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">YHR. </s>
            <s xml:id="echoid-s3196" xml:space="preserve">quare
              <lb/>
            multo minor eſt ang. </s>
            <s xml:id="echoid-s3197" xml:space="preserve">NY R quadruplo N Π R eſt autem ang. </s>
            <s xml:id="echoid-s3198" xml:space="preserve">NXR
              <lb/>
            quadruplus anguli N Π R; </s>
            <s xml:id="echoid-s3199" xml:space="preserve">igitur ang. </s>
            <s xml:id="echoid-s3200" xml:space="preserve">NXR &</s>
            <s xml:id="echoid-s3201" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3202" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s3203" xml:space="preserve">NYR. </s>
            <s xml:id="echoid-s3204" xml:space="preserve">pona-
              <lb/>
            tur jam, ſi fieri poteſt, punctum X ipſis Y, Z interjacere. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">erit igitur
              <lb/>
            angulus externus NYR interno NXR major; </s>
            <s xml:id="echoid-s3206" xml:space="preserve">atqui minor oſtenſus
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s3207" xml:space="preserve">quæ repugnant. </s>
            <s xml:id="echoid-s3208" xml:space="preserve">itaque potiùs eſt ZY &</s>
            <s xml:id="echoid-s3209" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3210" xml:space="preserve">ZX: </s>
            <s xml:id="echoid-s3211" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3212" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3213" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3215" xml:space="preserve">Ad alteras partes haud abſimilis erit diſcurſus; </s>
            <s xml:id="echoid-s3216" xml:space="preserve">parco faſtidioſæ re-
              <lb/>
            petitioni. </s>
            <s xml:id="echoid-s3217" xml:space="preserve">‖</s>
          </p>
          <p>
            <s xml:id="echoid-s3218" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s3219" xml:space="preserve">Hinc obiter patet ad eaſdem partes incidentium reflexos ſeſe
              <lb/>
            priùs (velut ad φ) quàm ipſum N Π decuſſare.</s>
            <s xml:id="echoid-s3220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3221" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s3222" xml:space="preserve">Quinimò rurſus hinc conſtat ad eaſdem axis partes plures
              <lb/>
            duobus in uno puncto reflexos non concurrere.</s>
            <s xml:id="echoid-s3223" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3224" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s3225" xml:space="preserve">Demùm (utaliquando tandem deſtinatum attingamus </s>
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